Abstract: Considering a target traveling in constant acceleration in a 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 dimentional space with a constant velocity is directly deduced from the criterion presented in this paper.