The Analysis of the Unobservable Criteria on the Single Platform Bearings-Only Target Tracking System

Bearings-only tracking (BOT) is considered to be observable if, and only if, the target motion parameter can be uniquely determined by noise-free bearings measurements. The unobservable phenomenon is probably caused by relative geometric position between an observer and a target. The unobservable properties for BOT are discussed based on the target and the observer traveling in a same plane with a constant velocity or a constant acceleration. By utilizing orthogonal vectors and characteristic of linear matrix equation, some unobservable criteria for BOT system are presented. It is shown that for a certain type of observer´s movement the estimation process remains unobservable, even if the target moves at a uniform acceleration. And farther, ratio of the acceleration relative between the target and the observer to the initial range may be solved for the BOT system. The results are valuable in avoiding unobservable for BOT problem when the trajectory of observer is perfectly formulated.