EFFICIENT EVALUATION OF NARROW-BAND SPATIAL AMBIGUITY FUNCTIONS

The evaluation of spatial ambiguity functions is required for several acoustical signal processing applications including matched-field proc essing (MFP) and computing bounds on array localization error. In both of these applications, the ambiguity function is usually evaluated re peatedly over a region of interest for a specific acoustic array. When either the region or the array is large, computational efficiency is an issue. In this paper, two algorithms are presented for efficiently evaluating the spatial ambiguity function over weakly range-dependent regions utilizing an adiabatic normal mode signal model. The algorithm s are referred to as the direct method and the indirect method. The di rect method involves a recursive update in range of the so-called repl icant vector. The computational complexity of the direct method for ea ch range step is proportional to the product of the number of array se nsors and the number of modes. In contrast, the indirect method recurs ively updates the entire ambiguity function and has an incremental com putational complexity proportional to the number of modes squared. Thu s, for low-frequency operation with a large array, the indirect method is more efficient. Computational results are presented in which the r elative efficiency of the two algorithms is compared.