基于纯角度量测的二维运动目标可观性判据

针对在二维空间作匀加速运动的目标,获得基于纯角度量测的目标运动状态可观测的数学判据.在求解数学判据的过程中,巧妙利用数学变换手段,将非线性角度观测方程转换成线性框架进行处理;利用满秩矩阵的一些特点,把高阶非线性微分方程转化成一阶线性微分方程组求解,获得了可观测性判据.并从本判据直接推出了关于二维空间匀速运动目标状态可观测性判据.

Observability Criterion for Two-Dimensional Targets in Motion Based on Bearing-Only Measurements

Considering a target traveling in constant acceleration in a 2 dimentional space, a mathematical observability criterion of the target states is established in this paper. In the course of obtaining the criterion, first, the non linear bearing measurement equation is changed into linear framework by subtly making use of some mathematical transformations. Next, a high order non linear differential equation is converted into a set of one order linear differential equations by utilizing some characteristics of the full rank matrix. The observability criterion given by some previous researchers for the target traveling in a 2 dimentional space with a constant velocity is directly deduced from the criterion presented in this paper.