MATLAB Implementation of Particle Filter Algorithm

Implementation logic of particle filter in MATLAB As a nonlinear system state estimation tool based on Monte Carlo methods, particle filters are commonly used in scenarios such as target tracking and robot localization. The core concept involves approximating probability distribution functions through a set of random samples (particles) and their corresponding weights. Below is an analysis of key implementation steps: Initialization Phase The system generates N particles according to the prior distribution, where each particle contains a state vector (e.g., target position, velocity) and an initial weight (typically set to 1/N). In image sequence processing, initial states may originate from manual annotation in the first frame or detector outputs. Code implementation would involve defining particle structures and distributing them across the state space. Prediction Phase (Importance Sampling) Each particle undergoes state prediction through motion models. For target tracking applications, a constant velocity model can be employed to update particle positions. Process noise is incorporated to simulate system uncertainties, where noise magnitude directly affects the dispersion degree of the particle swarm. Implementation requires coding kinematic equations with Gaussian noise addition using MATLAB's randn function. Weight Update Likelihood values for each particle are calculated based on observation data (e.g., image features). Common approaches include: - Color histogram similarity (suitable for targets with minimal appearance changes) - Edge feature matching (provides stronger robustness against deformation) After normalization, weights reflect the posterior probability relationship between particles and the true state. Implementation involves comparing observed features with particle-predicted features using distance metrics. Resampling To prevent particle degeneracy (where few particles dominate all weights), algorithms like roulette wheel selection eliminate low-weight particles while replicating high-weight ones. Adequate randomness must be maintained to avoid sample impoverishment. MATLAB implementation can utilize systematic resampling with cumsum and rand functions for efficient computation. State Estimation Final outputs typically use weighted averages (for continuous states) or the highest-weight particle (for discrete states). For image sequences, steps 2-4 are repeated frame-by-frame to achieve continuous tracking. Code implementation involves calculating weighted mean states or applying max function to weight arrays. Implementation Recommendations - Particle count selection should balance accuracy and computational overhead (typically 100-1000 particles) - Resampling strategy directly impacts algorithm stability - Visualization can plot particle swarm distributions overlaid on image sequences using scatter plots - During debugging, fix random seeds using rng for reproducibility This implementation can be extended to multi-target tracking by incorporating data association techniques like JPDA. Beginners are advised to start with single-target constant velocity scenarios before progressively increasing motion model complexity. MATLAB's object-oriented programming capabilities facilitate modular implementation of filter components.