MATLAB Implementation of Particle Filter for Target Tracking

This article explores the operational principles of particle filtering algorithms and their application in target tracking systems. Particle filters serve as powerful tools for state estimation and Bayesian filtering, particularly effective for handling nonlinear and non-Gaussian state-space models. The algorithm operates on Monte Carlo simulation principles, representing probability density functions through a set of random samples called particles. The implementation involves systematic weighting and resampling techniques to predict and refine target states through sequential importance sampling. In MATLAB implementation, key functions typically include: - Particle initialization using `randn` or specific distribution functions - Importance sampling through `systematic_resample` custom functions - State prediction via numerical integration of system dynamics equations - Weight update mechanisms incorporating measurement likelihood calculations The state equation (system dynamics) and measurement equation (observation model) form the core mathematical framework. The state equation, often implemented as a function handle or separate m-file, propagates particle states through time using differential or difference equations. The measurement equation, typically incorporating sensor characteristics and noise models, calculates likelihood weights for each particle. These equations integrate into the particle filter through prediction-correction cycles, where: 1. Prediction step propagates particles using state transition models 2. Correction step updates weights based on measurement innovations 3. Resampling prevents degeneracy using stratified or multinomial methods The MATLAB code structure generally follows: - Initialization of particle swarm and parameters - Main loop implementing prediction, update, and resampling stages - Estimation output through weighted average or MAP approaches - Performance evaluation using RMSE or consistency metrics This integrated approach enables accurate target tracking by combining Bayesian inference with numerical approximation techniques, making particle filters particularly valuable for challenging tracking scenarios with nonlinearities and multimodal distributions.