二维单站纯方位运动目标跟踪的可观测性

Observability for Two-dimensional Single Observer Tracking Based on Bearing-only Measurements

利用量测目标方位序列求解目标运动参数的纯方位跟踪(BOT)系统会发生解的不惟一的问题,即不可观测性。针对二维空间单目标和单平台(观测器)情形,利用向量变换以及线性矩阵方程解的性质,对BOT的可观测性问题进行了讨论;给出了当目标匀加速直线运动下,观测器保持匀加速直线运动时BOT系统不存在惟一解的命题;同时给出当量测方位序列和采样时间满足一定的条件,系统可以求出目标某些运动参数比值的算法。进一步将结论推广到观测器和目标都作任意阶次时间序列机动的一般场合,推导出当观测器机动阶次不超过目标机动阶次下,系统不可观测的重要结论;向量法以及得出的结论为进一步分析观测器的机动策略具有重要的指导意义。

The problems of no unique solution for bearing-only target （BOT） locating and tracking come into existence sometimes, namely unobservable. By utilizing the method of vector transformation and characteristic of linear matrix equation, the problem of observability for BOT in noise-free bearing measurements from single observer was discussed based on the target and observer traveling in the 2-dimensional space. A proposition that BOT with constant acceleration remains unsolvable was presented and proved. By proving the proposition, it is also showed that some motion parameters ratios of target can be estimated under certain condition satisfied by measurement bearing sequence and time sample. When the proposition is extended to arbitrary rank of maneuver for the observer and the target, and the rank of target maneuver is higher than that of the observer maneuver, the important proposition, in which BOT remains unobservable property, was deduced. The vector method and the given proposition provide the guidelines for further analyzing the maneuver strategy of the observer.