A spline filter for multidimensional nonlinear state estimation

The problem of nonlinear/non-Gaussian filtering has generated significant interest in the literature. Sequential Monte Carlo (SMC)/Markov Chain Monte Carlo (MCMC) approaches are the most commonly used. The success of nonlinear/non-Gaussian filtering depends on the accurate representation of the pdf of the system state as well as the likelihood function. However, the commonly used Monte Carlo approaches only provide weighted samples at discrete points in the state space. In this paper, a comprehensive solution for nonlinear non-Gaussian state estimation that can provide a continuous estimate of the pdf of the system state is developed based on B-splines. This method is capable of modeling any arbitrary pdf of the system state. In addition, the developed B-spline filter is able to provide statistically the same estimation accuracy as the particle filter and without suffering from the degeneracy alike problem due to its continuous nature. Further, the spline filter is also able to handle systems with multiple models, which are justified through simulations.