Abstract
The problem of detecting the onset of a signal impinging at an unknown angle on a sensor array is considered. An algorithm based on parallel CUSUM tests matched to each of a set of discrete beamforming angles is proposed. Analytical approximations are developed for the mean time between false alarms, and for the detection delay of this algorithm. Simulations are included to verify the results of this analysis.
Highlights
In this paper, we consider the problem of detecting, as soon as possible, a target that appears abruptly and at an unknown angle in a sensor array
We look at the mean time to a false alarm for each CUSUM test in the parallel algorithm
Given L and the requirement on the false alarm rate determined by the value of the exponent s0, we can obtain from (37) c = (1/s) log(1/(1−s))−1, the value of the bias term c that is needed to satisfy this requirement; and corresponding to that bias value, we can retrieve from Figure 5 the signal tonoise-ratio (SNR) value for which we can achieve mean detection delay performance equivalent to that of the optimal algorithm
Summary
We consider the problem of detecting, as soon as possible, a target that appears abruptly and at an unknown angle in a sensor array. For a fixed angle of incidence and known signal and noise distributions, this is a classical problem in statistical change detection, and can be solved, for example, by the Page’s CUSUM algorithm. Here we consider the situation in which the angle of incidence and the signal and noise statistics are unknown In this case, alternatives to the classic CUSUM must be considered, and a number of such methods have been developed for such problems [1, 2, 3, 4, 5].
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