Spline filter for Nonlinear/Non-Gaussian Bayesian tracking

This paper presents a method for the realization of nonlinear/non-Gaussian Bayesian filtering based on spline interpolation. Sequential Monte Carlo (SMC) approaches are widely used in nonlinear/non-Gaussian Bayesian filtering in which the densities are approximated by taking discrete set of points in the state space. In contrast to the SMC methods, the proposed approach uses spline polynomial interpolation to approximate the probability densities as well as the likelihood functions. A good representation of the probability densities is an essential issue in the success of the filtering algorithm, especially in nonlinear filtering, since the probability densities in nonlinear filtering could be multi-modal. An advantage of the proposed approach is that it retains the accurate density information and thus a target probability at any region in the state space can easily be obtained by evaluating the integral of the polynomial. Further, the probability densities are represented with polynomials of fixed order and any further processing on probability densities could be performed with less computation. This paper uses the B-spline interpolation in order to maintain the positivity of probability density functions and likelihood functions. Simulation results are presented to compare the performance and computational cost of the proposed algorithm with an SMC method.