What you see
- Dark cells are walls. Open cells are traversable.
- Yellow circle is Pacman; colored sprites are true ghost positions.
- The red heatmap shows belief over the ghost’s location (probability mass per cell).
Algorithms
- Exact: full probability table; Bayes update with observation then spread to neighbors.
- Particle: 1000 samples; weight by sensor (λ=0.2, noise±2), resample, then move (including stay).
Why beliefs differ from sprites
- Noisy distance fits many symmetric cells; belief can be multi‑modal.
- Strict sensors (small noise, larger λ) can collapse weights and trigger resets; more particles help.
Real‑world applications
- Robot localization and tracking (GPS/LiDAR/IMU).
- Autonomous driving and radar multi‑target tracking.
- SLAM and AR/VR head tracking.
- Signal processing and econometrics (state‑space inference).