Analysis of log-homotopy based particle flow filters

The state estimation plays an important role in analyzing many real world systems. Such systems can be classified into being linear or non-linear, and depending on the statistical properties of the inherent uncertainties as being Gaussian or non-Gaussian. Unlike linear Gaussian systems, a close form estimator does not exist for non-linear/non-Gaussian systems. Typical solutions like EKF/UKF can fail, whileMonte Carlo methods even though more accurate, are computationally expensive. Recently proposed log homotopy based particle flow filters, also known as Daum-Huang filters (DHF) provide an alternative way for non-linear, non-Gaussian state estimation. There have been a number of DHF derived, based on solutions of the homotopy flow equation. The performance of these new filters depends strongly on the implementation methodology. In this paper, we study a non-linear system, perturbed by Gaussian and non-Gaussian noises.We highlight the key factors affecting the DHF performance, and investigate them individually in detail. We then make recommendations based on our results. It is shown that a properly designed DHF can outperform a basic particle filter, with less execution time.