SIR Particle Filter

When implementing SIR (Sampling Importance Resampling) Particle Filter, we select p(xk|xk-1) as the importance distribution. This distribution plays a crucial role in guiding the algorithm to achieve more accurate estimation and prediction of the target during iterative processing. In SIR particle filtering, p(xk|xk-1) is not merely a simple probability distribution - it incorporates both prior knowledge about the target state and comprehensive analysis of current observational data. From an implementation perspective, this importance distribution is typically implemented through a state transition function that models the system dynamics. In code, this might be represented as a function that propagates particles from time k-1 to time k based on the system model. The resampling step then eliminates particles with low importance weights while replicating those with higher weights. By appropriately selecting p(xk|xk-1), we can significantly enhance the algorithm's accuracy and robustness, making it better suited for handling complex target tracking problems. This selection directly affects the particle weighting calculation, where weights are updated using the likelihood function p(zk|xk) that evaluates how well particles match current observations.