Robust sequential detection using acoustical arrays in undefined noise
Roger F. Dwyer · The Journal of the Acoustical Society of America · 1977
A technique is introduced which allows the design of a robust sequential detector in undefined noise based on quantiles. For each sampled output of M hydrophones, a set of m quantiles from the unknown noise field are estimated and used to partition the observation space into known probability regions which assure distribution-free performance. In addition, the effects of hydrophone noise variations and non-uniform spatial noise distributions are removed from degrading performance. It is assumed that the noise samples are both spatially and temporally independent and the signal is a plane wave arriving from a specific direction. Once the m quantiles are estimated a partitioned log likelihood ratio (PLLR) statistic is formed assuming a shift of scale alternative. The quantiles are estimated in real time using a stochastic approximation algorithm which allows the PLLR to adapt to slowly changing noise distributions in order to maintain its distribution-free performance. An efficiency measure for the sequential partition detector is calculated and it's shown to be bounded by Fisher's Information. The equations for the average sample number and operating characteristic function are given in terms of the number of quantiles estimated. For practical implementation, it is shown that only a small number of quantiles need be estimated to give high efficiency. For example, estimating only two quantiles gives an efficiency of 0.65 in Gaussian noise. Efficiencies as a function of m are given for Gaussian as well as non-Gaussian noise distributions. [Work supported by CNM.]