Linear Filtering for a Class of Jump Processes Arising in Navigation Systems

Abstract

In this paper, the filtering problem for a class of jump processes with discrete observations is considered. Using a minimum variance approach, a linear recursive unbiased filter is obtained with the help of which the required estimate and the corresponding covariance can be determined. The proposed filter allows multiple jumps for the state process, thereby making the theory applicable to modern navigation problems (Omega and Loran-C receivers), where multiple jumps have been reported to be a common occurrence. Further, utilizing the filter equations, the question of continuous dependence of the filter on system parameters is studied. Finally, a numerical example based on a navigation system model is presented, to illustrate some of the results of this paper.