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Analysis of log-homotopy based particle flow filters

: Altamash Khan, M.; Ulmke, Martin; Koch, Wolfgang

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Journal of Advances in Information Fusion : JAIF 12 (2017), No.1, pp.73-94
ISSN: 1557-6418
Journal Article, Electronic Publication
Fraunhofer FKIE ()

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.