Approximate and exact nonlinear target tracking based on MAP-estimation
Luca Livio Bagnaschi, STEPHAN HEPNER, Hans Peter Geering · Guidance, Navigation and Control Conference · 1990
In a recent paper an approximate maximum-a-posteriori probability (MAP) filter based on a local approximation of the conditional probability density has been proposed. It turns out that this filter is divergent when applied to the planar tracking problem. In this paper the mechanism of divergence of the approximate MAP-filter is analyzed. It is shown that the unstable behaviour is due to an inconsistency of the approximation that underlies the filter design. A modified version of the approximate MAP-filter is presented that is stable for the planar tracking problem. Subsequently the equations of the exact nonlinear MAP-estimator are derived and implemented. The exact filter provides useful reference results against which the approximate MAP-filters and a version of the extended Kalman filter are compared.