Temporal integration for array processing

Abstract

This paper deals with the study of the performance of array processings in the presence of moving sources. A simplified model of the spatial frequencies of a moving source is derived for the first time. It allows one to obtain analytical formulation of the variance of the estimated source bearings and of the probability of detection. A major parameter for the optimization of the (classical) array processing performance is the optimal integration time. It is related to the cinematic parameters of the (moving) source and to the array length. It is thus shown that the gain in array performance expected by increasing the sensor number can be severly degraded by the source motions. This analysis stresses the importance of the use of a suitable integration time. Under very simple hypotheses (e.g., a unique source with known motion parameters) the optimal integration time (for classical criteria) can be analytically calculated. In the general case, i.e., multiple sources with unknown motion parameters, the analytical results cannot be strictly applied; however they are still relevant to a wide class of practical problems such as contact loss, source crossings, sources with partially known parameters, etc. For all these problems, the aim of this paper consists mainly in defining a general frame for incorporating the source motion into the calculation of the array processing performance and trying thus to optimize it.