  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.
