MATLAB Implementation of Particle Filter Algorithm

Particle Filter (PF) is a nonlinear filtering algorithm based on Monte Carlo sampling, particularly suitable for state estimation problems in complex systems. It approximates posterior probability distributions using a set of weighted random samples (particles), effectively handling non-Gaussian noise and nonlinear system models. Implementing particle filter in MATLAB typically involves these key steps: Initialization of Particle Swarm: Generate a set of random particles according to the prior distribution. Each particle represents a possible system state and is assigned equal initial weights. In MATLAB code, this can be implemented using random number generation functions like rand or randn to create initial particle states. Prediction Phase: Propagate each particle's state according to the system model (state equation), simulating potential states at the next time step. This process must account for system nonlinear dynamics and process noise. The implementation typically involves applying system transition equations to each particle, often using vectorized operations for efficiency. Weight Update: Calculate the likelihood probability for each particle using observation data (measurement equation) and update particle weights accordingly. Weights reflect how well the current observation data supports each particle's state. This is implemented by computing probability density functions based on measurement residuals, commonly using Gaussian probability density functions through normpdf or custom likelihood functions. Resampling: To prevent particle degeneracy (where few particles dominate the weights), resample particles proportionally to their weights, retaining high-weight particles while eliminating low-weight ones. This maintains particle diversity. MATLAB implementations often use systematic resampling algorithms or the resample function from toolboxes, which can be coded using cumulative sum operations and random threshold comparisons. State Estimation: Based on the resampled particle set, output the current system state through weighted averaging or maximum a posteriori estimation. The final state estimate is typically computed as the weighted mean of particle states using dot product operations between particle states and their normalized weights. The advantage of particle filters lies in their adaptability to strongly nonlinear and non-Gaussian scenarios, such as target tracking and robot localization. In MATLAB, these algorithms can be efficiently implemented using loop structures and random number generation functions (like randn), combined with visualization tools (like plot) to intuitively display particle distributions and state convergence processes. It's crucial to balance particle quantity and computational complexity: more particles yield higher accuracy but reduce real-time performance. Additionally, the choice of resampling strategy (such as systematic resampling or residual resampling) significantly impacts algorithm stability and efficiency. MATLAB implementations should include configurable parameters for particle count and resampling method selection to optimize performance for specific applications.