Research on range observability of 2-dimensional motion target based-on bearing measurements of IR sensor

Considering the target traveling with a constant acceleration in the 2-dimentional space, a mathematical observability criterion of the target states is established in this paper. In the middle 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 convened into a set of one-order linear differential equations by utilizing some characteristics of the full-rank matrix. At the end of this paper, 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 by this paper.