Gauss-Newton filtering incorporating Levenberg-Marquardt methods for tracking

Authors:
Roaldje Nadjiasngar;Michael Inggs
Affiliations:
Department of Electrical Engineering, University of Cape Town, Private Bag, Rondebosch, Cape Town, South Africa;Department of Electrical Engineering, University of Cape Town, Private Bag, Rondebosch, Cape Town, South Africa
Venue:
Digital Signal Processing
Year:
2013

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Abstract

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.