Add GPU MegaParticles LSH neighbor index demo

[rsasaki0109]

Summary

MegaParticles-style relocalization with an explicit p-stable LSH neighbor index, replacing the fixed-grid neighbor stand-in of the earlier gpu_megaparticles_stein_mcl demo. The grid was a single axis-aligned partition, so particles near a cell boundary never aggregated with their true neighbors one cell over. This demo uses the actual Datar et al. (2004) p-stable LSH scheme: L=8 independent hash tables, each formed from K=3 random Gaussian projections of the 4-D pose feature (x, y, s·cos θ, s·sin θ) quantised at bin width r. Two particles are neighbors if they collide in at least one table; the random offsets and multiple tables recover the cross-boundary neighbors the grid misses.

Both filter paths are identical except for the neighbor structure — one million globally-distributed particles, the same range-field likelihood, the same Gauss-Newton-like per-particle step, the same posterior smoothing, the same shared coarse-grid representative-state readout, and the same hidden-kidnap blackout. The only independent variable is grid-neighbor vs LSH-neighbor aggregation, so the reported neighbor recall and post-kidnap RMSE isolate the contribution of the explicit LSH index.

Neighbor recall is measured directly: on a sampled particle pool, brute-force kNN within a fixed feature radius defines the ground-truth neighbor set, and each method is scored by the fraction of true neighbors it recovers (same-grid-cell vs collide-in-any-LSH-table).

Results

Metric	Fixed grid	Explicit LSH
Neighbor recall vs brute-force kNN	58.2%	87.8%
Post-kidnap RMSE	0.099 m	0.088 m
Reacquisition after blackout	0 frames	0 frames
Avg GPU step	4.9 ms	9.6 ms

The LSH index recovers ~30 points more of the true neighbor set (the multi-table OR overcomes the single grid's boundary misses), with comparable-to-slightly-better relocalization, at ~2× the per-step cost from the 8-table OR atomics — an honest trade the demo reports rather than hides.

Test plan

• cmake .. && make gpu_megaparticles_lsh -j$(nproc) builds clean
• ./bin/gpu_megaparticles_lsh runs end-to-end, writes the GIF
• neighbor recall 58.2% → 87.8%, post-kidnap RMSE 0.099 → 0.088 m
• git diff --check clean (no whitespace errors)
• GIF ≤ 3 MB (1.5 MB), deployed to gh-pages, URL returns HTTP 200