Some quick and efficient methods for bearing-only target motion analysis

Batch processing estimation methods for a target´s trajectory, assumed to be linear and uniform, based only on the observation of its bearings, are presented. First, the observer is assumed to have constant velocity, so that one can only estimate the target´s motion, up to a multiplicative constant. This motion is parameterized by three bearings at three judiciously chosen times, and some simple, quick, yet highly efficient estimators for them are proposed. The case of an observer moving nonuniformly is then considered. A quadratic estimator that is similar to the pseudolinear estimator but does not have bias is introduced. For the case in which the observer´s motion can be decomposed into a finite number of constant velocity segments, two sets of quasi-sufficient statistics that permit considerable saving in computation with no significant loss of efficiency are also introduced. Expressions for the covariance matrix of the estimators and for their Cramer-Rao bounds are provided