Spline Filter for Target Tracking

Abstract

<p>In this thesis an efficient approach to nonlinear non-Gaussian state estimation based on spline filtering is presented. The estimation of the conditional probability density of the unknown state can be ideally achieved through Bayes rule. However, the associated computational requirements make it impossible to implement this online filter in practice. In the general particle filtering problem, estimation accuracy increases with the number of particles at the expense of increased computational load. In this thesis, B-Spline interpolation is used to represent the density of the state pdf through a low order continuous polynomial. The motivation is to reduce the computational load and to improve accuracy. The motion of spline control points and corresponding coefficients is achieved through implementation of the Fokker-Planck equation, which describes the propagation of state probability density function between measurement instants. The solution of the Fokker Planck equation is achieved by calculating the state transition probability matrix. The state transition matrix is calculated using Dirac Feynman approximation. This filter is applicable for a general state estimation problem as no assumptions are made about the underlying probability density. Finally, simulation results are presented to demonstrate the effectiveness of the proposed algorithm.</p>