Improved extended Kalman filter design for passive tracking

Extended Kalman filters are here modified for coordinate estimation of a stationary object using bearing measurements taken from a moving platform. The modifications improve significantly the coordinate estimation on the initial period of data collection when otherwise the performance is far from optimal. The modifications are to the nonlinearities and could, in some instances, be implemented by the introduction of a time decreasing amplitude dither signal in the extended Kalman filter prior to the output nonlinearity. A bound on a Lyapunov function decay rate is also given which assists in the design of the modified nonlinearities and in the selection of an appropriate coordinate basis to be used in the extended Kalman filter.