Underwater segmented sparse decomposition ranging method

Sparse decomposition method can be used to reduce the noise and reconstruct the underwater echo submerged in strong background noise. But if the distance between sonar and underwater target is larger than the maximum detection range of a given dictionary, this target will not be detected. Besides, if the target is near the boundary of a given dictionary but in an off-grid situation, this target will be detected with some errors. Aiming to solve the two special situations mentioned above, this paper proposes a segmented sparse decomposition ranging method based on Chinese Remainder Theorem (CRT). Firstly, two dictionaries with the same range resolution but different detection ranges are built up by time shift of continuous waveform (CW) functions. Then, the echo signal is divided into two channels and segmented with two different time windows. Based on the two predefined dictionaries, the segmented echo signals are decomposed and the background noise is reduced. The relative distance of the underwater target is obtained by let the reconstructed signals through matching filter and find the peaks of the output. Finally, CRT is used to estimate the real distance of the target. Simulation results verify the validity of the proposed method. Its performance is superior to the traditional sparse decomposition method when the target is located beyond the detection range of a given dictionary or near the dictionary boundary but in an off-grid situation. Moreover, method in this paper requires less storage space for the dictionaries than the classical sparse method with the same range resolution.