Fundamental properties and performance of conventional bearings-only target motion analysis

This paper considers the problem of estimating the position and velocity of an object from noise corrupted bearing measurements obtained by a single moving observation platform. The process is inherently nonlinear and exhibits unusual observability properties that are geometry-dependent. A maximum likelihood estimate (MLE) of the target motion analysis solution is developed and its performance analyzed. A comparison is drawn between the MLE and two previously reported methods, a nonlinear modified-instrumental variable estimate (MIV) and the pseudo-linear estimate (PLE). Both the MIV and PLE are shown to derive from approximations to the nonlinear measurement equation and therefore share some common properties with the MLE. 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.