Simple expressions of CEP and covariance matrix for localization using LOB measurements for circular trajectory

Abstract

In this paper, a passive localization of an emitter using bearing measurements named Brown algorithm is considered. We derived simple and intuitive expressions of the covariance matrix of the estimate and the CEP (Circular Error Probable) when the distances between the emitter and the moving sensor locations are constant. By using the derived explicit expressions, we propose how to get an insight on the dependence of the CEP on the various parameters such as measurement interval and a speed of sensor. From the derived expression, it is quite easy to see how the CEP changes with respect to some parameters. Intuitively, we can see that the CEP value can become very large when the parameters such as a sampling interval and a speed of the moving sensor are around some specific values. We derive closed-form expressions of the parameter values for the smallest CEP and the very large CEP.