Example of Auxiliary Particle Filter Implementation

In this article, we present an implementation example of the Auxiliary Particle Filter, originally introduced in Gordon's Tutorial on Particle Filters. The program successfully implements the auxiliary particle filter algorithm for this specific case, with RMS errors closely matching the results reported in the original paper. The auxiliary particle filter is a Bayesian filtering method based on Monte Carlo techniques, particularly effective for estimating nonlinear, non-Gaussian state-space models. In this implementation, particle weights are calculated based on their likelihood and prior probabilities, with key functions handling the auxiliary variable selection and systematic resampling. This approach finds applications in various fields including target tracking, object recognition, robotic navigation, and financial forecasting. The code structure follows the standard auxiliary particle filter workflow: prediction step, weight calculation using auxiliary variables, resampling, and update step.