Implementation of Particle Filter

Particle filtering is a nonlinear probability estimation technique based on Monte Carlo methods, widely applied in fields such as robot localization and target tracking. Implementing particle filtering in MATLAB involves several core stages that can be structured using specific functions and algorithms. During the initialization phase, the number of particles must be determined and the initial state distribution generated. Typically, normal or uniform distributions are used to create a weighted particle set, where each particle represents a possible state hypothesis. In code implementation, this can be achieved using functions like randn() for Gaussian distributions or rand() for uniform distributions to initialize particle states. The prediction stage propagates each particle's state according to the system model. Process noise is incorporated to simulate system uncertainties, with commonly used motion models including constant velocity models, acceleration models, and other nonlinear equations. In MATLAB, this step typically involves applying state transition equations to each particle while adding noise components using random number generators. The update phase integrates sensor measurement data into the filtering process. Particle weights are adjusted by calculating the likelihood between each particle and the observed data, typically using probability density functions such as Gaussian distributions to evaluate the matching degree. Implementation-wise, this involves computing measurement probabilities using functions like normpdf() and updating weights through element-wise operations. Resampling is a critical step to address particle degeneracy issues. When the effective particle count falls below a threshold, particles are resampled according to weight proportions, eliminating low-weight particles while replicating high-weight ones. Common resampling strategies include multinomial resampling and systematic resampling, which can be implemented using cumulative sum operations and systematic sampling algorithms. The system output typically uses weighted averages or maximum a posteriori probability to estimate the final state. In implementation, particle count selection requires balancing computational accuracy and efficiency, with optimal values recommended to be determined experimentally through performance analysis. The choice of resampling strategy significantly impacts algorithm performance, and different approaches may require testing with specific application scenarios. Code optimization should consider vectorization techniques for efficient weight calculations and state updates.