Asymptotic Approximation of the First Two Statistical Moments of Some Projection Type Algorithm

Abstract

The problem of detection in passive sonar is one of the most popular in all underwater acoustics field and it remains the one of the most sparse. Since the early seventies adaptive algorithms received an attention, but due to great difficulties in their implementation in the modern sonar systems, interest has weakened over time. In addition to adaptive algorithms in passive sonar rarely appear quantitative probabilistic characteristics for complex tactical environment, which significantly complicates the solution of the detection problem using them. With the current understanding of the sound propagation dynamics in the water environment, namely the presence of the effects of multipath propagation and scattering, the algorithms working on the short sample for adaptation become the main interest. In this article we derive approximations for the first two moments of the most promising fast projection type algorithms, which is built on a short sample of the antenna array elements. The results of modeling represented as the dependences for different configurations of antenna arrays. A comparison of the results from the output signal to noise ratio on weak signals with a classic non-adaptive algorithm Bartlett was presented. We propose a method to eliminate the loss of weak sources detection by using the spectral decomposition of the matrix involved in the construction of the orthogonal projector.