A novel robust filter called a Huber M-estimation delay Kalman filter is proposed for a strapdown inertial navigation system/ultra-short baseline (SINS/USBL) integrated navigation system to deal with time-varying delay in underwater acoustic communication and simultaneously cope with non-Gaussian noises induced by outliers. First, considering the influence of platform error angle, an SINS/USBL integrated navigation system is constructed and, according to the delay characteristics of USBL acoustic communication, a delay system model based on state inversion is derived to deal with the time-varying observations. Second, a linear recursive model based on the delay system model is constructed to update the posterior estimation and covariance matrix by combining it with Huber’s M-estimation theory whose performance has robustness when encountering outliers. Simultaneously, a fixed-point iteration method is introduced to obtain optimal estimation. The proposed algorithm not only solves the time-varying delay problem but also prevents outliers in the process and measurement noises. Simulation and experimental results verify that the proposed filter has improved accuracy and robustness compared with other existing filters.

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