Delay-Doppler deconvolution image formation for multiple targets in waveguide environment

The ranges and radial velocities of targets are interesting parameters in the active sonar, which can't be observed directly but rather estimated. Firstly, by making use of the delay-Doppler model of multi-targets in waveguide multipath environment, one finds that sample cross-ambiguity function is a two-dimensional (2D) convolution of the autoambiguity function of the transmitted signal with the generalized target reflectivity density, which is a 2D convolution of the spread function of channel with the reflectivity density as well. Secondly, from the perspective of information theory, an iterative deconvolution algorithm named R-L (Richardson-Lucy) is derived based on minimum Csiszar discrimination criterion. Finally, the blurs caused by both of the transmitted signal and channel are removed by 2D deconvolution of the expectation of sample cross-ambiguity function, 2D image and then parameters of time-delay and Doppler is estimated sequentially. Results of both numerical simulation and sea experimental data processing verify the feasibility and effectiveness of R-L deconvolution algorithm with improving the resolution and accuracy of the estimations, when compared to the classical match filtering and Wiener filtering.