We derive a new algorithm for particle flow with non-zero diffusion corresponding to Bayes’ rule, and we report the results of Monte Carlo simulations which show that the new filter is an order of magnitude more accurate than the extended Kalman filter for a difficult nonlinear filter problem. Our new algorithm is simple and fast to compute, and it has an especially nice intuitive formula, which is the same as Newton’s method to solve the maximum likelihood estimation (MLE) problem (but for each particle rather than only the MLE), and it is also the same as the extended Kalman filter for the special case of Gaussian densities (but for each particle rather than just the point estimate). All of these particle flows apply to arbitrary multimodal densities with smooth nowhere vanishing non- Gaussian densities.

Date Published: 30 September 2013
PDF: 9 pages
Proc. SPIE 8857, Signal and Data Processing of Small Targets 2013, 88570A (30 September 2013); doi: 10.1117/12.2021370

Published in SPIE Proceedings Vol. 8857:
Signal and Data Processing of Small Targets 2013
Oliver E. Drummond; Richard D. Teichgraeber, Editor(s)