  This paper presents a compact, recursive, non-linear, filter, derived from
the Gauss-Newton (GNF), which is an algorithm that is based on weighted least
squares and the Newton method of local linearisation. The recursive form
(RGNF), which is then adapted to the Levenberg-Maquardt method is applicable to
linear / nonlinear of process state models, coupled with the linear / nonlinear
observation schemes. Simulation studies have demonstrated the robustness of the
RGNF, and a large reduction in the amount of computational memory required,
identified in the past as a major limitation on the use of the GNF.
