Optimal passive localization from a single sensor using multiple linear hypotheses

Target localization from bearing measurements at a single sensor is subject to significant nonlinearity losses. Modified polar coordinates minimize the losses due to linearization about a single solution hypothesis for an extended Kalman filter (EKF). However, even the minimal linearization losses become significant at very long range and low signal-to-noise ratio (SNR). A new Multiple Linear Hypothesis Estimator (MLHE) effectively eliminates the linearization loss. Multiple linear bearing/bearing rate estimators are propagated for a deterministic set of inverse range and normalized range rate hypotheses, chosen to span the region of possible a priori solutions. The linear estimation solutions provide a basis for recursively updating the a posteriori probabilities of the multiple hypotheses. The resulting two-dimensional probability surface in hypothesis space, together with the linear estimation solutions, provide a sufficient statistic for optimal estimation.