Spline filter for multidimensional nonlinear/non-Gaussian Bayesian tracking
Kumaradevan Punithakumar, Mike McDonald, Thia Kirubarajan · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2008
This paper presents a novel continuous approximation approach to nonlinear/non-Gaussian Bayesian tracking. A good representation of the probability density and likelihood functions is essential for the effectiveness of nonlinear filtering algorithms since these functions could be multi-modal. The proposed approach uses B-spline interpolation to represent the density and likelihood functions and tensor product approaches to extend the filter to multidimensional case. The filter is applicable under most general circumstances since it does not make any assumption on the form of the underlying probability density. An advantage of the proposed method is that it retains accurate density information in a continuous low-order polynomial form and finding the target probability in any region of the state space is straightforward. Further processing based on probability density such as finding the higher order moments of the state estimates could also be performed with less computational power. Simulation results are presented to demonstrate the proposed algorithm.