An Indirect Range-Doppler Algorithm for Multireceiver Synthetic Aperture Sonar Based on Lagrange Inversion Theorem

This paper presents a novel imaging algorithm which has the capacity of processing multireceiver synthetic aperture sonar (SAS) data based on Vu's spectrum. There are two important issues when developing the fast Fourier-based imaging algorithms. One is the point target reference spectrum (PTRS) with analytical expression in the 2-D frequency domain; the other is the space variance of the PTRS. Vu has solved the first issue based on the Lagrange inversion theorem. However, the second issue has not been solved yet. Our approach in this paper is to apply Vu's spectral result in an indirect range-Doppler (R-D) imaging algorithm. For each transmitter/receiver pair, the close-form azimuth modulation is derived first, and then, range/azimuth coupling can be obtained via the difference between the PTRS and the azimuth modulation. Unlike traditional R-D algorithm, which utilizes the interpolation operation to eliminate the range cell migration (RCM), the RCM correction (RCMC) in this paper is carried out through two steps, i.e., bulk RCMC and differential RCMC. Bulk RCMC accounts for the RCMC in one reference range. Differential RCMC accomplished with a range-dependent subblock postprocessing method is used to compensate for the space variant deviation phase error. Via the proposed method, the echoed signal corresponding to each transmitter/receiver pair is processed first. Following which, a high-resolution SAS complex image is obtained by coherent superposition of all the coarse subimages. Numerical simulations and real data processing results show that the proposed method has the similar focusing capabilities with the accurate back projection algorithm across the whole swath. Although the presented method has the disadvantage of latency, it is very easy to make a complete phase center approximation correction, allowing for the tandem nature of the collected data. Besides, the proposed algorithm can handle general case with explicit point of stationary phase (PSP) no matter how complicated the PSP is, and it is also suitable for the imagery of tandem synthetic aperture radar.