Gauss–Newton filtering incorporating Levenberg–Marquardt methods for tracking

This paper shows that the Levenberg–Marquardt algorithms (LMA) can be merged into the Gauss–Newton filters (GNF) to track difficult, non-linear trajectories, with improved convergence. The GNF discussed first in this paper is an iterative filter, with memory that was introduced by Norman Morrison (1969) [1]. To improve the computation demands of the GNF, we adapted the GNF to a recursive version. The original GNF 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 (Marquardt, 1963 [2]). These optimisation techniques are iterative and guarantee local convergence.

► We showed that the Gauss–Newton filter (GNF) can be adapted to the Levenberg–Marquardt (LM) method.
► The recursive derivation of the filter shows its equivalence to the iterated extended Kalman filter.
► The recursive equations can also be adapted to the LM method.
► The filter memory and forgetting factor play important roles in the stability of the algorithms.