Efficient Active Sonar Parameter Estimation Using Linear FM Signals via Hermite Decompositions

Signals with finite time support are frequently encountered in sonar and radar processing. It is usually necessary to have a compact description of these signals' shape and time evolution. For this purpose, the Hermite series expansion is used in this paper to approximate an arbitrary enveloped linear frequency modulated (LFM) signal. The Hermite basis functions are based on the product of Hermite polynomials and a Gaussian function. The analytical expressions for the Fourier transform of LFM Hermite functions have been developed in this paper. It is proposed to use the Fourier transform of LFM Hermite functions for efficient computation of the wideband cross-ambiguity function (WCAF) for target parameter estimation in active sonar processing. Efficient two-dimensional (2-D) search methods are also proposed in this paper to obtain parameters from the WCAF.