Particle Filter Simulation with Odometer Sensor Noise
Monte Carlo methods use random sampling to solve problems that are difficult to solve deterministically. In robotics, particle filters use thousands of random samples (particles) to estimate a robot's position when sensors provide noisy measurements.
1. Prediction: Move particles according to motion model (odometer)
2. Update: Reweight particles based on sensor measurements
3. Resample: Keep high-weight particles, discard low-weight ones
4. Estimate: Average of particles gives position estimate
Particles: More particles = better accuracy but slower computation
Odometer Noise: Real sensors have measurement uncertainty
Motion Distance: How far the robot moves between measurements
As we use more particles, our position estimate converges to the true position. This demonstrates how Monte Carlo methods reduce uncertainty through sampling.
The distribution of particle positions approximates a normal distribution around the true position, demonstrating the Central Limit Theorem in action.
Create N particles distributed randomly across the environment. Each particle represents a possible robot position hypothesis.
Move particles according to odometer measurements with added noise. This accounts for uncertainty in robot motion.
Reweight particles based on how well they match sensor measurements. Particles near the true position get higher weights.
Create new particle set by sampling from high-weight particles. This concentrates particles around the most likely positions.