航向已知条件下纯方位跟踪的可观测性

Observability for bearings-only tracking with known course

利用已知的目标航向可以提高纯方位跟踪系统的性能,其前提条件是系统可观测.为了得到可观测条件,详细推导了观测系统Gram矩阵行列式的解析表达式,证明了已知航向的纯方位跟踪系统可观测的充分必要条件是存在由3个方位与已知航向构成的可观测判别式不等于0,证明了系统不可观测的充分必要条件是存在等效的匀速直线运动观测器且它与目标轨线平行,所获得的系统可观测性判据具有表达形式简洁的特点.研究成果表明了利用已知的目标航向降低了纯方位跟踪系统观测器机动的要求,可应用于被动观测系统目标跟踪的理论与工程.

It is a prerequisite for improving the performance of bearings-only tracking(BOT)by applying known course that the system is observable.In order to attain the observable condition an analytic expression of the Gram matrix determinant for the system is deduced in detail.Then it is strictly proved that a BOT system with known course is observable if and only if there exists a nonzero observable discriminant which consists of three bearings and the known course.It is further shown that a BOT system with known course is unobservable if and only if there exists an equivalent observer motion trajectory with constant velocity and course which parallels to target.The attained observability criterion are characterized by their simple expressions.These conclusions indicate that the application of known course may reduce the need of observer maneuver for BOT and may be applicable to passive target tracking.