Gauss-Newton Filtering incorporating Levenberg-Marquardt Methods for Radar Tracking

Abstract

This paper shows that the Levenberg-Marquardt Algorithms (LMA) algorithms can be merged into the Gauss Newton Filters (GNF) to track difficult, non-linear trajectories, without divergence. The GNF discusssed in this paper is an iterative filter with memory that was introduced by Norman Morrison [1]. The filter uses back propagation of the predicted state to compute the Jacobian matrix over the filter memory length. The LMA are optimisation techniques widely used for data fitting [2]. These optimisation techniques are iterative and guarantee local convergence. We also show through simulation studies that this filter performance is not affected by the process noise whose knowledge is central to the family of Kalman filters.