On filtering and smoothing algorithms for non-linear state estimation†

Abstract

This paper discusses a summary derivation of maximum a posteriori estimation for continuous and discrete non-linear systems. It is known that with Gaussian a priori statistics, the maximum a posteriori estimate is equivalent to an appropriate least squares fit. Filtering, fixed interval and fixed point smoothing algorithms for approximate non-linear estimation are obtained for the least squares eurve fit using ‘ running time ’ and ‘ fixed time ’ invariant embedding. Examples illustrating the use of the algorithms are presented.