diff --git a/.gitignore b/.gitignore
index e4a13795..b9286b30 100644
--- a/.gitignore
+++ b/.gitignore
@@ -113,6 +113,7 @@ target/
 
 # Jupyter Notebook
 .ipynb_checkpoints
+.jupyter/
 
 # IPython
 profile_default/
diff --git a/main.py b/main.py
index f316c80f..8169df6b 100644
--- a/main.py
+++ b/main.py
@@ -5,6 +5,7 @@
 from utama_core.strategy.examples import (
     DefenceStrategy,
     GoToBallExampleStrategy,
+    PointCycleStrategy,
     RobotPlacementStrategy,
     StartupStrategy,
     TwoRobotPlacementStrategy,
@@ -17,7 +18,7 @@ def main():
     custom_bounds = FieldBounds(top_left=(2.25, 1.5), bottom_right=(4.5, -1.5))
 
     runner = StrategyRunner(
-        strategy=TwoRobotPlacementStrategy(first_robot_id=0, second_robot_id=1, field_bounds=custom_bounds),
+        strategy=PointCycleStrategy(n_robots=2, field_bounds=custom_bounds, endpoint_tolerance=0.1, seed=42),
         my_team_is_yellow=True,
         my_team_is_right=True,
         mode="rsim",
@@ -25,7 +26,7 @@ def main():
         exp_enemy=0,
         replay_writer_config=ReplayWriterConfig(replay_name="test_replay", overwrite_existing=True),
         print_real_fps=True,
-        profiler_name=None
+        profiler_name=None,
     )
     runner.my_strategy.render()
     runner.run()
diff --git a/pixi.lock b/pixi.lock
index d75f512f..038b03df 100644
--- a/pixi.lock
+++ b/pixi.lock
@@ -9,9 +9,9 @@ environments:
       linux-64:
       - conda: https://prefix.dev/conda-forge/linux-64/_libgcc_mutex-0.1-conda_forge.tar.bz2
       - conda: https://prefix.dev/conda-forge/linux-64/_openmp_mutex-4.5-2_gnu.tar.bz2
-      - conda: https://prefix.dev/conda-forge/noarch/adwaita-icon-theme-48.1-unix_1.conda
+      - conda: https://prefix.dev/conda-forge/noarch/adwaita-icon-theme-49.0-unix_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/alsa-lib-1.2.14-hb9d3cd8_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/anyio-4.10.0-pyhe01879c_0.conda
+      - conda: https://prefix.dev/conda-forge/noarch/anyio-4.11.0-pyhcf101f3_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/aom-3.9.1-hac33072_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/at-spi2-atk-2.38.0-h0630a04_3.tar.bz2
       - conda: https://prefix.dev/conda-forge/linux-64/at-spi2-core-2.40.3-h0630a04_0.tar.bz2
@@ -19,24 +19,24 @@ environments:
       - conda: https://prefix.dev/conda-forge/linux-64/attr-2.5.2-h39aace5_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/backports-1.0-pyhd8ed1ab_5.conda
       - conda: https://prefix.dev/conda-forge/noarch/backports.tarfile-1.2.0-pyhd8ed1ab_1.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/bzip2-1.0.8-h4bc722e_7.conda
-      - conda: https://prefix.dev/conda-forge/noarch/ca-certificates-2025.8.3-hbd8a1cb_0.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/bzip2-1.0.8-hda65f42_8.conda
+      - conda: https://prefix.dev/conda-forge/noarch/ca-certificates-2025.11.12-hbd8a1cb_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/cairo-1.18.4-h3394656_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/certifi-2025.8.3-pyhd8ed1ab_0.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/cffi-1.17.1-py311h5b438cf_1.conda
+      - conda: https://prefix.dev/conda-forge/noarch/certifi-2025.11.12-pyhd8ed1ab_0.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/cffi-2.0.0-py311h03d9500_1.conda
       - conda: https://prefix.dev/conda-forge/noarch/cfgv-3.3.1-pyhd8ed1ab_1.conda
-      - conda: https://prefix.dev/conda-forge/noarch/click-8.2.1-pyh707e725_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/cloudpickle-3.1.1-pyhd8ed1ab_0.conda
+      - conda: https://prefix.dev/conda-forge/noarch/click-8.3.1-pyh707e725_0.conda
+      - conda: https://prefix.dev/conda-forge/noarch/cloudpickle-3.1.2-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/colorama-0.4.6-pyhd8ed1ab_1.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/cryptography-45.0.7-py311h8488d03_1.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/cryptography-46.0.3-py311h8488d03_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/dav1d-1.2.1-hd590300_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/dbus-1.16.2-h3c4dab8_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/distlib-0.4.0-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/editables-0.5-pyhd8ed1ab_1.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/epoxy-1.5.10-h166bdaf_1.tar.bz2
+      - conda: https://prefix.dev/conda-forge/linux-64/epoxy-1.5.10-hb03c661_2.conda
       - conda: https://prefix.dev/conda-forge/noarch/exceptiongroup-1.3.0-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/farama-notifications-0.0.4-pyhd8ed1ab_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/filelock-3.19.1-pyhd8ed1ab_0.conda
+      - conda: https://prefix.dev/conda-forge/noarch/filelock-3.20.0-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/fluidsynth-2.3.7-hd992666_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/font-ttf-dejavu-sans-mono-2.37-hab24e00_0.tar.bz2
       - conda: https://prefix.dev/conda-forge/noarch/font-ttf-inconsolata-3.000-h77eed37_0.tar.bz2
@@ -44,21 +44,21 @@ environments:
       - conda: https://prefix.dev/conda-forge/noarch/font-ttf-ubuntu-0.83-h77eed37_3.conda
       - conda: https://prefix.dev/conda-forge/linux-64/fontconfig-2.15.0-h7e30c49_1.conda
       - conda: https://prefix.dev/conda-forge/noarch/fonts-conda-ecosystem-1-0.tar.bz2
-      - conda: https://prefix.dev/conda-forge/noarch/fonts-conda-forge-1-0.tar.bz2
-      - conda: https://prefix.dev/conda-forge/linux-64/freetype-2.13.3-ha770c72_1.conda
+      - conda: https://prefix.dev/conda-forge/noarch/fonts-conda-forge-1-hc364b38_1.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/freetype-2.14.1-ha770c72_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/fribidi-1.0.16-hb03c661_0.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/gdk-pixbuf-2.44.1-h2b0a6b4_0.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/gdk-pixbuf-2.44.4-h2b0a6b4_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/gettext-0.25.1-h3f43e3d_1.conda
       - conda: https://prefix.dev/conda-forge/linux-64/gettext-tools-0.25.1-h3f43e3d_1.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/glib-tools-2.86.0-hf516916_0.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/glib-tools-2.86.1-hf516916_2.conda
       - conda: https://prefix.dev/conda-forge/linux-64/graphite2-1.3.14-hecca717_2.conda
       - conda: https://prefix.dev/conda-forge/linux-64/graphviz-13.1.2-h87b6fe6_0.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/gtk3-3.24.43-h0c6a113_5.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/gtk3-3.24.43-h993cebd_6.conda
       - conda: https://prefix.dev/conda-forge/linux-64/gts-0.7.6-h977cf35_4.conda
       - conda: https://prefix.dev/conda-forge/linux-64/gymnasium-1.0.0-np2py311hec5889a_2.conda
       - conda: https://prefix.dev/conda-forge/noarch/h11-0.16.0-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/h2-4.3.0-pyhcf101f3_0.conda
-      - conda: https://prefix.dev/conda-forge/linux-64/harfbuzz-11.4.5-h15599e2_0.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/harfbuzz-12.2.0-h15599e2_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/hatch-1.14.1-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/hatchling-1.27.0-pypyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/hicolor-icon-theme-0.17-ha770c72_2.tar.bz2
@@ -68,85 +68,87 @@ environments:
       - conda: https://prefix.dev/conda-forge/noarch/hyperframe-6.1.0-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/hyperlink-21.0.0-pyh29332c3_1.conda
       - conda: https://prefix.dev/conda-forge/linux-64/icu-75.1-he02047a_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/identify-2.6.14-pyhd8ed1ab_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/idna-3.10-pyhd8ed1ab_1.conda
+      - conda: https://prefix.dev/conda-forge/noarch/identify-2.6.15-pyhd8ed1ab_0.conda
+      - conda: https://prefix.dev/conda-forge/noarch/idna-3.11-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/noarch/importlib-metadata-8.7.0-pyhe01879c_1.conda
       - conda: https://prefix.dev/conda-forge/noarch/importlib_resources-6.5.2-pyhd8ed1ab_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/iniconfig-2.0.0-pyhd8ed1ab_1.conda
+      - conda: https://prefix.dev/conda-forge/noarch/iniconfig-2.3.0-pyhd8ed1ab_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/jack-1.9.22-hf4617a5_3.conda
       - conda: https://prefix.dev/conda-forge/noarch/jaraco.classes-3.4.0-pyhd8ed1ab_2.conda
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       - conda: https://prefix.dev/conda-forge/noarch/jeepney-0.9.0-pyhd8ed1ab_0.conda
-      - conda: https://prefix.dev/conda-forge/noarch/keyring-25.6.0-pyha804496_0.conda
+      - conda: https://prefix.dev/conda-forge/noarch/keyring-25.7.0-pyha804496_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/keyutils-1.6.3-hb9d3cd8_0.conda
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-      - conda: https://prefix.dev/conda-forge/linux-64/ld_impl_linux-64-2.44-h1423503_1.conda
+      - conda: https://prefix.dev/conda-forge/linux-64/ld_impl_linux-64-2.45-h1aa0949_0.conda
       - conda: https://prefix.dev/conda-forge/linux-64/lerc-4.0.0-h0aef613_1.conda
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+      - conda: https://prefix.dev/conda-forge/linux-64/libexpat-2.7.3-hecca717_0.conda
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   depends:
   - __glibc >=2.17,<3.0.a0
-  - libexpat >=2.7.0,<3.0a0
-  - libffi >=3.4.6,<3.5.0a0
-  - libgcc >=13
-  - libstdcxx >=13
+  - libexpat >=2.7.1,<3.0a0
+  - libffi >=3.5.2,<3.6.0a0
+  - libgcc >=14
+  - libstdcxx >=14
   license: MIT
   license_family: MIT
   purls: []
-  size: 330474
-  timestamp: 1751817998141
-- conda: https://prefix.dev/conda-forge/linux-64/xkeyboard-config-2.45-hb9d3cd8_0.conda
-  sha256: a5d4af601f71805ec67403406e147c48d6bad7aaeae92b0622b7e2396842d3fe
-  md5: 397a013c2dc5145a70737871aaa87e98
+  size: 329779
+  timestamp: 1761174273487
+- conda: https://prefix.dev/conda-forge/linux-64/xkeyboard-config-2.46-hb03c661_0.conda
+  sha256: aa03b49f402959751ccc6e21932d69db96a65a67343765672f7862332aa32834
+  md5: 71ae752a748962161b4740eaff510258
   depends:
   - __glibc >=2.17,<3.0.a0
-  - libgcc >=13
+  - libgcc >=14
   - xorg-libx11 >=1.8.12,<2.0a0
   license: MIT
   license_family: MIT
   purls: []
-  size: 392406
-  timestamp: 1749375847832
+  size: 396975
+  timestamp: 1759543819846
 - conda: https://prefix.dev/conda-forge/linux-64/xorg-libice-1.1.2-hb9d3cd8_0.conda
   sha256: c12396aabb21244c212e488bbdc4abcdef0b7404b15761d9329f5a4a39113c4b
   md5: fb901ff28063514abb6046c9ec2c4a45
@@ -5122,17 +4996,17 @@ packages:
   purls: []
   size: 835896
   timestamp: 1741901112627
-- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxau-1.0.12-hb9d3cd8_0.conda
-  sha256: ed10c9283974d311855ae08a16dfd7e56241fac632aec3b92e3cfe73cff31038
-  md5: f6ebe2cb3f82ba6c057dde5d9debe4f7
+- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxau-1.0.12-hb03c661_1.conda
+  sha256: 6bc6ab7a90a5d8ac94c7e300cc10beb0500eeba4b99822768ca2f2ef356f731b
+  md5: b2895afaf55bf96a8c8282a2e47a5de0
   depends:
   - __glibc >=2.17,<3.0.a0
-  - libgcc >=13
+  - libgcc >=14
   license: MIT
   license_family: MIT
   purls: []
-  size: 14780
-  timestamp: 1734229004433
+  size: 15321
+  timestamp: 1762976464266
 - conda: https://prefix.dev/conda-forge/linux-64/xorg-libxcomposite-0.4.6-hb9d3cd8_2.conda
   sha256: 753f73e990c33366a91fd42cc17a3d19bb9444b9ca5ff983605fa9e953baf57f
   md5: d3c295b50f092ab525ffe3c2aa4b7413
@@ -5174,17 +5048,17 @@ packages:
   purls: []
   size: 13217
   timestamp: 1727891438799
-- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxdmcp-1.1.5-hb9d3cd8_0.conda
-  sha256: 6b250f3e59db07c2514057944a3ea2044d6a8cdde8a47b6497c254520fade1ee
-  md5: 8035c64cb77ed555e3f150b7b3972480
+- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxdmcp-1.1.5-hb03c661_1.conda
+  sha256: 25d255fb2eef929d21ff660a0c687d38a6d2ccfbcbf0cc6aa738b12af6e9d142
+  md5: 1dafce8548e38671bea82e3f5c6ce22f
   depends:
   - __glibc >=2.17,<3.0.a0
-  - libgcc >=13
+  - libgcc >=14
   license: MIT
   license_family: MIT
   purls: []
-  size: 19901
-  timestamp: 1727794976192
+  size: 20591
+  timestamp: 1762976546182
 - conda: https://prefix.dev/conda-forge/linux-64/xorg-libxext-1.3.6-hb9d3cd8_0.conda
   sha256: da5dc921c017c05f38a38bd75245017463104457b63a1ce633ed41f214159c14
   md5: febbab7d15033c913d53c7a2c102309d
@@ -5197,18 +5071,18 @@ packages:
   purls: []
   size: 50060
   timestamp: 1727752228921
-- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxfixes-6.0.1-hb9d3cd8_0.conda
-  sha256: 2fef37e660985794617716eb915865ce157004a4d567ed35ec16514960ae9271
-  md5: 4bdb303603e9821baf5fe5fdff1dc8f8
+- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxfixes-6.0.2-hb03c661_0.conda
+  sha256: 83c4c99d60b8784a611351220452a0a85b080668188dce5dfa394b723d7b64f4
+  md5: ba231da7fccf9ea1e768caf5c7099b84
   depends:
   - __glibc >=2.17,<3.0.a0
-  - libgcc >=13
-  - xorg-libx11 >=1.8.10,<2.0a0
+  - libgcc >=14
+  - xorg-libx11 >=1.8.12,<2.0a0
   license: MIT
   license_family: MIT
   purls: []
-  size: 19575
-  timestamp: 1727794961233
+  size: 20071
+  timestamp: 1759282564045
 - conda: https://prefix.dev/conda-forge/linux-64/xorg-libxi-1.8.2-hb9d3cd8_0.conda
   sha256: 1a724b47d98d7880f26da40e45f01728e7638e6ec69f35a3e11f92acd05f9e7a
   md5: 17dcc85db3c7886650b8908b183d6876
@@ -5290,6 +5164,30 @@ packages:
   purls: []
   size: 32808
   timestamp: 1727964811275
+- conda: https://prefix.dev/conda-forge/linux-64/xorg-libxxf86vm-1.1.6-hb9d3cd8_0.conda
+  sha256: 8a4e2ee642f884e6b78c20c0892b85dd9b2a6e64a6044e903297e616be6ca35b
+  md5: 5efa5fa6243a622445fdfd72aee15efa
+  depends:
+  - __glibc >=2.17,<3.0.a0
+  - libgcc >=13
+  - xorg-libx11 >=1.8.10,<2.0a0
+  - xorg-libxext >=1.3.6,<2.0a0
+  license: MIT
+  license_family: MIT
+  purls: []
+  size: 17819
+  timestamp: 1734214575628
+- conda: https://prefix.dev/conda-forge/linux-64/xorg-xorgproto-2024.1-hb9d3cd8_1.conda
+  sha256: 1316680be6edddee0156b86ec1102fc8286f51c1a5440366ed1db596a2dc3731
+  md5: 7c21106b851ec72c037b162c216d8f05
+  depends:
+  - __glibc >=2.17,<3.0.a0
+  - libgcc >=13
+  license: MIT
+  license_family: MIT
+  purls: []
+  size: 565425
+  timestamp: 1726846388217
 - conda: https://prefix.dev/conda-forge/linux-64/xz-5.8.1-hbcc6ac9_2.conda
   sha256: 802725371682ea06053971db5b4fb7fbbcaee9cb1804ec688f55e51d74660617
   md5: 68eae977d7d1196d32b636a026dc015d
@@ -5422,40 +5320,40 @@ packages:
   purls: []
   size: 77606
   timestamp: 1727963209370
-- conda: https://prefix.dev/conda-forge/linux-64/zstandard-0.24.0-py311h4854a17_1.conda
-  sha256: 0c13155c0eaeda24d1b208a4e9af28db025fd3388eca05fec872ce8d155d4e26
-  md5: d0d623c1cd5a9515de1b2260d21a92aa
+- conda: https://prefix.dev/conda-forge/linux-64/zstandard-0.25.0-py311haee01d2_1.conda
+  sha256: d534a6518c2d8eccfa6579d75f665261484f0f2f7377b50402446a9433d46234
+  md5: ca45bfd4871af957aaa5035593d5efd2
   depends:
-  - __glibc >=2.17,<3.0.a0
+  - python
   - cffi >=1.11
-  - libgcc >=14
-  - python >=3.11,<3.12.0a0
-  - python_abi 3.11.* *_cp311
   - zstd >=1.5.7,<1.5.8.0a0
+  - libgcc >=14
+  - __glibc >=2.17,<3.0.a0
   - zstd >=1.5.7,<1.6.0a0
+  - python_abi 3.11.* *_cp311
   license: BSD-3-Clause
   license_family: BSD
   purls:
-  - pkg:pypi/zstandard?source=compressed-mapping
-  size: 426304
-  timestamp: 1756841168805
-- conda: https://prefix.dev/conda-forge/osx-arm64/zstandard-0.25.0-py311h5bb9006_0.conda
-  sha256: fb1443a1479a6d709b4af7a2cdcea3ef2a5e859378de19814086fa86ca6f934e
-  md5: c7e0f1b714bd12d39899a4f0c296dd86
+  - pkg:pypi/zstandard?source=hash-mapping
+  size: 466893
+  timestamp: 1762512695614
+- conda: https://prefix.dev/conda-forge/osx-arm64/zstandard-0.25.0-py311h5bb9006_1.conda
+  sha256: 2ee455765fe831cca8fe127c56ae99938e353797135fe33140b28abb4fbe1049
+  md5: 651594b8f9b9cccc5948287a18903c34
   depends:
   - python
   - cffi >=1.11
   - zstd >=1.5.7,<1.5.8.0a0
-  - __osx >=11.0
   - python 3.11.* *_cpython
-  - zstd >=1.5.7,<1.6.0a0
+  - __osx >=11.0
   - python_abi 3.11.* *_cp311
+  - zstd >=1.5.7,<1.6.0a0
   license: BSD-3-Clause
   license_family: BSD
   purls:
   - pkg:pypi/zstandard?source=hash-mapping
-  size: 390089
-  timestamp: 1757930124840
+  size: 390026
+  timestamp: 1762512731928
 - conda: https://prefix.dev/conda-forge/linux-64/zstd-1.5.7-hb8e6e7a_2.conda
   sha256: a4166e3d8ff4e35932510aaff7aa90772f84b4d07e9f6f83c614cba7ceefe0eb
   md5: 6432cb5d4ac0046c3ac0a8a0f95842f9
diff --git a/pyproject.toml b/pyproject.toml
index 55b2722a..762fe35b 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -10,7 +10,11 @@ authors = [
     { name = "Hamish Starling", email = "hamish.starling22@imperial.ac.uk" },
     { name = "Luke Moran", email = "luke.moran22@imperial.ac.uk" },
     { name = "Sadig Sadikhzada", email = "sadig.sadikhzada23@imperial.ac.uk" },
-    { name = "Li Han", email = "han.li124@imperial.ac.uk" }
+    { name = "Li Han", email = "han.li124@imperial.ac.uk" },
+    { name = "Valentin Bruhl", email = "valentin.bruhl24@imperial.ac.uk" },
+    { name = "Sarthak Agarwal", email = "sarthak.agarwal25@imperial.ac.uk" },
+    { name = "Low Sze Yoong", email = "szeyoong.low25@imperial.ac.uk" },
+    { name = "Jiaming Liu", email = "jiaming.liu25@imperial.ac.uk" },
 ]
 requires-python = ">=3.11"
 
diff --git a/utama_core/global_utils/math_utils.py b/utama_core/global_utils/math_utils.py
index a6eeefd0..926f2b93 100644
--- a/utama_core/global_utils/math_utils.py
+++ b/utama_core/global_utils/math_utils.py
@@ -56,7 +56,7 @@ def normalise_heading_deg(angle):
         The normalized angle in the range [-180, 180] degrees.
     """
     half_rev = 180
-    
+
     return (angle + half_rev) % (2 * half_rev) - half_rev
 
 
diff --git a/utama_core/rsoccer_simulator/src/ssl/envs/standard_ssl.py b/utama_core/rsoccer_simulator/src/ssl/envs/standard_ssl.py
index b1bb4de3..58faf973 100644
--- a/utama_core/rsoccer_simulator/src/ssl/envs/standard_ssl.py
+++ b/utama_core/rsoccer_simulator/src/ssl/envs/standard_ssl.py
@@ -1,8 +1,9 @@
 import logging
-from numpy.random import normal
 import random
 from typing import List, Tuple
 
+from numpy.random import normal
+
 from utama_core.config.formations import LEFT_START_ONE, RIGHT_START_ONE
 from utama_core.config.robot_params import RSIM_PARAMS
 from utama_core.config.settings import (
@@ -13,11 +14,15 @@
 )
 from utama_core.entities.data.command import RobotResponse
 from utama_core.entities.data.raw_vision import RawBallData, RawRobotData, RawVisionData
-from utama_core.global_utils.math_utils import deg_to_rad, rad_to_deg, normalise_heading_deg
+from utama_core.global_utils.math_utils import (
+    deg_to_rad,
+    normalise_heading_deg,
+    rad_to_deg,
+)
 from utama_core.rsoccer_simulator.src.Entities import Ball, Frame, Robot
 from utama_core.rsoccer_simulator.src.ssl.ssl_gym_base import SSLBaseEnv
-from utama_core.rsoccer_simulator.src.Utils.gaussian_noise import RsimGaussianNoise
 from utama_core.rsoccer_simulator.src.Utils import KDTree
+from utama_core.rsoccer_simulator.src.Utils.gaussian_noise import RsimGaussianNoise
 
 logger = logging.getLogger(__name__)
 
@@ -38,19 +43,19 @@ class SSLStandardEnv(SSLBaseEnv):
         Description:
             list of (x, y, theta) coords for each robot to spawn in (in meters and radians).
             See the default BLUE_START_ONE/YELLOW_START_ONE for reference.
-        
+
         gaussian_noise
         Type: RsimGaussianNoise
         Description:
             When running in rsim, add Gaussian noise to ball and robots with the given standard deviations.
             Mutates the Robot object in place. The 3 parameters are for x (in m), y (in m), and orientation (in degrees)
             respectively. Defaults to 0 for each.
-            
+
         vanishing
         Type: float
         Description:
             When running in rsim, cause robots and ball to vanish with the given probability. Defaults to 0.
-            
+
     Observation:
         Type: Tuple[FrameData, List[RobotInfo], List[RobotInfo]]
         Num     Item
@@ -78,7 +83,7 @@ def __init__(
         blue_starting_formation: list[tuple] = None,
         yellow_starting_formation: list[tuple] = None,
         gaussian_noise: RsimGaussianNoise = RsimGaussianNoise(),
-        vanishing: float = 0
+        vanishing: float = 0,
     ):
         super().__init__(
             field_type=field_type,
@@ -108,11 +113,11 @@ def __init__(
         self.latest_observation = (-1, None)
 
         logger.info(f"{n_robots_blue}v{n_robots_yellow} SSL Environment Initialized")
-        
+
         # Adding Gaussian noise and vanishing. Refer to StrategyRunner
         self.gaussian_noise = gaussian_noise
-        
-        assert vanishing >= 0
+
+        assert vanishing >= 0, "Negative vanishing probability not allowed"
         self.vanishing = vanishing
 
     def reset(self, *, seed=None, options=None):
@@ -172,7 +177,7 @@ def _frame_to_observations(
         yellow_robots_info: feedback from individual yellow robots that returns a List[RobotInfo]
         blue_robots_info: feedback from individual blue robots that returns a List[RobotInfo]
         """
-        
+
         if self.latest_observation[0] == self.steps:
             return self.latest_observation[1]
 
@@ -189,7 +194,7 @@ def _frame_to_observations(
         for i in range(len(self.frame.robots_blue)):
             if self._vanishing():
                 continue
-            
+
             robot = self.frame.robots_blue[i]
             robot_pos, robot_info = self._get_robot_observation(robot)
             blue_obs.append(robot_pos)
@@ -200,7 +205,7 @@ def _frame_to_observations(
         for i in range(len(self.frame.robots_yellow)):
             if self._vanishing():
                 continue
-                
+
             robot = self.frame.robots_yellow[i]
             robot_pos, robot_info = self._get_robot_observation(robot)
             yellow_obs.append(robot_pos)
@@ -221,7 +226,7 @@ def _frame_to_observations(
 
     def _get_robot_observation(self, robot):
         SSLStandardEnv._add_gaussian_noise_robot(robot, self.gaussian_noise)
-        
+
         robot_pos = RawRobotData(robot.id, robot.x, -robot.y, -float(deg_to_rad(robot.theta)), 1)
         robot_info = RobotResponse(robot.id, robot.infrared)
         return robot_pos, robot_info
@@ -415,47 +420,45 @@ def in_gk_area(obj):
 
         return pos_frame
 
-
     def _vanishing(self) -> bool:
         """Determines whether a frame should vanish. Only runs after Game Gater is passed"""
         return self.steps > 0 and self.vanishing and (random.random() < self.vanishing)
 
-    
     @staticmethod
     def _add_gaussian_noise_ball(ball: Ball, noise: RsimGaussianNoise):
         """
         When running in rsim, add Gaussian noise to ball with the given standard deviations.
         Mutates the Robot object in place.
-        
+
         Args:
             noise (RsimGaussianNoise): The 3 parameters are for x (in m), y (in m), and orientation (in degrees) respectively.
                 Defaults to 0 for each.
         """
-        
+
         if noise.x_stddev:
             ball.x += normal(scale=noise.x_stddev)
-            
+
         if noise.y_stddev:
             ball.y += normal(scale=noise.y_stddev)
-            
+
         # No noise addition for z, since rSim is 2-D
-        
+
     @staticmethod
     def _add_gaussian_noise_robot(robot: Robot, noise: RsimGaussianNoise):
         """
         When running in rsim, add Gaussian noise to robot with the given standard deviations.
         Mutates the Robot object in place.
-        
+
         Args:
             noise (RsimGaussianNoise): The 3 parameters are for x (in m), y (in m), and orientation (in degrees) respectively.
                 Defaults to 0 for each.
         """
-        
+
         if noise.x_stddev:
             robot.x += normal(scale=noise.x_stddev)
-            
+
         if noise.y_stddev:
             robot.y += normal(scale=noise.y_stddev)
-            
+
         if noise.th_stddev_deg:
-            robot.theta = normalise_heading_deg(robot.theta + normal(scale=noise.th_stddev_deg))
\ No newline at end of file
+            robot.theta = normalise_heading_deg(robot.theta + normal(scale=noise.th_stddev_deg))
diff --git a/utama_core/run/refiners/kalman.py b/utama_core/run/refiners/kalman.py
new file mode 100644
index 00000000..5579a882
--- /dev/null
+++ b/utama_core/run/refiners/kalman.py
@@ -0,0 +1,404 @@
+from typing import Optional
+
+import numpy as np
+
+from utama_core.entities.data.vector import Vector3D
+from utama_core.entities.data.vision import VisionRobotData
+from utama_core.entities.game import Ball, Robot
+from utama_core.global_utils.math_utils import deg_to_rad, normalise_heading
+
+
+class KalmanFilter:
+    """
+    Kalman filter for 2D position and orientation of robots.
+
+    It works in 2 phases:
+    1. Prediction: The object's last known velocity and kinematics formulae are
+    used to estimate its current position. (Orientation is assumed to be constant
+    due to a lack of data on angular velocity.)
+
+    2. Updating: New vision data is used to update the filter's estimate. The
+    information is weighed using the Kalman gain, a constant that depends on
+    the system's noise level.
+
+    If no data is received, the filter's prediction is used.
+
+    Note: The filter's parameters are the standard deviations of random noise.
+    The rsim noise generator also uses standard deviation, so the optimal parameter
+    should be the same as the argument to it. Do not use variance (standard deviation squared).
+
+    More about the methodology and formulae used can be found at https://kalmanfilter.net/.
+
+    Args:
+        id (int): The associated robot's ID, used for associating the filter
+            with the robot. Defaults to 0.
+
+        noise_xy_sd (float): A hyper-parameter, used to weigh the filter's
+            predictions and the vision data received during the "update" phase.
+            Unit is metres.
+            Defaults to 0.01 (In simulation, this should match the argument
+            passed to the rsim noise generator, but should be adjusted based on
+            real-world conditions when live robots are used).
+
+        noise_th_sd_deg (float): A hyper-parameter, used to weigh the filter's
+            predictions and the vision data received during the "update" phase.
+            Unit is degrees. Conversion to radians is done internally.
+            Defaults to 5 (In simulation, this should match the argument
+            passed to the rsim noise generator, but should be adjusted based on
+            real-world conditions when live robots are used).
+    """
+
+    def __init__(self, id: int = 0, noise_xy_sd: float = 0.01, noise_th_sd_deg: float = 5):
+        assert noise_xy_sd > 0, "The standard deviation must be greater than 0"
+        assert noise_th_sd_deg > 0, "The standard deviation must be greater than 0"
+
+        self.id = id
+
+        # For position
+        # s; to be initialised by strategy runner with 1st GameFrame
+        self.state_xy = None
+
+        # sigma squared x, sigma squared y
+        noise_xy_var = pow(noise_xy_sd, 2)
+        var_x, var_y = noise_xy_var, noise_xy_var
+
+        # sigma xy; assume their errors are uncorrelated
+        covariance_xy = 0
+
+        dimensions_xy = 2
+        self.identity_xy = np.identity(dimensions_xy)
+
+        # R_n
+        self.measurement_cov_xy = np.array([[var_x, covariance_xy], [covariance_xy, var_y]])
+        # P_n,n; initialised with uncertainty in 1st frame
+        self.covariance_mat_xy = self.measurement_cov_xy
+        # Q
+        self.process_noise_xy = (2 * noise_xy_var) * self.identity_xy
+
+        # Observation matrix H and state transition matrix F are just the identity matrix.
+        # Multiplications with them are omitted.
+
+        # For orientation
+        # s; to be initialised by strategy runner with 1st GameFrame
+        self.state_th = None
+
+        # sigma squared th
+        noise_th_var = pow(deg_to_rad(noise_th_sd_deg), 2)
+
+        # r_n
+        self.measurement_cov_th = noise_th_var
+        # p_n,n; initialised with uncertainty in 1st frame
+        self.covariance_th = noise_th_var
+        # q
+        self.process_noise_th = noise_th_var
+
+    def _step_xy(
+        self,
+        new_data: Optional[tuple[float, float]],
+        last_robot: Robot,
+        time_elapsed: float,
+    ) -> tuple[float, float]:
+        """
+        A single iteration of the filter for x and y coordinates.
+
+        Args:
+            new_data (tuple[float, float]): New vision data received (x coordinates in metres, y coordinates in metres),
+                passed by filter_data.
+            last_robot (Robot): An object storing the robot's last known position and velocity, among others.
+            time_elapsed (float): Time since last vision data was received.
+
+        Returns:
+            tuple[float, float]: Filtered vision data (x coordinates, y coordinates),
+                returned to filter_data for packaging.
+
+        """
+
+        # class Robot: id: int; is_friendly: bool; has_ball: bool
+        # p: Vector2D; v: Vector2D; a: Vector2D; orientation: float
+
+        # Phase 0: Initialised with the 1st valid GameFrame (only on initialisation)
+        if self.state_xy is None:
+            self.state_xy = np.array((last_robot.p.x, last_robot.p.y))
+
+        # Phase 1: Predicting the current state given the last state.
+        # u
+        control_velocities_xy = np.array((last_robot.v.x, last_robot.v.y))
+        # G
+        control_mat_xy = time_elapsed * self.identity_xy
+
+        # s_n,n-1
+        pred_state_xy = self.state_xy + np.matmul(control_mat_xy, control_velocities_xy)
+        # P_n,n-1
+        pred_cov_xy = self.covariance_mat_xy + self.process_noise_xy
+
+        # Phase 2: Adjust this prediction based on new data
+        if new_data is not None:  # Received frame.
+            # z
+            measurement_xy = np.array(new_data)
+
+            # K_n
+            kalman_gain_xy = np.linalg.solve((pred_cov_xy + self.measurement_cov_xy).T, pred_cov_xy.T).T
+
+            # s_n,n
+            self.state_xy = pred_state_xy + np.matmul(kalman_gain_xy, (measurement_xy - pred_state_xy))
+
+            ident_less_kalman_xy = self.identity_xy - kalman_gain_xy
+            measurement_uncertainty_xy = np.matmul(
+                kalman_gain_xy,
+                np.matmul(self.measurement_cov_xy, kalman_gain_xy.T),
+            )
+
+            # P_n,n
+            self.covariance_mat_xy = (
+                np.matmul(ident_less_kalman_xy, np.matmul(pred_cov_xy, ident_less_kalman_xy.T))
+                + measurement_uncertainty_xy
+            )
+
+        # We can rely on the invariant that vanished frames have null x values
+        # as they are imputed with a null VisionRobotData in the Position Refiner.
+        else:  # Vanished frame: use predicted values.
+            self.state_xy = pred_state_xy
+            self.covariance_mat_xy = pred_cov_xy
+
+        return tuple(self.state_xy)
+
+    def _step_th(self, new_data: Optional[float], last_th: float) -> float:
+        """
+        A single iteration of the filter for orientation.
+
+        Args:
+            new_data (float): New vision data received (orientation in radians),
+                passed by the externally callable function filter_data.
+            last_th (float): The robot's last known orientation
+
+        Returns:
+            float: Filtered vision data orientation,
+                returned to filter_data for packaging.
+
+        """
+
+        # Phase 0: Initialised with the 1st valid GameFrame (only on initialisation)
+        if self.state_th is None:
+            self.state_th = last_th
+
+        # Phase 1: Predicting the current state given the last state.
+        # s_n,n-1 = s_n-1,n-1 (Assuming constant velocity)
+        # P_n,n-1
+        pred_cov_th = self.covariance_th + self.process_noise_th
+
+        # Phase 2: Adjust this prediction based on new data
+        if new_data is not None:  # Received frame.
+            # z
+            measurement_th = normalise_heading(new_data)
+
+            # K_n
+            kalman_gain_th = pred_cov_th / (pred_cov_th + self.measurement_cov_th)
+
+            # Taking a circular weighted average
+            weights_th = (kalman_gain_th, 1 - kalman_gain_th)
+            values_th = (measurement_th, self.state_th)
+            sines_th = np.dot(weights_th, np.sin(values_th))
+            cosines_th = np.dot(weights_th, np.cos(values_th))
+            # s_n,n; already wrapped to (-pi, pi] as we're taking a circular average
+            self.state_th = float(np.arctan2(sines_th, cosines_th))
+
+            # P_n,n
+            self.covariance_th = (1 - kalman_gain_th) * pred_cov_th
+
+        # We can rely on the invariant that vanished frames have null x values
+        # as they are imputed with a null VisionRobotData in the Position Refiner.
+        else:  # Vanished frame: use predicted values.
+            # self.state_th is unchanged
+            self.covariance_th = pred_cov_th
+
+        return self.state_th
+
+    def filter_data(
+        self,
+        data: Optional[VisionRobotData],
+        last_frame: Robot,
+        time_elapsed: float,
+    ) -> VisionRobotData:
+        """
+        Performs one prediction–update cycle of the Kalman filter for the
+        associated robot.
+
+        The robot's state is first predicted using its last known velocity and
+        the elapsed time. If new vision data is available, the prediction is
+        corrected using the Kalman gain. If the vision frame is missing, the
+        predicted state is used directly.
+
+        Args:
+            data (VisionRobotData): New vision measurement containing position
+                (x, y) in metres and orientation in radians.
+            last_frame (dict[int, Robot]): Mapping of robot IDs to their last
+                known state (position, velocity, orientation), used for motion
+                prediction.
+            time_elapsed (float): Time in seconds since the previous update.
+
+        Returns:
+            VisionRobotData: Filtered estimate of the robot's position (x, y)
+                and orientation, packaged as a VisionRobotData object.
+        """
+
+        # class VisionRobotData: id: int; x: float; y: float; orientation: float
+        xy_tuple = (data.x, data.y) if data is not None else None
+        x_f, y_f = self._step_xy(xy_tuple, last_frame, time_elapsed)
+        th_f = self._step_th(
+            data.orientation if data is not None else None,
+            last_frame.orientation,
+        )
+
+        return VisionRobotData(self.id, x_f, y_f, th_f)
+
+
+class KalmanFilterBall:
+    """
+    Kalman filter for 3D position of ball.
+
+    See above for details about the methodology.
+
+    Args:
+        noise_sd (float): A hyper-parameter, used to weigh the filter's
+            predictions and the vision data received during the "update" phase.
+            Unit is metres.
+            Defaults to 0.01 (In simulation, this should match the argument
+            passed to the rsim noise generator, but should be adjusted based on
+            real-world conditions when live robots are used).
+    """
+
+    def __init__(self, noise_sd: float = 0.01):
+        assert noise_sd > 0, "The standard deviation must be greater than 0"
+
+        # s; to be initialised by strategy runner with 1st GameFrame
+        self.state = None
+
+        # sigma squared x, y, z
+        noise_var = pow(noise_sd, 2)
+        var_x, var_y, var_z = noise_var, noise_var, noise_var
+
+        # sigma xy, xz, yz
+        noise_covariance = 0  # assume their errors are uncorrelated
+        covariance_xy, covariance_xz, covariance_yz = (
+            noise_covariance,
+            noise_covariance,
+            noise_covariance,
+        )
+
+        dimensions = 3
+        self.identity = np.identity(dimensions)
+
+        # R_n
+        self.measurement_cov = np.array(
+            [
+                [var_x, covariance_xy, covariance_xz],
+                [covariance_xy, var_y, covariance_yz],
+                [covariance_xz, covariance_yz, var_z],
+            ]
+        )
+        # P_n,n; initialised with uncertainty in 1st frame
+        self.covariance_mat = self.measurement_cov
+        # Q
+        self.process_noise = (2 * noise_var) * self.identity
+
+        # Observation matrix H and state transition matrix F are just the identity matrix.
+        # Multiplications with them are omitted.
+
+    def _step(
+        self,
+        new_data: Optional[tuple[float, float, float]],
+        last_ball: Ball,
+        time_elapsed: float,
+    ) -> tuple[float, float, float]:
+        """
+        A single iteration of the filter.
+
+        Args:
+            new_data (Optional[tuple[float, float, float]]): New vision data received (xyz coordinates in metres),
+                passed by the filter_data function. None if the ball is not detected.
+            last_ball (Ball): An object storing the ball's last known position and velocity.
+            time_elapsed (float): Time since last vision data was received.
+
+        Returns:
+            tuple[float, float, float]: Filtered vision data (xyz coordinates),
+                returned to the filter_data function for packaging.
+        """
+
+        # class Ball: p: Vector3D; v: Vector3D; a: Vector3D
+
+        # Phase 0: Initialised with the 1st valid GameFrame (only on initialisation)
+        if self.state is None:
+            self.state = np.array((last_ball.p.x, last_ball.p.y, last_ball.p.z))
+
+        # Phase 1: Predicting the current state given the last state.
+        # u
+        control_velocities = np.array((last_ball.v.x, last_ball.v.y, last_ball.v.z))
+        # G
+        control_mat = time_elapsed * self.identity
+        # s_n,n-1
+        pred_state = self.state + np.matmul(control_mat, control_velocities)
+        # P_n,n-1
+        pred_cov = self.covariance_mat + self.process_noise
+
+        # Phase 2: Adjust this prediction based on new data
+        if new_data is not None:  # Received frame.
+            # z
+            measurement = np.array(new_data)
+
+            # K_n
+            kalman_gain = np.linalg.solve((pred_cov + self.measurement_cov).T, pred_cov.T).T
+
+            # s_n,n
+            self.state = pred_state + np.matmul(kalman_gain, (measurement - pred_state))
+
+            ident_less_kalman = self.identity - kalman_gain
+            measurement_uncertainty = np.matmul(kalman_gain, np.matmul(self.measurement_cov, kalman_gain.T))
+
+            # P_n,n
+            self.covariance_mat = (
+                np.matmul(ident_less_kalman, np.matmul(pred_cov, ident_less_kalman.T)) + measurement_uncertainty
+            )
+
+        # We can rely on the invariant that vanished frames have null x values
+        # as they are imputed with None by filter_data
+        else:  # Vanished frame: use predicted values.
+            self.state = pred_state
+            self.covariance_mat = pred_cov
+
+        return tuple(self.state)
+
+    def filter_data(self, data: Optional[Ball], last_frame: Ball, time_elapsed: float) -> Ball:
+        """
+        Performs one prediction–update cycle of the Kalman filter for the ball.
+
+        The ball's position is first predicted using its last known velocity
+        and the elapsed time. If new vision data is available, the prediction
+        is corrected using the Kalman gain. If the vision frame is missing,
+        the predicted state is used directly.
+
+        Args:
+            data (Optional[Ball]): New vision measurement containing the ball's position
+                (x, y, z) in metres. May be None if the ball is not detected.
+            last_frame (Ball): The ball's last known state, including position,
+                velocity, and acceleration, used for motion prediction.
+            time_elapsed (float): Time in seconds since the previous update.
+
+        Returns:
+            Ball: Filtered estimate of the ball's position, returned as a Ball
+                object with updated position and preserved velocity and
+                acceleration.
+        """
+
+        # class Ball: p: Vector3D, v: Vector3D, a: Vector3D
+        if data is not None:
+            new_data = (data.p.x, data.p.y, data.p.z)
+            velocity, acceleration = data.v, data.a
+        else:
+            # If the ball data vanished, PositionRefiner._get_most_confident_ball returns null.
+            new_data = None
+            zero_vector = Vector3D(0, 0, 0)
+            velocity, acceleration = zero_vector, zero_vector
+
+        filtered_data = self._step(new_data, last_frame, time_elapsed)
+
+        return Ball(Vector3D(*filtered_data), velocity, acceleration)
diff --git a/utama_core/run/refiners/position.py b/utama_core/run/refiners/position.py
index 661c8681..b2a5ee3f 100644
--- a/utama_core/run/refiners/position.py
+++ b/utama_core/run/refiners/position.py
@@ -1,256 +1,390 @@
-from collections import defaultdict
-from dataclasses import replace
-from typing import Dict, List, Optional, Tuple
-
-import numpy as np
-
-from utama_core.config.settings import BALL_MERGE_THRESHOLD
-from utama_core.entities.data.raw_vision import RawBallData, RawRobotData, RawVisionData
-from utama_core.entities.data.vector import Vector2D, Vector3D
-from utama_core.entities.data.vision import VisionBallData, VisionData, VisionRobotData
-from utama_core.entities.game import Ball, FieldBounds, GameFrame, Robot
-from utama_core.run.refiners.base_refiner import BaseRefiner
-
-
-class AngleSmoother:
-    def __init__(self, alpha=0.3):
-        self.alpha = alpha  # Smoothing factor for angle
-        self.smoothed_angles = {}  # Stores last smoothed angle for each robot
-
-    def smooth(self, old_angle: float, new_angle: float) -> float:
-        # Compute the shortest angular difference
-        diff = np.atan2(np.sin(new_angle - old_angle), np.cos(new_angle - old_angle))
-        smoothed_angle = old_angle + self.alpha * diff
-
-        return smoothed_angle
-
-
-class PositionRefiner(BaseRefiner):
-    def __init__(self, field_bounds: FieldBounds, bounds_buffer: float = 1.0):
-        # alpha=0 means no change in angle (inf smoothing), alpha=1 means no smoothing
-        self.angle_smoother = AngleSmoother(alpha=1)
-        self.x_min = field_bounds.top_left[0] - bounds_buffer  # expand left
-        self.x_max = field_bounds.bottom_right[0] + bounds_buffer  # expand right
-        self.y_min = field_bounds.bottom_right[1] - bounds_buffer  # expand bottom
-        self.y_max = field_bounds.top_left[1] + bounds_buffer  # expand top
-        self.BOUNDS_BUFFER = bounds_buffer
-
-    # Primary function for the Refiner interface
-    def refine(self, game_frame: GameFrame, data: List[RawVisionData]) -> GameFrame:
-        frames = [frame for frame in data if frame is not None]
-
-        # If no information just return the original
-        # TODO: this needs to be replaced by an extrapolation function (otherwise we will be using old data forever)
-        if not frames:
-            return game_frame
-        # Can combine previous position from game with new data to produce new position if desired
-        combined_vision_data = CameraCombiner().combine_cameras(frames)
-        
-        # for robot in combined_vision_data.yellow_robots:
-        #         if robot.id == 0:
-        #             print(f"robot orientation: {robot.orientation}")
-
-        new_yellow_robots, new_blue_robots = self._combine_both_teams_game_vision_positions(
-            game_frame,
-            combined_vision_data.yellow_robots,
-            combined_vision_data.blue_robots,
-        )
-
-        # After the balls have been combined, take the most confident
-        new_ball = PositionRefiner._get_most_confident_ball(combined_vision_data.balls)
-        if new_ball is None:
-            # If none, take the ball from the last frame of the game
-            new_ball = game_frame.ball
-
-        if game_frame.my_team_is_yellow:
-            new_game_frame = replace(
-                game_frame,
-                ts=combined_vision_data.ts,
-                friendly_robots=new_yellow_robots,
-                enemy_robots=new_blue_robots,
-                ball=new_ball,
-            )
-        else:
-            new_game_frame = replace(
-                game_frame,
-                ts=combined_vision_data.ts,
-                friendly_robots=new_blue_robots,
-                enemy_robots=new_yellow_robots,
-                ball=new_ball,
-            )
-        return new_game_frame
-
-    # Static methods
-    @staticmethod
-    def _combine_robot_vision_data(
-        old_robot: Robot, robot_data: VisionRobotData, angle_smoother: AngleSmoother
-    ) -> Robot:
-        assert old_robot.id == robot_data.id
-        new_x, new_y = robot_data.x, robot_data.y
-
-        # Needs fixing the bounds are off oren becoming -3.9rad
-        # # Smoothing
-        # new_orientation = angle_smoother.smooth(
-        #     old_robot.orientation, robot_data.orientation
-        # )
-        return replace(
-            old_robot,
-            id=robot_data.id,
-            p=Vector2D(new_x, new_y),
-            orientation=robot_data.orientation,
-        )
-
-    # Used at start of the game so assume robot does not have the ball
-    # Also assume velocity and acceleration are zero
-    @staticmethod
-    def _robot_from_vision(robot_data: VisionRobotData, is_friendly: bool) -> Robot:
-        return Robot(
-            id=robot_data.id,
-            is_friendly=is_friendly,
-            has_ball=False,
-            p=Vector2D(robot_data.x, robot_data.y),
-            v=Vector2D(0, 0),
-            a=Vector2D(0, 0),
-            orientation=robot_data.orientation,
-        )
-
-    @staticmethod
-    def _ball_from_vision(ball_data: VisionBallData) -> Ball:
-        zv = Vector3D(0, 0, 0)
-        return Ball(Vector3D(ball_data.x, ball_data.y, ball_data.z), zv, zv)
-
-    @staticmethod
-    def _get_most_confident_ball(balls: List[VisionBallData]) -> Ball:
-        balls_by_confidence = sorted(balls, key=lambda ball: ball.confidence, reverse=True)
-        if not balls_by_confidence:
-            return None
-        return PositionRefiner._ball_from_vision(balls_by_confidence[0])
-
-    def _combine_single_team_positions(
-        self,
-        new_game_robots: Dict[int, Robot],
-        vision_robots: List[VisionRobotData],
-        friendly: bool,
-    ) -> Dict[int, Robot]:
-        for robot in vision_robots:
-            new_x, new_y = robot.x, robot.y
-
-            if not (self.x_min <= new_x <= self.x_max and self.y_min <= new_y <= self.y_max):
-                # Out of bounds so ignore this robot
-                continue
-
-            if robot.id not in new_game_robots:
-                # At the start of the game, we haven't seen anything yet, so just create a new robot
-                new_game_robots[robot.id] = PositionRefiner._robot_from_vision(robot, is_friendly=friendly)
-            else:
-                # Update with smoothed data.
-                new_game_robots[robot.id] = PositionRefiner._combine_robot_vision_data(
-                    new_game_robots[robot.id], robot, self.angle_smoother
-                )
-        return new_game_robots
-
-    def _combine_both_teams_game_vision_positions(
-        self,
-        game_frame: GameFrame,
-        yellow_vision_robots: List[VisionRobotData],
-        blue_vision_robots: List[VisionRobotData],
-    ) -> Tuple[Dict[int, Robot], Dict[int, Robot]]:
-        if game_frame.my_team_is_yellow:
-            old_yellow_robots = game_frame.friendly_robots.copy()
-            old_blue_robots = game_frame.enemy_robots.copy()
-        else:
-            old_yellow_robots = game_frame.enemy_robots.copy()
-            old_blue_robots = game_frame.friendly_robots.copy()
-
-        new_yellow_robots = self._combine_single_team_positions(
-            old_yellow_robots,
-            yellow_vision_robots,
-            friendly=game_frame.my_team_is_yellow,
-        )
-        new_blue_robots = self._combine_single_team_positions(
-            old_blue_robots,
-            blue_vision_robots,
-            friendly=not game_frame.my_team_is_yellow,
-        )
-
-        return new_yellow_robots, new_blue_robots
-
-
-class CameraCombiner:
-    def combine_cameras(self, frames: List[RawVisionData]) -> VisionData:
-        # Now we have access to the game we can do more sophisticated things
-        # Such as ignoring outlier cameras etc
-
-        ts = []
-        # maps robot id to list of frames seen for that robot
-        yellow_captured = defaultdict(list)
-        blue_captured = defaultdict(list)
-        balls_captured = defaultdict(list)
-
-        # Each frame is from a different camera
-        for frame_ind, frame in enumerate(frames):
-            for yr in frame.yellow_robots:
-                yellow_captured[yr.id].append(yr)
-
-            for br in frame.blue_robots:
-                blue_captured[br.id].append(br)
-
-            for b in frame.balls:
-                balls_captured[frame_ind].append(b)
-            ts.append(frame.ts)
-
-        avg_yellows = list(map(self._avg_robots, yellow_captured.values()))
-        avg_blues = list(map(self._avg_robots, blue_captured.values()))
-        # Current strategy is just to take the most confident ball
-        balls = self._combine_balls_by_proximity(balls_captured)
-
-        return VisionData(sum(ts) / len(ts), avg_yellows, avg_blues, balls)
-
-    def _avg_robots(self, rs: List[RawRobotData]) -> Optional[VisionRobotData]:
-        # All these robots should have the same id
-        if not rs:
-            return None
-        base_id = rs[0].id
-        tx, ty, tc = 0, 0, 0
-
-        sum_orientation_x_component = 0.0
-        sum_orientation_y_component = 0.0
-        for r in rs:
-            assert base_id == r.id
-            tx += r.x
-            ty += r.y
-            sum_orientation_x_component += np.cos(r.orientation)
-            sum_orientation_y_component += np.sin(r.orientation)
-            tc += r.confidence
-
-        avg_orientation_x = sum_orientation_x_component / len(rs)
-        avg_orientation_y = sum_orientation_y_component / len(rs)
-        avg_orientation = np.atan2(avg_orientation_y, avg_orientation_x)
-
-        return VisionRobotData(base_id, tx / len(rs), ty / len(rs), avg_orientation)
-
-    def _combine_balls_by_proximity(self, bs: Dict[int, List[RawBallData]]) -> List[VisionBallData]:
-        combined_balls: List[VisionBallData] = []
-        for ball_list in bs.values():
-            for b in ball_list:
-                found = False
-                for i, cb in enumerate(combined_balls):
-                    if CameraCombiner.ball_merge_predicate(b, cb):
-                        found = True
-                        combined_balls[i] = CameraCombiner.ball_merge(cb, b)
-                        break
-
-                if not found:
-                    # If no ball close enough, must have found a new separate ball
-                    combined_balls.append(b)
-        return combined_balls
-
-    def ball_merge_predicate(b1: RawBallData, b2: RawBallData) -> bool:
-        return abs(b1.x - b2.x) + abs(b1.y - b2.y) < BALL_MERGE_THRESHOLD
-
-    def ball_merge(b1: RawBallData, b2: RawBallData) -> RawBallData:
-        nx = (b1.x + b2.x) / 2
-        ny = (b1.y + b2.y) / 2
-        nz = (b1.z + b2.z) / 2
-        nc = max(b1.confidence, b2.confidence)
-        return RawBallData(nx, ny, nz, nc)
+from collections import defaultdict
+from dataclasses import replace
+from functools import partial
+from typing import Dict, List, Optional, Tuple
+
+import numpy as np
+
+from utama_core.config.settings import BALL_MERGE_THRESHOLD
+from utama_core.entities.data.raw_vision import RawBallData, RawRobotData, RawVisionData
+from utama_core.entities.data.vector import Vector2D, Vector3D
+from utama_core.entities.data.vision import VisionBallData, VisionData, VisionRobotData
+from utama_core.entities.game import Ball, FieldBounds, GameFrame, Robot
+from utama_core.global_utils.mapping_utils import map_friendly_enemy_to_colors
+from utama_core.run.refiners.base_refiner import BaseRefiner
+from utama_core.run.refiners.kalman import KalmanFilter, KalmanFilterBall
+
+
+class AngleSmoother:
+    def __init__(self, alpha=0.3):
+        self.alpha = alpha  # Smoothing factor for angle
+        self.smoothed_angles = {}  # Stores last smoothed angle for each robot
+
+    def smooth(self, old_angle: float, new_angle: float) -> float:
+        # Compute the shortest angular difference
+        diff = np.atan2(np.sin(new_angle - old_angle), np.cos(new_angle - old_angle))
+        smoothed_angle = old_angle + self.alpha * diff
+
+        return smoothed_angle
+
+
+class PositionRefiner(BaseRefiner):
+    def __init__(
+        self,
+        field_bounds: FieldBounds,
+        bounds_buffer: float = 1.0,
+        filtering: bool = True,
+    ):
+        # alpha=0 means no change in angle (inf smoothing), alpha=1 means no smoothing
+        self.angle_smoother = AngleSmoother(alpha=1)
+        self.x_min = field_bounds.top_left[0] - bounds_buffer  # expand left
+        self.x_max = field_bounds.bottom_right[0] + bounds_buffer  # expand right
+        self.y_min = field_bounds.bottom_right[1] - bounds_buffer  # expand bottom
+        self.y_max = field_bounds.top_left[1] + bounds_buffer  # expand top
+        self.BOUNDS_BUFFER = bounds_buffer
+
+        # For Kalman filtering and imputing vanished values.
+        self.filtering = filtering
+        self._filter_running = (
+            False  # Only start filtering once we have valid data to filter (i.e. after the first valid game frame)
+        )
+
+        if self.filtering:
+            # Instantiate a dedicated Kalman filter for each robot so filtering can be kept independent.
+            self.kalman_filters_yellow: dict[int, KalmanFilter] = {}
+            self.kalman_filters_blue: dict[int, KalmanFilter] = {}
+            self.kalman_filter_ball = KalmanFilterBall()
+
+    # Primary function for the Refiner interface
+    def refine(self, game_frame: GameFrame, data: List[RawVisionData]) -> GameFrame:
+        frames = [frame for frame in data if frame is not None]
+
+        # If no information just return the original
+        if not frames:
+            return game_frame
+
+        # class VisionData: ts: float; yellow_robots: List[VisionRobotData]; blue_robots: List[VisionRobotData]; balls: List[VisionBallData]
+        # class VisionRobotData: id: int; x: float; y: float; orientation: float
+        combined_vision_data: VisionData = CameraCombiner().combine_cameras(frames)
+
+        time_elapsed = combined_vision_data.ts - game_frame.ts
+
+        # For filtering and vanishing
+        if self.filtering and self._filter_running:  # Checks if the first valid game frame has been received.
+            # For vanishing: imputes combined_vision_data with null vision frames in place.
+            vision_yellow, vision_blue = self._include_vanished_robots(combined_vision_data, game_frame)
+
+            yellow_rbt_last_frame, blue_rbt_last_frame = map_friendly_enemy_to_colors(
+                game_frame.my_team_is_yellow,
+                game_frame.friendly_robots,
+                game_frame.enemy_robots,
+            )
+
+            filtered_yellow_robots = []
+            for y_rbt_id, vision_y_rbt in vision_yellow.items():
+                if y_rbt_id not in self.kalman_filters_yellow:
+                    self.kalman_filters_yellow[y_rbt_id] = KalmanFilter(id=y_rbt_id)
+
+                filtered_robot = self.kalman_filters_yellow[y_rbt_id].filter_data(
+                    vision_y_rbt,  # new measurement
+                    yellow_rbt_last_frame[y_rbt_id],  # last frame
+                    time_elapsed,
+                )
+
+                filtered_yellow_robots.append(filtered_robot)
+
+            filtered_blue_robots = []
+            for b_rbt_id, vision_b_rbt in vision_blue.items():
+                if b_rbt_id not in self.kalman_filters_blue:
+                    self.kalman_filters_blue[b_rbt_id] = KalmanFilter(id=b_rbt_id)
+
+                filtered_robot = self.kalman_filters_blue[b_rbt_id].filter_data(
+                    vision_b_rbt,  # new measurement
+                    blue_rbt_last_frame[b_rbt_id],  # last frame
+                    time_elapsed,
+                )
+
+                filtered_blue_robots.append(filtered_robot)
+
+            combined_vision_data = VisionData(
+                ts=combined_vision_data.ts,
+                yellow_robots=filtered_yellow_robots,
+                blue_robots=filtered_blue_robots,
+                balls=combined_vision_data.balls,
+            )
+
+        # Some processing of robot vision data
+        new_yellow_robots, new_blue_robots = self._combine_both_teams_game_vision_positions(
+            game_frame,
+            combined_vision_data.yellow_robots,
+            combined_vision_data.blue_robots,
+        )
+
+        # After the balls have been combined, take the most confident
+        new_ball: Ball = PositionRefiner._get_most_confident_ball(combined_vision_data.balls)
+
+        # For filtering and vanishing
+        if self.filtering and self._filter_running:
+            new_ball = self.kalman_filter_ball.filter_data(
+                new_ball,
+                game_frame.ball,
+                time_elapsed,
+            )
+        elif new_ball is None:
+            # If none, take the ball from the last frame of the game
+            new_ball = game_frame.ball
+
+        if game_frame.my_team_is_yellow:
+            new_game_frame = replace(
+                game_frame,
+                ts=combined_vision_data.ts,
+                friendly_robots=new_yellow_robots,
+                enemy_robots=new_blue_robots,
+                ball=new_ball,
+            )
+        else:
+            new_game_frame = replace(
+                game_frame,
+                ts=combined_vision_data.ts,
+                friendly_robots=new_blue_robots,
+                enemy_robots=new_yellow_robots,
+                ball=new_ball,
+            )
+
+        return new_game_frame
+
+    def reset(self):
+        """
+        Resets the internal state of the refiner, including Kalman filters and vanishing trackers.
+        Should be called at the start of each game to ensure no leakage of information between games.
+        """
+        self._filter_running = False
+        if self.filtering:
+            self.kalman_filters_yellow = {}
+            self.kalman_filters_blue = {}
+            self.kalman_filter_ball = KalmanFilterBall()
+
+    def start_filtering(self):
+        """
+        Start filtering after first valid frame is received from GameGater.
+        """
+        self._filter_running = True
+
+    def _include_vanished_robots(
+        self, vision_data: VisionData, game_frame: GameFrame
+    ) -> Tuple[dict[int, Optional[VisionRobotData]], dict[int, Optional[VisionRobotData]]]:
+        """
+        Augment the VisionData lists with None for vanished robots so that the Kalman filter
+        knows that data vanished.
+
+        Returns:
+            Tuple of (yellow_vision_dict, blue_vision_dict) where vanished robots are represented as None.
+        """
+
+        # TODO: major issue is that if we do a robot substitution, the
+        # Kalman filter will think the old robot vanished and a new robot appeared.
+        # needs to be adjusted when referee system is in place.
+        # see issue #107 on GitHub for more details.
+
+        yellow_ids_last_frame, blue_ids_last_frame = map_friendly_enemy_to_colors(
+            game_frame.my_team_is_yellow,
+            game_frame.friendly_robots.keys(),
+            game_frame.enemy_robots.keys(),
+        )
+
+        # Current vision IDs
+        yellow_present = {r.id for r in vision_data.yellow_robots}
+        blue_present = {r.id for r in vision_data.blue_robots}
+
+        # Start with current measurements
+        yellow_vision_dict: dict[int, Optional[VisionRobotData]] = {r.id: r for r in vision_data.yellow_robots}
+        blue_vision_dict: dict[int, Optional[VisionRobotData]] = {r.id: r for r in vision_data.blue_robots}
+
+        # Add None for vanished robots
+        for robot_id in yellow_ids_last_frame - yellow_present:
+            yellow_vision_dict[robot_id] = None
+        for robot_id in blue_ids_last_frame - blue_present:
+            blue_vision_dict[robot_id] = None
+
+        return yellow_vision_dict, blue_vision_dict
+
+    # Static methods
+    @staticmethod
+    def _combine_robot_vision_data(
+        old_robot: Robot, robot_data: VisionRobotData, angle_smoother: AngleSmoother
+    ) -> Robot:
+        assert old_robot.id == robot_data.id
+        new_x, new_y = robot_data.x, robot_data.y
+
+        # Needs fixing the bounds are off oren becoming -3.9rad
+        # # Smoothing
+        # new_orientation = angle_smoother.smooth(
+        #     old_robot.orientation, robot_data.orientation
+        # )
+        return replace(
+            old_robot,
+            id=robot_data.id,
+            p=Vector2D(new_x, new_y),
+            orientation=robot_data.orientation,
+        )
+
+    # Used at start of the game so assume robot does not have the ball
+    # Also assume velocity and acceleration are zero
+    @staticmethod
+    def _robot_from_vision(robot_data: VisionRobotData, is_friendly: bool) -> Robot:
+        return Robot(
+            id=robot_data.id,
+            is_friendly=is_friendly,
+            has_ball=False,
+            p=Vector2D(robot_data.x, robot_data.y),
+            v=Vector2D(0, 0),
+            a=Vector2D(0, 0),
+            orientation=robot_data.orientation,
+        )
+
+    @staticmethod
+    def _ball_from_vision(ball_data: VisionBallData) -> Ball:
+        zv = Vector3D(0, 0, 0)
+        return Ball(Vector3D(ball_data.x, ball_data.y, ball_data.z), zv, zv)
+
+    @staticmethod
+    def _get_most_confident_ball(balls: List[VisionBallData]) -> Ball:
+        balls_by_confidence = sorted(balls, key=lambda ball: ball.confidence, reverse=True)
+        if not balls_by_confidence:
+            return None
+        return PositionRefiner._ball_from_vision(balls_by_confidence[0])
+
+    def _combine_single_team_positions(
+        self,
+        new_game_robots: Dict[int, Robot],
+        vision_robots: List[VisionRobotData],
+        friendly: bool,
+    ) -> Dict[int, Robot]:
+        for robot in vision_robots:
+            new_x, new_y = robot.x, robot.y
+
+            if not (self.x_min <= new_x <= self.x_max and self.y_min <= new_y <= self.y_max):
+                # Out of bounds so ignore this robot
+                continue
+
+            if robot.id not in new_game_robots:
+                # At the start of the game, we haven't seen anything yet, so just create a new robot
+                new_game_robots[robot.id] = PositionRefiner._robot_from_vision(robot, is_friendly=friendly)
+            else:
+                # Update with smoothed data.
+                new_game_robots[robot.id] = PositionRefiner._combine_robot_vision_data(
+                    new_game_robots[robot.id], robot, self.angle_smoother
+                )
+        return new_game_robots
+
+    def _combine_both_teams_game_vision_positions(
+        self,
+        game_frame: GameFrame,
+        yellow_vision_robots: List[VisionRobotData],
+        blue_vision_robots: List[VisionRobotData],
+    ) -> Tuple[Dict[int, Robot], Dict[int, Robot]]:
+        if game_frame.my_team_is_yellow:
+            old_yellow_robots = game_frame.friendly_robots.copy()
+            old_blue_robots = game_frame.enemy_robots.copy()
+        else:
+            old_yellow_robots = game_frame.enemy_robots.copy()
+            old_blue_robots = game_frame.friendly_robots.copy()
+
+        new_yellow_robots = self._combine_single_team_positions(
+            old_yellow_robots,
+            yellow_vision_robots,
+            friendly=game_frame.my_team_is_yellow,
+        )
+        new_blue_robots = self._combine_single_team_positions(
+            old_blue_robots,
+            blue_vision_robots,
+            friendly=not game_frame.my_team_is_yellow,
+        )
+
+        return new_yellow_robots, new_blue_robots
+
+    @property
+    def filter_running(self) -> bool:
+        return self._filter_running
+
+
+class CameraCombiner:
+    def combine_cameras(self, frames: List[RawVisionData]) -> VisionData:
+        # Now we have access to the game we can do more sophisticated things
+        # Such as ignoring outlier cameras etc
+
+        ts = []
+        # maps robot id to list of frames seen for that robot
+        yellow_captured = defaultdict(list)
+        blue_captured = defaultdict(list)
+        balls_captured = defaultdict(list)
+
+        # Each frame is from a different camera
+        for frame_ind, frame in enumerate(frames):
+            for yr in frame.yellow_robots:
+                yellow_captured[yr.id].append(yr)
+
+            for br in frame.blue_robots:
+                blue_captured[br.id].append(br)
+
+            for b in frame.balls:
+                balls_captured[frame_ind].append(b)
+            ts.append(frame.ts)
+
+        avg_yellows = list(map(self._avg_robots, yellow_captured.values()))
+        avg_blues = list(map(self._avg_robots, blue_captured.values()))
+        # Current strategy is just to take the most confident ball
+        balls = self._combine_balls_by_proximity(balls_captured)
+
+        return VisionData(sum(ts) / len(ts), avg_yellows, avg_blues, balls)
+
+    def _avg_robots(self, rs: List[RawRobotData]) -> Optional[VisionRobotData]:
+        # All these robots should have the same id
+        if not rs:
+            return None
+        base_id = rs[0].id
+        tx, ty, tc = 0, 0, 0
+
+        sum_orientation_x_component = 0.0
+        sum_orientation_y_component = 0.0
+        for r in rs:
+            assert base_id == r.id
+            tx += r.x
+            ty += r.y
+            sum_orientation_x_component += np.cos(r.orientation)
+            sum_orientation_y_component += np.sin(r.orientation)
+            tc += r.confidence
+
+        avg_orientation_x = sum_orientation_x_component / len(rs)
+        avg_orientation_y = sum_orientation_y_component / len(rs)
+        avg_orientation = np.atan2(avg_orientation_y, avg_orientation_x)
+
+        return VisionRobotData(base_id, tx / len(rs), ty / len(rs), avg_orientation)
+
+    def _combine_balls_by_proximity(self, bs: Dict[int, List[RawBallData]]) -> List[VisionBallData]:
+        combined_balls: List[VisionBallData] = []
+        for ball_list in bs.values():
+            for b in ball_list:
+                found = False
+                for i, cb in enumerate(combined_balls):
+                    if CameraCombiner.ball_merge_predicate(b, cb):
+                        found = True
+                        combined_balls[i] = CameraCombiner.ball_merge(cb, b)
+                        break
+
+                if not found:
+                    # If no ball close enough, must have found a new separate ball
+                    combined_balls.append(b)
+        return combined_balls
+
+    @staticmethod
+    def ball_merge_predicate(b1: RawBallData, b2: RawBallData) -> bool:
+        return abs(b1.x - b2.x) + abs(b1.y - b2.y) < BALL_MERGE_THRESHOLD
+
+    @staticmethod
+    def ball_merge(b1: RawBallData, b2: RawBallData) -> RawBallData:
+        nx = (b1.x + b2.x) / 2
+        ny = (b1.y + b2.y) / 2
+        nz = (b1.z + b2.z) / 2
+        nc = max(b1.confidence, b2.confidence)
+        return RawBallData(nx, ny, nz, nc)
diff --git a/utama_core/run/strategy_runner.py b/utama_core/run/strategy_runner.py
index fe6b73a5..fb27428b 100644
--- a/utama_core/run/strategy_runner.py
+++ b/utama_core/run/strategy_runner.py
@@ -82,6 +82,7 @@ class StrategyRunner:
             Defaults to 0 for each.
         rsim_vanishing (float, optional): When running in rsim, cause robots and ball to vanish with the given probability.
             Defaults to 0.
+        filtering (bool, optional): Turn on Kalman filtering. Defaults to true.
     """
 
     def __init__(
@@ -100,7 +101,8 @@ def __init__(
         print_real_fps: bool = False,  # Turn this on for RSim
         profiler_name: Optional[str] = None,
         rsim_noise: RsimGaussianNoise = RsimGaussianNoise(),
-        rsim_vanishing: float = 0
+        rsim_vanishing: float = 0,
+        filtering: bool = True,
     ):
         self.logger = logging.getLogger(__name__)
 
@@ -129,9 +131,26 @@ def __init__(
         self._load_robot_controllers()
 
         assert_valid_bounding_box(self.field_bounds)
-        self.position_refiner = PositionRefiner(self.field_bounds)
-        self.velocity_refiner = VelocityRefiner()
-        self.robot_info_refiner = RobotInfoRefiner()
+
+        (
+            self.my_position_refiner,
+            self.my_velocity_refiner,
+            self.my_robot_info_refiner,
+        ) = self._init_refiners(
+            field_bounds,
+            filtering,
+        )
+
+        if self.opp_strategy:
+            (
+                self.opp_position_refiner,
+                self.opp_velocity_refiner,
+                self.opp_robot_info_refiner,
+            ) = self._init_refiners(
+                field_bounds,
+                filtering,
+            )
+
         # self.referee_refiner = RefereeRefiner()
         (
             self.my_game_history,
@@ -224,14 +243,12 @@ def start_threads(self, vision_receiver: VisionReceiver):  # , referee_receiver)
         # referee_thread.start()
 
     def _load_sim(
-        self,
-        rsim_noise: RsimGaussianNoise,
-        rsim_vanishing: float
+        self, rsim_noise: RsimGaussianNoise, rsim_vanishing: float
     ) -> Tuple[Optional[SSLStandardEnv], Optional[AbstractSimController]]:
         """Mode RSIM: Loads the RSim environment with the expected number of robots and corresponding sim controller.
         Mode GRSIM: Loads corresponding sim controller and teleports robots in GRSim to ensure the expected number of
         robots is met.
-        
+
         Args:
             rsim_noise (RsimGaussianNoise, optional): When running in rsim, add Gaussian noise to balls and robots with the
                 given standard deviation. The 3 parameters are for x (in m), y (in m), and orientation (in degrees) respectively.
@@ -245,7 +262,13 @@ def _load_sim(
         """
         if self.mode == Mode.RSIM:
             n_yellow, n_blue = map_friendly_enemy_to_colors(self.my_team_is_yellow, self.exp_friendly, self.exp_enemy)
-            rsim_env = SSLStandardEnv(n_robots_yellow=n_yellow, n_robots_blue=n_blue, render_mode=None, gaussian_noise=rsim_noise, vanishing=rsim_vanishing)
+            rsim_env = SSLStandardEnv(
+                n_robots_yellow=n_yellow,
+                n_robots_blue=n_blue,
+                render_mode=None,
+                gaussian_noise=rsim_noise,
+                vanishing=rsim_vanishing,
+            )
 
             if self.opp_strategy:
                 self.opp_strategy.load_rsim_env(rsim_env)
@@ -386,6 +409,28 @@ def _load_robot_controllers(self):
             self.opp_strategy.load_robot_controller(opp_robot_controller)
             self.opp_strategy.load_motion_controller(self.opp_motion_controller(self.mode, self.rsim_env))
 
+    def _init_refiners(
+        self,
+        field_bounds: FieldBounds,
+        filtering: bool,
+    ) -> tuple[PositionRefiner, VelocityRefiner, RobotInfoRefiner]:
+        """
+        Initialize the position, velocity, and robot info refiners.
+        Args:
+            field_bounds (FieldBounds): The bounds of the field.
+            filtering (bool): Whether to use filtering in the position refiner.
+        Returns:
+            tuple: The initialized PositionRefiner, VelocityRefiner, and RobotInfoRefiner.
+        """
+        position_refiner = PositionRefiner(
+            field_bounds,
+            filtering=filtering,
+        )
+        velocity_refiner = VelocityRefiner()
+        robot_info_refiner = RobotInfoRefiner()
+
+        return position_refiner, velocity_refiner, robot_info_refiner
+
     def _load_game(self):
         """
         Load the game state for both friendly and opponent strategies after waiting for valid game data with GameGater.
@@ -398,10 +443,15 @@ def _load_game(self):
             self.exp_friendly,
             self.exp_enemy,
             self.vision_buffers,
-            self.position_refiner,
+            self.my_position_refiner,
             is_pvp=self.opp_strategy is not None,
             rsim_env=self.rsim_env,
         )
+
+        self.my_position_refiner.start_filtering()
+        if self.opp_strategy:
+            self.opp_position_refiner.start_filtering()
+
         my_field = Field(self.my_team_is_right, self.field_bounds)
         my_game_history = GameHistory(MAX_GAME_HISTORY)
         my_game = Game(my_game_history, my_current_game_frame, field=my_field)
@@ -435,6 +485,9 @@ def _reset_game(self):
         """
         _ = self.my_strategy.robot_controller.get_robots_responses()
 
+        self.my_position_refiner.reset()
+        if self.opp_strategy:
+            self.opp_position_refiner.reset()
         (
             self.my_game_history,
             self.my_current_game_frame,
@@ -676,19 +729,25 @@ def _step_game(
             current_game_frame = self.opp_current_game_frame
             game_history = self.opp_game_history
             game = self.opp_game
+            position_refiner = self.opp_position_refiner
+            velocity_refiner = self.opp_velocity_refiner
+            robot_info_refiner = self.opp_robot_info_refiner
         else:
             strategy = self.my_strategy
             current_game_frame = self.my_current_game_frame
             game_history = self.my_game_history
             game = self.my_game
+            position_refiner = self.my_position_refiner
+            velocity_refiner = self.my_velocity_refiner
+            robot_info_refiner = self.my_robot_info_refiner
 
         # Pull responses from robot controller
         responses = strategy.robot_controller.get_robots_responses()
 
         # Update game frame with refined information
-        new_game_frame = self.position_refiner.refine(current_game_frame, vision_frames)
-        new_game_frame = self.velocity_refiner.refine(game_history, new_game_frame)  # , robot_frame.imu_data)
-        new_game_frame = self.robot_info_refiner.refine(new_game_frame, responses)
+        new_game_frame = position_refiner.refine(current_game_frame, vision_frames)
+        new_game_frame = velocity_refiner.refine(game_history, new_game_frame)  # , robot_frame.imu_data)
+        new_game_frame = robot_info_refiner.refine(new_game_frame, responses)
         # new_game_frame = self.referee_refiner.refine(new_game_frame, responses)
 
         # Store updated game frame
@@ -703,16 +762,3 @@ def _step_game(
 
         game.add_game_frame(new_game_frame)
         strategy.step()
-
-
-# if __name__ == "__main__":
-# runner = StrategyRunner(
-#     strategy=RobotPlacementStrategy(id=3),
-#     my_team_is_yellow=True,
-#     my_team_is_right=True,
-#     mode="grsim",
-#     exp_friendly=6,
-#     exp_enemy=6,
-#     opp_strategy=RobotPlacementStrategy(id=3, invert=True),
-# )
-# runner.run()
diff --git a/utama_core/strategy/examples/__init__.py b/utama_core/strategy/examples/__init__.py
index c97860c0..dffe12f6 100644
--- a/utama_core/strategy/examples/__init__.py
+++ b/utama_core/strategy/examples/__init__.py
@@ -5,3 +5,4 @@
 )
 from utama_core.strategy.examples.startup_strategy import StartupStrategy
 from utama_core.strategy.examples.two_robot_placement import TwoRobotPlacementStrategy
+from utama_core.strategy.examples.point_cycle_strategy import PointCycleStrategy
diff --git a/utama_core/strategy/examples/point_cycle_strategy.py b/utama_core/strategy/examples/point_cycle_strategy.py
new file mode 100644
index 00000000..0b725616
--- /dev/null
+++ b/utama_core/strategy/examples/point_cycle_strategy.py
@@ -0,0 +1,182 @@
+"""Strategy for random movement within bounded area."""
+
+from __future__ import annotations
+
+import random
+from collections import deque
+from typing import Optional, Tuple
+
+import py_trees
+
+from utama_core.entities.data.vector import Vector2D
+from utama_core.entities.game.field import FieldBounds
+from utama_core.skills.src.utils.move_utils import move
+from utama_core.strategy.common.abstract_behaviour import AbstractBehaviour
+from utama_core.strategy.common.abstract_strategy import AbstractStrategy
+
+
+class PointCycleBehaviour(AbstractBehaviour):
+    """
+    Behaviour that makes a robot move to randomly sampled targets within bounds.
+
+    Args:
+        robot_id (int): The robot ID to control.
+        field_bounds (FieldBounds): ((min_x, max_x), (min_y, max_y)) bounds for movement.
+        endpoint_tolerance (float): Distance to consider target reached.
+        seed (Optional[int]): Seed for deterministic random sampling.
+    """
+
+    def __init__(
+        self,
+        robot_id: int,
+        field_bounds: FieldBounds,
+        endpoint_tolerance: float,
+        seed: Optional[int] = None,
+    ):
+        super().__init__(name=f"RandomPoint_{robot_id}")
+        self.robot_id = robot_id
+        self.field_bounds = field_bounds
+        self.endpoint_tolerance = endpoint_tolerance
+
+        self.current_target = None
+        self.points = RandomPointSampler(field_bounds, seed=seed)
+
+    def initialise(self):
+        """Initialize with a random target and speed."""
+        # Will set target on first update when we have robot position
+        pass
+
+    def update(self) -> py_trees.common.Status:
+        """Command robot to move to random targets."""
+        game = self.blackboard.game
+        rsim_env = self.blackboard.rsim_env
+
+        if not game.friendly_robots or self.robot_id not in game.friendly_robots:
+            return py_trees.common.Status.RUNNING
+
+        robot = game.friendly_robots[self.robot_id]
+        robot_pos = Vector2D(robot.p.x, robot.p.y)
+
+        # Generate initial target if needed
+        if self.current_target is None:
+            self.current_target = self.points.next_point
+
+        # Check if target reached
+        distance_to_target = robot_pos.distance_to(self.current_target)
+        if distance_to_target <= self.endpoint_tolerance:
+            # Generate new target and speed
+            self.current_target = self.points.next_point
+
+        # Visualize target
+        if rsim_env:
+            rsim_env.draw_point(self.current_target.x, self.current_target.y, color="green")
+            # Draw a line to show path
+            rsim_env.draw_line(
+                [
+                    (robot_pos.x, robot_pos.y),
+                    (self.current_target.x, self.current_target.y),
+                ],
+                color="blue",
+                width=1,
+            )
+
+        # Generate movement command
+        cmd = move(
+            game,
+            self.blackboard.motion_controller,
+            self.robot_id,
+            self.current_target,
+            0.0,  # Face forward
+        )
+
+        self.blackboard.cmd_map[self.robot_id] = cmd
+        return py_trees.common.Status.RUNNING
+
+
+class PointCycleStrategy(AbstractStrategy):
+    """
+    Strategy that instantiates one PointCycleBehaviour per friendly robot
+    and executes them in parallel within specified field bounds.
+
+    Args:
+        n_robots (int): Number of robots to control.
+        field_bounds (FieldBounds): Movement bounds.
+        endpoint_tolerance (float): Distance to consider target reached.
+        seed (Optional[int]): Base seed for deterministic behaviour.
+    """
+
+    def __init__(
+        self,
+        n_robots: int,
+        field_bounds: FieldBounds,
+        endpoint_tolerance: float,
+        seed: Optional[int] = None,
+    ):
+        self.n_robots = n_robots
+        self.field_bounds = field_bounds
+        self.endpoint_tolerance = endpoint_tolerance
+        self.seed = seed
+        super().__init__()
+
+    def assert_exp_robots(self, n_runtime_friendly: int, n_runtime_enemy: int):
+        """Requires number of friendly robots to match."""
+        return n_runtime_friendly >= self.n_robots
+
+    def assert_exp_goals(self, includes_my_goal_line: bool, includes_opp_goal_line: bool):
+        return True
+
+    def get_min_bounding_zone(self) -> Optional[FieldBounds]:
+        """Return the movement bounds."""
+        return self.field_bounds
+
+    def create_behaviour_tree(self) -> py_trees.behaviour.Behaviour:
+        """Create parallel behaviour tree with all robot random movement behaviours."""
+        if self.n_robots == 1:
+            return PointCycleBehaviour(
+                robot_id=0,
+                field_bounds=self.field_bounds,
+                endpoint_tolerance=self.endpoint_tolerance,
+                seed=self.seed,
+            )
+
+        behaviours = []
+        for robot_id in range(self.n_robots):
+            behaviour = PointCycleBehaviour(
+                robot_id=robot_id,
+                field_bounds=self.field_bounds,
+                endpoint_tolerance=self.endpoint_tolerance,
+                seed=None if self.seed is None else self.seed + robot_id,
+            )
+            behaviours.append(behaviour)
+
+        return py_trees.composites.Parallel(
+            name="RandomPoint",
+            policy=py_trees.common.ParallelPolicy.SuccessOnAll(),
+            children=behaviours,
+        )
+
+
+class RandomPointSampler:
+    """
+    Uniform random point sampler within rectangular field bounds.
+
+    Args:
+        field_bounds (FieldBounds): ((min_x, max_x), (min_y, max_y))
+        seed (Optional[int]): Random seed for deterministic sampling.
+    """
+
+    def __init__(self, field_bounds: FieldBounds, seed: int = 42):
+        self.field_bounds = field_bounds
+        self.rng = random.Random(seed)
+
+    @property
+    def next_point(self) -> Vector2D:
+        min_x = self.field_bounds.bottom_right[0]
+        max_x = self.field_bounds.top_left[0]
+        min_y = self.field_bounds.bottom_right[1]
+        max_y = self.field_bounds.top_left[1]
+
+        x = self.rng.uniform(min_x, max_x)
+        y = self.rng.uniform(min_y, max_y)
+
+        return Vector2D(x=x, y=y)
diff --git a/utama_core/tests/entities/test_proximity_lookup.py b/utama_core/tests/entities/test_proximity_lookup.py
index 3c5dd438..ff4a414c 100644
--- a/utama_core/tests/entities/test_proximity_lookup.py
+++ b/utama_core/tests/entities/test_proximity_lookup.py
@@ -1,10 +1,12 @@
 import numpy as np
+import pytest
 
 from utama_core.entities.data.vector import Vector2D
 from utama_core.entities.game.proximity_lookup import ProximityLookup
 from utama_core.entities.game.robot import Robot
 
 
+@pytest.mark.filterwarnings("ignore:Invalid closest_to_ball query")  # Ignore warning about no ball
 def test_proximity_lookup_handles_none_inputs():
     lookup = ProximityLookup(friendly_robots=None, enemy_robots=None, ball=None)
     obj, dist = lookup.closest_to_ball()
@@ -12,6 +14,7 @@ def test_proximity_lookup_handles_none_inputs():
     assert np.isinf(dist)
 
 
+@pytest.mark.filterwarnings("ignore:Invalid closest_to_ball query")  # Ignore warning about no ball
 def test_proximity_lookup_with_no_ball():
     robots = {
         1: Robot(
diff --git a/utama_core/tests/refiners/kalman_test.py b/utama_core/tests/refiners/kalman_test.py
new file mode 100644
index 00000000..c0c742fb
--- /dev/null
+++ b/utama_core/tests/refiners/kalman_test.py
@@ -0,0 +1,450 @@
+"""
+Correctness tests for KalmanFilter and KalmanFilterBall.
+
+Key properties checked:
+- Filtered output is a weighted blend of prediction and measurement.
+- Vanished frames fall back to velocity-based prediction.
+- Repeated identical measurements converge to the true value.
+- Orientation wrapping is handled correctly near the ±π boundary.
+- Return types and shapes are always correct.
+"""
+
+import math
+
+import numpy as np
+import pytest
+
+from utama_core.entities.data.vector import Vector2D, Vector3D
+from utama_core.entities.data.vision import VisionRobotData
+from utama_core.entities.game import Ball
+from utama_core.entities.game.robot import Robot
+from utama_core.run.refiners.kalman import KalmanFilter, KalmanFilterBall
+
+# ---------------------------------------------------------------------------
+# Helpers
+# ---------------------------------------------------------------------------
+
+
+def make_robot(
+    x: float = 0.0,
+    y: float = 0.0,
+    vx: float = 0.0,
+    vy: float = 0.0,
+    orientation: float = 0.0,
+) -> Robot:
+    return Robot(
+        id=0,
+        is_friendly=True,
+        has_ball=False,
+        p=Vector2D(x, y),
+        v=Vector2D(vx, vy),
+        a=Vector2D(0, 0),
+        orientation=orientation,
+    )
+
+
+def make_ball(
+    x: float = 0.0,
+    y: float = 0.0,
+    z: float = 0.0,
+    vx: float = 0.0,
+    vy: float = 0.0,
+    vz: float = 0.0,
+) -> Ball:
+    return Ball(
+        p=Vector3D(x, y, z),
+        v=Vector3D(vx, vy, vz),
+        a=Vector3D(0, 0, 0),
+    )
+
+
+def make_vision(x: float | None, y: float | None, orientation: float | None, robot_id: int = 0) -> VisionRobotData:
+    return VisionRobotData(id=robot_id, x=x, y=y, orientation=orientation)
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilter – construction guards
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterInit:
+    def test_default_construction(self):
+        kf = KalmanFilter()
+        assert kf.id == 0
+
+    def test_custom_id(self):
+        kf = KalmanFilter(id=3)
+        assert kf.id == 3
+
+    def test_zero_noise_xy_raises(self):
+        with pytest.raises(AssertionError):
+            KalmanFilter(noise_xy_sd=0)
+
+    def test_negative_noise_xy_raises(self):
+        with pytest.raises(AssertionError):
+            KalmanFilter(noise_xy_sd=-0.5)
+
+    def test_zero_noise_th_raises(self):
+        with pytest.raises(AssertionError):
+            KalmanFilter(noise_th_sd_deg=0)
+
+    def test_negative_noise_th_raises(self):
+        with pytest.raises(AssertionError):
+            KalmanFilter(noise_th_sd_deg=-1)
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilter – _step_xy
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterStepXY:
+    def _make_last_frame(self, robot: Robot) -> dict[int, Robot]:
+        return {robot.id: robot}
+
+    def test_returns_tuple_of_two_floats(self):
+        kf = KalmanFilter()
+        robot = make_robot(x=1.0, y=2.0)
+        result = kf._step_xy((1.0, 2.0), robot, time_elapsed=0.1)
+        assert isinstance(result, tuple) and len(result) == 2
+
+    def test_initialises_state_on_first_call(self):
+        kf = KalmanFilter()
+        assert kf.state_xy is None
+        robot = make_robot(x=3.0, y=4.0)
+        kf._step_xy((3.0, 4.0), robot, time_elapsed=0.1)
+        assert kf.state_xy is not None
+
+    def test_exact_repeated_measurement_converges(self):
+        """After many steps with zero velocity and the same measurement the filter should
+        converge very close to the true position."""
+        kf = KalmanFilter(noise_xy_sd=0.01)
+        robot = make_robot(x=2.0, y=5.0)
+        for _ in range(50):
+            result = kf._step_xy((2.0, 5.0), robot, time_elapsed=0.1)
+        assert abs(result[0] - 2.0) < 1e-3
+        assert abs(result[1] - 5.0) < 1e-3
+
+    def test_output_between_prediction_and_measurement(self):
+        """When prediction and measurement differ, filtered output must lie strictly
+        between them (weighted blend)."""
+        kf = KalmanFilter()
+        robot = make_robot(x=0.0, y=0.0)
+        # Initialise filter state
+        kf._step_xy((0.0, 0.0), robot, time_elapsed=0.1)
+
+        # Now send a measurement far from the prediction
+        robot_stationary = make_robot(x=0.0, y=0.0, vx=0.0, vy=0.0)
+        result = kf._step_xy((3.0, 3.0), robot_stationary, time_elapsed=0.1)
+        # Should be pulled toward measurement but not all the way
+        assert 0.0 < result[0] < 3.0 + 1e-9
+        assert 0.0 < result[1] < 3.0 + 1e-9
+
+    def test_vanished_frame_uses_velocity_prediction(self):
+        """Consecutive vanished steps must each advance position by exactly v * dt."""
+        kf = KalmanFilter()
+        vx, vy = 1.0, 0.5
+        robot = make_robot(x=0.0, y=0.0, vx=vx, vy=vy)
+        kf._step_xy(None, robot, time_elapsed=0.1)  # init (no Kalman update)
+
+        dt = 0.1
+        result1 = kf._step_xy(None, robot, time_elapsed=dt)
+        result2 = kf._step_xy(None, robot, time_elapsed=dt)
+        # Each vanished step should advance by v * dt
+        assert abs((result2[0] - result1[0]) - vx * dt) < 1e-6
+        assert abs((result2[1] - result1[1]) - vy * dt) < 1e-6
+
+    def test_state_advances_with_velocity_over_multiple_vanished_steps(self):
+        kf = KalmanFilter()
+        vx = 2.0
+        robot = make_robot(x=0.0, y=0.0, vx=vx, vy=0.0)
+        kf._step_xy((0.0, 0.0), robot, time_elapsed=0.1)
+
+        dt = 0.1
+        steps = 5
+        for _ in range(steps):
+            result = kf._step_xy(None, robot, time_elapsed=dt)
+
+        # After n vanished steps starting from 0 the position grows monotonically
+        assert result[0] > 0.0
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilter – _step_th
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterStepTH:
+    def test_returns_float(self):
+        kf = KalmanFilter()
+        result = kf._step_th(0.5, last_th=0.0)
+        assert isinstance(result, float)
+
+    def test_initialises_state_on_first_call(self):
+        kf = KalmanFilter()
+        assert kf.state_th is None
+        kf._step_th(1.0, last_th=1.0)
+        assert kf.state_th is not None
+
+    def test_exact_repeated_measurement_converges(self):
+        kf = KalmanFilter(noise_th_sd_deg=5)
+        th = math.pi / 4
+        for _ in range(50):
+            result = kf._step_th(th, last_th=th)
+        assert abs(result - th) < 1e-3
+
+    def test_vanished_frame_preserves_state(self):
+        kf = KalmanFilter()
+        kf._step_th(1.0, last_th=1.0)  # init
+        state_before = kf.state_th
+        kf._step_th(None, last_th=1.0)
+        assert kf.state_th == state_before
+
+    def test_output_wrapped_to_minus_pi_plus_pi(self):
+        kf = KalmanFilter()
+        # Initialise near +π
+        kf._step_th(math.pi - 0.1, last_th=math.pi - 0.1)
+        # Measurement just past +π (wraps to ≈ -π)
+        result = kf._step_th(-math.pi + 0.1, last_th=math.pi)
+        assert -math.pi <= result <= math.pi
+
+    def test_circular_average_across_pi_boundary(self):
+        """Averaging π-0.1 and -π+0.1 should stay near ±π, not collapse to 0."""
+        kf = KalmanFilter()
+        th1 = math.pi - 0.1
+        th2 = -math.pi + 0.1
+        kf._step_th(th1, last_th=th1)
+        result = kf._step_th(th2, last_th=th1)
+        # Result must be close to ±π, not near 0
+        assert abs(result) > math.pi / 2
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilter – filter_data (public API)
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterFilterData:
+    def _last_frame(self, robot: Robot) -> dict[int, Robot]:
+        return {robot.id: robot}
+
+    def test_returns_vision_robot_data(self):
+        kf = KalmanFilter()
+        robot = make_robot()
+        result = kf.filter_data(make_vision(1.0, 2.0, 0.5), self._last_frame(robot)[robot.id], 0.1)
+        assert isinstance(result, VisionRobotData)
+
+    def test_id_preserved(self):
+        kf = KalmanFilter(id=2)
+        robot = Robot(
+            id=2,
+            is_friendly=True,
+            has_ball=False,
+            p=Vector2D(0, 0),
+            v=Vector2D(0, 0),
+            a=Vector2D(0, 0),
+            orientation=0.0,
+        )
+        result = kf.filter_data(make_vision(1.0, 2.0, 0.3, robot_id=2), robot, 0.1)
+        assert result.id == 2
+
+    def test_valid_data_returns_finite_values(self):
+        kf = KalmanFilter()
+        robot = make_robot(x=0.0, y=0.0)
+        result = kf.filter_data(make_vision(1.0, 1.0, 0.2), self._last_frame(robot)[robot.id], 0.1)
+        assert math.isfinite(result.x)
+        assert math.isfinite(result.y)
+        assert math.isfinite(result.orientation)
+
+    def test_vanished_data_returns_finite_values(self):
+        kf = KalmanFilter()
+        robot = make_robot(x=1.0, y=1.0)
+        # First call to initialise
+        kf.filter_data(make_vision(1.0, 1.0, 0.0), self._last_frame(robot)[robot.id], 0.1)
+        # Second call with vanished data
+        result = kf.filter_data(None, self._last_frame(robot)[robot.id], 0.1)
+        assert math.isfinite(result.x)
+        assert math.isfinite(result.y)
+        assert math.isfinite(result.orientation)
+
+    def test_convergence_with_repeated_measurement(self):
+        kf = KalmanFilter()
+        robot = make_robot(x=5.0, y=3.0)
+        for _ in range(50):
+            result = kf.filter_data(make_vision(5.0, 3.0, 1.0), self._last_frame(robot)[robot.id], 0.1)
+        assert abs(result.x - 5.0) < 1e-3
+        assert abs(result.y - 3.0) < 1e-3
+        assert abs(result.orientation - 1.0) < 1e-2
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilterBall – construction guards
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterBallInit:
+    def test_default_construction(self):
+        kf = KalmanFilterBall()
+        assert kf.state is None
+
+    def test_zero_noise_raises(self):
+        with pytest.raises(AssertionError):
+            KalmanFilterBall(noise_sd=0)
+
+    def test_negative_noise_raises(self):
+        with pytest.raises(AssertionError):
+            KalmanFilterBall(noise_sd=-1)
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilterBall – _step
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterBallStep:
+    def test_returns_tuple_of_three_floats(self):
+        kf = KalmanFilterBall()
+        ball = make_ball()
+        result = kf._step((0.0, 0.0, 0.0), ball, time_elapsed=0.1)
+        assert isinstance(result, tuple) and len(result) == 3
+
+    def test_initialises_state_on_first_call(self):
+        kf = KalmanFilterBall()
+        assert kf.state is None
+        kf._step((1.0, 2.0, 0.0), make_ball(1.0, 2.0), time_elapsed=0.1)
+        assert kf.state is not None
+
+    def test_exact_repeated_measurement_converges(self):
+        kf = KalmanFilterBall(noise_sd=0.01)
+        ball = make_ball(x=1.0, y=-2.0, z=0.0)
+        for _ in range(50):
+            result = kf._step((1.0, -2.0, 0.0), ball, time_elapsed=0.1)
+        assert abs(result[0] - 1.0) < 1e-3
+        assert abs(result[1] - (-2.0)) < 1e-3
+        assert abs(result[2] - 0.0) < 1e-3
+
+    def test_vanished_frame_uses_velocity_prediction(self):
+        """Consecutive vanished steps must each advance position by exactly v * dt."""
+        kf = KalmanFilterBall()
+        vx, vy, vz = 1.0, 2.0, 0.5
+        ball = make_ball(x=0.0, y=0.0, z=0.0, vx=vx, vy=vy, vz=vz)
+        kf._step(None, ball, time_elapsed=0.1)  # init (no Kalman update)
+
+        dt = 0.1
+        result1 = kf._step(None, ball, time_elapsed=dt)
+        result2 = kf._step(None, ball, time_elapsed=dt)
+        # Each vanished step should advance by v * dt
+        assert abs((result2[0] - result1[0]) - vx * dt) < 1e-6
+        assert abs((result2[1] - result1[1]) - vy * dt) < 1e-6
+        assert abs((result2[2] - result1[2]) - vz * dt) < 1e-6
+
+    def test_output_between_prediction_and_measurement(self):
+        kf = KalmanFilterBall()
+        ball = make_ball()
+        kf._step((0.0, 0.0, 0.0), ball, time_elapsed=0.1)
+
+        stationary_ball = make_ball(x=0.0, y=0.0, z=0.0)
+        result = kf._step((4.0, 4.0, 1.0), stationary_ball, time_elapsed=0.1)
+        assert 0.0 < result[0] < 4.0 + 1e-9
+        assert 0.0 < result[1] < 4.0 + 1e-9
+
+
+# ---------------------------------------------------------------------------
+# KalmanFilterBall – filter_data (public API)
+# ---------------------------------------------------------------------------
+
+
+class TestKalmanFilterBallFilterData:
+    def test_returns_ball(self):
+        kf = KalmanFilterBall()
+        ball = make_ball(1.0, 2.0, 0.0)
+        result = kf.filter_data(ball, ball, time_elapsed=0.1)
+        assert isinstance(result, Ball)
+
+    def test_valid_data_returns_finite_position(self):
+        kf = KalmanFilterBall()
+        ball = make_ball(1.0, 2.0, 0.0)
+        result = kf.filter_data(ball, ball, time_elapsed=0.1)
+        assert math.isfinite(result.p.x)
+        assert math.isfinite(result.p.y)
+        assert math.isfinite(result.p.z)
+
+    def test_none_data_returns_finite_position(self):
+        """A None ball (not detected) should produce a predicted ball, not crash."""
+        kf = KalmanFilterBall()
+        last = make_ball(1.0, 1.0, 0.0)
+        kf.filter_data(last, last, time_elapsed=0.1)  # init
+        result = kf.filter_data(None, last, time_elapsed=0.1)
+        assert isinstance(result, Ball)
+        assert math.isfinite(result.p.x)
+        assert math.isfinite(result.p.y)
+        assert math.isfinite(result.p.z)
+
+    def test_none_data_velocity_zeroed(self):
+        """When the ball has vanished, velocity is set to zero in the returned Ball."""
+        kf = KalmanFilterBall()
+        last = make_ball(0.0, 0.0, 0.0)
+        kf.filter_data(last, last, time_elapsed=0.1)
+        result = kf.filter_data(None, last, time_elapsed=0.1)
+        assert result.v.x == 0.0
+        assert result.v.y == 0.0
+        assert result.v.z == 0.0
+
+    def test_velocity_passed_through_from_measurement(self):
+        """Velocity from a valid Ball measurement should be passed through unchanged."""
+        kf = KalmanFilterBall()
+        ball = make_ball(1.0, 2.0, 0.0, vx=3.0, vy=4.0, vz=0.5)
+        result = kf.filter_data(ball, ball, time_elapsed=0.1)
+        assert result.v.x == 3.0
+        assert result.v.y == 4.0
+        assert result.v.z == 0.5
+
+    def test_convergence_with_repeated_measurement(self):
+        kf = KalmanFilterBall(noise_sd=0.01)
+        ball = make_ball(x=3.0, y=-1.0, z=0.0)
+        for _ in range(50):
+            result = kf.filter_data(ball, ball, time_elapsed=0.1)
+        assert abs(result.p.x - 3.0) < 1e-3
+        assert abs(result.p.y - (-1.0)) < 1e-3
+        assert abs(result.p.z - 0.0) < 1e-3
+
+    def test_prediction_tracks_moving_ball_after_vanish(self):
+        """After the ball vanishes, successive None steps should accumulate displacement."""
+        kf = KalmanFilterBall()
+        vx = 1.0
+        ball = make_ball(x=0.0, y=0.0, z=0.0, vx=vx)
+        kf.filter_data(ball, ball, time_elapsed=0.1)  # init
+
+        dt = 0.1
+        steps = 5
+        prev_x = 0.0
+        for _ in range(steps):
+            result = kf.filter_data(None, ball, time_elapsed=dt)
+            assert result.p.x > prev_x
+            prev_x = result.p.x
+
+    def test_ball_covariance_shrinks_with_repeated_measurement(self):
+        """After many identical measurements, the covariance should shrink (filter gains confidence)."""
+        kf = KalmanFilterBall(noise_sd=0.001)
+        ball = make_ball(x=1.0, y=2.0)
+        initial_cov = kf.covariance_mat.copy()
+        for _ in range(50):
+            kf._step((1.0, 2.0, 0.0), ball, 0.1)
+
+        # Diagonal elements (variances) should shrink
+        assert np.all(np.diag(kf.covariance_mat) < np.diag(initial_cov))
+
+    def test_robot_xy_covariance_shrinks_with_repeated_measurement(self):
+        kf = KalmanFilter(id=1, noise_xy_sd=0.001, noise_th_sd_deg=5)
+
+        robot = make_robot(x=1.0, y=2.0, orientation=0.0)
+
+        # First call initializes state
+        kf._step_xy((1.0, 2.0), robot, time_elapsed=0.1)
+
+        initial_cov = kf.covariance_mat_xy.copy()
+
+        for _ in range(50):
+            kf._step_xy((1.0, 2.0), robot, time_elapsed=0.1)
+
+        assert np.all(np.diag(kf.covariance_mat_xy) < np.diag(initial_cov))