Optimization of proposal distribution in particle filtering

This study introduces a novel filter, termed the high-order unscented particle filter (HUPF). Utilizing the HUKF, HUPF advances the sample particles toward regions of higher likelihood and consequently derives an improved importance proposal distribution, closely aligned with the posterior probability. Distinct from the unscented particle filter, HUPF implements the high-order unscented transform instead of the conventional second-order variant. Due to the superior accuracy of the HUKF over the standard UKF, HUPF not only selects particles more judiciously, enhancing particle utilization, but also more effectively manages the tail decay rate of the proposal distribution. This approach enables HUPF to closely approximate the optimal posterior probability under typical Gaussian conditions. The efficacy of this method is demonstrated through a bearing-only tracking model example.