Observability Requirements for Three-Dimensional Tracking via Angle Measurements

Observability requirements previously established for bearings-only tracking in two dimensions are extended to a class of three-dimensional estimation algorithms capable of processing any pairwise combination of azimuth bearing, conical bearing, and depth/elevation angle measurements. Although these algorithms are intrinsically nonlinear, it is shown that they can be analyzed in a linear framework without sacrificing mathematical rigor. A simplified observability criterion, applicable to both autonomous and nonautonomous linear systems, is presented and utilized to specify conditions on own-ship motion which are both necessary and sufficient for a unique tracking solution. Further analysis reveals that observability dependence on own-ship maneuvers for the three-dimensional algorithms considered here parallels the concomitant two-dimensional requirements. An interesting difference, however, is that under certain conditions, a unique tracking solution can be obtained in three dimensions for unaccelerated own-ship motion.