Analysis of Log-Homotopy Based Particle Flow Filters

摘要

The state estimation plays an important role in analyzing manyreal world systems. Such systems can be classified into being linearor non-linear, and depending on the statistical properties of theinherent uncertainties as being Gaussian or non-Gaussian. Unlikelinear Gaussian systems, a close form estimator does not exist fornon-linearon-Gaussian systems. Typical solutions like EKF/UKFcan fail, whileMonte Carlo methods even though more accurate, arecomputationally expensive. Recently proposed log homotopy basedparticle flow filters, also known as Daum-Huang filters (DHF) providean alternative way for non-linear, non-Gaussian state estimation.There have been a number of DHF derived, based on solutionsof the homotopy flow equation. The performance of these new filtersdepends strongly on the implementation methodology. In thispaper, we study a non-linear system, perturbed by Gaussian andnon-Gaussian noises.We highlight the key factors affecting the DHFperformance, and investigate them individually in detail. We thenmake recommendations based on our results. It is shown that aproperly designed DHF can outperform a basic particle filter, withless execution time.