Fixed-Interval Optimal Smoothing for Linear Impulsive Systems

Abstract

In this paper we study the fixed-interval optimal smoothing problems for a class of linear continuous-time systems with impulsive effects. We adopt a maximum likelihood (ML) approach and derive a maximum likelihood noncausal estimator on the fixed time interval. We derive an extension of the Fraser's algorithm for the linear discrete-time smoother to the impulsive systems utilizing the filtering theory of the impulsive systems.