Posterior Weights in Single-Target and Multitarget Gaussian Mixture Filters

This work advocates for computing weights using posterior estimates rather than priors because the posterior typically offers a more accurate representation of the system after incorporating the latest measurement data. Several posterior weight formulations are presented and applied to the Gaussian sum filter (GSF) for single-target filtering (STF) and the Gaussian mixture probability hypothesis density (GM-PHD) filter for multitarget filtering (MTF). Under linear Gaussian conditions, the presented weight formulations are shown to be equal to each other and to the exact Bayesian weights. For nonlinear systems, however, all methods are approximate, and the various weight updates are neither equal to each other nor equal to the exact Bayesian weights. The results suggest that posterior weights improve filter accuracy and consistency for STF and improve multitarget accuracy for MTF, without considerable additional computational cost. Code: https://github.com/daltondurant/Posterior-Weights_GM-PHD.git .