基于纯角度的三维运动目标可观性研究

本文针对在三维空间作匀加速运动的目标,推导出了基于纯角度测量的运动目标状态可观测的必要条件.在求解这一必要条件的过程中,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来进行处理;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来求解,获得了可观测性必要条件.另外根据此必要条件直接推出了前人所证明的关于三维空间匀速运动目标状态可观测性判据.

OBSERVABILITY CRITERIA BASED ON BEARING-ONLY MEASUREMENTS FOR THREE-DIMENSIONAL MOVING TARGETS

Based on the study on a target moving in a 3-dimentional space with constant acceleration, a necessary condition based on bearing-only measurements was deduced to assert the observability of the states for the moving target. In the course of obtaining this condition, the non-linear bearing measurement equation is first changed into a linear framework by subtly making use of some mathematical transformations; and then a high-order non-linear differential equation is recasted into a set of single order linear differential equations utilizing some characteristics of full-rank matrices. At the end of this paper, the observability criteria given by previous researchers for a target traveling in 3-dimentional space with a constant velocity is directly derived from the conditions presented in this paper.