MATLAB Implementation of Particle Filter Algorithm

Particle filter is a nonlinear state estimation technique based on Monte Carlo methods, widely applied in target tracking, navigation, and signal processing. Implementing particle filter in MATLAB typically involves the following core steps:

Initialization Phase: First, determine the number of particles and randomly generate initial particle sets according to the prior distribution. In MATLAB code, this can be implemented using functions like randn() or mvnrnd() for Gaussian distributions. These particles represent hypotheses of possible system states.

Prediction Phase: Each particle undergoes state propagation based on the system model. This step simulates the evolution of system states over time, requiring consideration of process noise. In code implementation, this involves applying state transition equations to each particle, often using vectorized operations for efficiency.

Update Phase: When new observation data arrives, calculate the weight for each particle. The weight reflects how well the current observation supports the particle's state hypothesis, typically computed using the observation likelihood function. MATLAB implementation often uses probability density functions like normpdf() for Gaussian measurements.

Resampling Phase: This critical step prevents particle degeneracy through three main strategies: - Multinomial Resampling: Random sampling based on weight proportions - simple to implement using rand() and cumulative sum operations but may introduce high variance - Systematic Resampling: Deterministic sampling with fixed intervals reduces randomness using regular spacing algorithms - Residual Resampling: Combines deterministic and random sampling to balance computational efficiency and sampling quality, involving floor operations and additional random sampling

State Estimation: Finally, compute the system state estimate based on the particle set and their weights, typically using weighted average or maximum a posteriori probability methods. In MATLAB, this can be implemented with mean() or max() functions applied to weighted particles.

In practical applications, suitable resampling strategies should be selected based on specific problem characteristics. For example, systematic resampling may be chosen for high computational efficiency requirements, while residual resampling may be preferred for high precision scenarios. The performance of particle filters largely depends on the selection of particle quantity and resampling strategy, which requires tuning according to specific application contexts. Code optimization techniques like preallocation of arrays and parallel processing can significantly improve MATLAB implementation efficiency.