Optimal observer motion for bearings-only localization and tracking
This research examines the nonlinear tracking problem where a single moving observer passively monitors noisy bearings emitted from a source and processes this data to obtain estimates of source position and velocity. Specific optimal paths are derived for general scenarios characterized by the effective range-to-baseline ratio. Although the work addresses bearings-only estimation, the theoretical findings are applicable to a large class of optimization problems. This is illustrated by extending the analysis to include localization with a more general angle-of-arrival measurement.^ Observability requirements are the first consideration with regard to observer motion. A simplified criterion for establishing such requirements is presented. This criterion is then utilized to determine necessary and sufficient conditions for a unique tracking solution in a class of nonlinear problems involving both bearing and other angle-of-arrival measurements.^ Emphasis is then directed toward establishing a theoretical relationship between system observability, observer motion, and estimation accuracy. This is accomplished by analyzing properties of the error covariance matrix and Fisher Information matrix. The index of optimality is the Cramer Rao lower bound.^ As is common with nonlinear optimization problems, an explicit analytical solution for optimal observer motion is difficult to obtain. The formation of the estimation problems considered here leads to a cost function that is not amenable to conventional study. However, it is shown in this work how decomposition of the Fisher Information matrix leads to a numerical procedure that generates optimal (and suboptimal) observer motion comprised of a series of constant course trajectories. In the limit, these trajectories converge to the continuous solution. Observer trajectories are also derived analytically for bearings-only estimation by utilizing an alternative criterion. Optimality is defined here as those paths that maximize this criterion. The problem is solved within the context of classical control theory by invoking necessary conditions involving the Hamiltonian.^ The error ellipses associated with the trajectories are compared and analyzed. It is shown that observer motion involves a trade-off between increasing bearing-rate and decreasing range. Particular characteristics of an observer path and its effect on estimation accuracy depend on the range-to-baseline ratio of the scenario initially encountered. (Abstract shortened with permission of author.) ^
Sherry Elizabeth Hammel,
"Optimal observer motion for bearings-only localization and tracking"
Dissertations and Master's Theses (Campus Access).