The Recursive Bayesian Estimation Problem Via Orthogonal Expansions: An Error Bound

When solving the non linear non Gaussian filtering problem via orthognal series expansions the involved probability density functions are approximated with truncated series expansions. Inevitable the truncation introduces an error. In this paper an upper bound on the 1-norm of the approximation error in the probability density function of the state vector conditional on the system output measurements, due to the truncation, is derived and numerically evaluated in a simulation example. The bound quantifies the proximity of the obtained approximate solution to the true one. To explore the choice of orthonormal basis as a degree of freedom in the proposed method, a comparison between the Fourier and Legendre bases in a bearings-only tracking problem is performed.