Abstruct -This paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single m o h g observation platform. The process is inherently nonlinear and exbibits unusual obsenability properties that are geometrydependent. A maximum likelihood estimate W E ) of the target motion analysis solution is developed and its performance analyzed. A comparison is drawn between the lMLE and two previously reported methods, a nonlinear modified-instrumental variable estimate (MW) and the pseudolinear estimate (PIX). Both the MIV and PLE are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the -%LE. The limits on performance that can be expected from processing bearing data are detailed. Specifically, for long range-to-baseline geometries, approximate expressions for the Cramer-Rao bound are derived. Extension of the results to the practical filters approximately predicts numerically observed behavior.For less restrictive geometries, bounds are presented. Incorporation of a target speed constraint on the MLE results in a transition to a lower dimensional problem as noise level and range increases. Monte Carlo experimental results are presented and the improvements realized by the MLE techniques are evident.

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A structure is presented for passive estimation of range and bearing as well as velocity of a source from a linear array. It uses a quasi-optimal post processor of the time delays, which are obtained from a generalized correlator with finite observation time. The post processor ultimately maps the sequential time-delay observations onto invariant source trajectory parameters over which smoothing is performed to reduce, jointly, the variance and the bias in the estimate of the source kinematics. The present approach remains viable for moving sources at long ranges, off-broadside source directions and high time-delay variances. Analysis and simulation results are presented to justify its usefulness under the stated stringent conditions. Review of and comparison to existing approaches are made to highlight the viability of present approach in the estimation of source trajectory.