**7. Conclusions**

In this paper, we present a novel imaging algorithm for the multireceiver SAS based on the accurate time delay and numerical evaluation method. The presented method first deduces the PTRS and azimuth modulation using the numerical evaluation method. Then the difference between the PTRS and azimuth modulation denotes the coupling term. The key issue of the SAS imagery is the decoupling operation, which consists of two parts: the bulk and differential decoupling. The bulk decoupling mainly deals with the spatial invariance of the coupling term. Considering targets at reference range, the coupling is completely removed after this step. However, other targets suffer from the residual coupling error. The differential decoupling is carried out to solve this problem. Considering the spatial variance of the residual coupling error, the sub-block processing in range is exploited.

Based on the simulations, the focusing performance of the traditional method is greatly degraded at far range, as the residual error introduced by the stop-and-hop approximation increases with the range. Using the optimal width of the sub-block, the presented method achieves high performance results compared with traditional method.

**Author Contributions:** X.Z. and W.Y. carried out all of the analysis and algorithms and wrote the paper. C.T. designed part of experiments. All authors read and approved the final manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (61601473) and National Key Laboratory Foundation (9140C290401150C29132).

**Acknowledgments:** The authors would like to thank the anonymous reviewers and editors for their constructive comments and suggestions. Wei Chen offered advice on the language and revision.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

1. Williams, D.P. The Mondrian detection algorithm for sonar imagery. *IEEE Trans. Geosci. Remote Sens.* **2018**, *56*, 1091–1102. [CrossRef]


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