MVDR Multi-Beam Azimuth-Delay- Doppler Three-Dimensional Deconvolution Filter And Algorithm

In spatial plane-wave processing, the interesting target parameter of active sonar are the horizontal azimuth. In spatial processing, the high-reliability and high-resolution estimation of target parameters requires the wave front design for the concentration of the array response function. Wave equation can explain the duality of space and time. The interesting target parameters of active sonar in time domain are target range and radial velocity, which, however, can't be observed directly but rather estimated through time-delay and Doppler. In order to achieve the high-reliability and high-resolution estimation of target distance and radial velocity, waveform design is required for the concentration of the ambiguity function in two-dimensional (2D) delay-Doppler plane. One-dimensional (1D) temporal signal utilizes the delay-Doppler 2D function to describe it's time and frequency joint characteristics. The 2D function, namely called ambiguity function characterizes matched filtering in essence.Detection is always together with estimation. In the Gaussian noise model, the optimum detector or estimator is called matched filter which is data correlator with copies. Temporal match includes time-delay matched filtering and delay-Doppler matched filtering. Spatial match includes plane-wave beamforming and matched-field processing in waveguide environment. In this paper, we joint the temporal match and spatial match. Because of space-time decomposability in the narrowband case, we can just do time processing after space processing to finish correlated processing of space-time. Spatial beamforming transforms the array element domain to beam domain, and multi-beam system is adopted which can observe all beams continuously and simultaneously. Minimum Variance Distortionless Response (MVDR) beamforming can suppress the interference to improve azimuth resolution. According to the space-time duality, MVDR azimuth-delay-Doppler 3D process in beam domain can also suppress the interference and improve the resolution of the three dimensions.The target parameter estimation from the observed signal is inverse problem which can be solved by match as a fitting method and deconvolution as a reverse method. In this paper, the main deconvolution algorithm is Richardson-Lucy (R-L) iterative deconvolution algorithm. The matched filtering of the spatial beamformer output and transmitted signal is blurred delay-Doppler 2D function, namely sample cross ambiguity function. The expectation of the sample cross ambiguity function can be modeled as the 2D convolution of the ambiguity function of the transmitted signal and the target reflectivity density function. The blurs introduced by transmitted signal are removed by 2D R-L iterative deconvolution of the expectation, and then the target reflectivity density function is reconstructed, and so sequentially a high-resolution estimation of multiple target parameters are obtained.The combination of 3D MVDR interference suppression and R-L iterative deconvolution builds MVDR multi-beam azimuth-delay-Doppler 3D deconvolution filtering system in the paper. Simulation results and experimental data processing results verify the effectiveness of the system.