## 1 Introduction  
Autonomous underwater vehicles (AUVs) are widely used for both military and civilian purposes, such as submarine resource investigation, surveying, and detection [1; 2; 3]. Because of the specificity of submarine conditions, especially the strong attenuation of the GNSS signals in the water of global navigation satellite system (GNSS), satellite-based technology is ineffective underwater; thus, high accurate positioning technology underwater becomes one of the key and difficult technologies of AUV [1; 2; 3]. The strapdown inertial navigation system (SINS) is self-directed, highly robust, has a high update frequency of enriched navigation data and small size, and is successfully used for AUV navigation [1; 2; 3; 4]. Due to the inherent errors in sensors and initial alignment errors, the errors of SINS navigation data are accumulated with time [3]. The error accumulation problem is the inherent and is a bottleneck problem of SINS based on integrated operation. To solve the error accumulation problem of SINS, external aided positioning data should be introduced to correct SINS regularly. The most commonly used submarine positioning methodsinclude GNSS, long/short baseline acoustic system (L/SBL), and geophysical field database (such as terrain and gravity). To access the GNSS data, the AUV should rise or sail near to the water surface because radio signals are easily damped and not feasible in deep water. At the same time, LBL and the geophysical database rely on the presence of a known transponder network or a known terrain, that is to say, there are preconditions to using these methods [5; 6; 7; 8]. Recently, with the development of acoustic velocity measuring technology, the measuring distance and accuracy of Doppler velocity log (DVL) have been improved significantly. Taking RDI WHN-600 as an example, the error of the velocity is within 0.2% and the maximum operating distance is 90 m with a working frequency of 600 kHz, whereas the error is 0.5% and the distance is 500-525 m with 150 kHz [5; 6]. Currently, DVL is widely used for AUV navigation and the integrated SINS/DVL has become a standard device for AUV [1; 2; 3; 5; 6]. When the integrated system of SINS/DVL is used in AUV, the level position accuracies, including the latitude and longitude, are mainly determined by the accuracy of the DVL velocity due to the lack of external position reference. Whereas the accuracy of DVL is fixed, the accuracy of SINS/DVL is mainly determined by the data fusion algorithm [1; 2; 3]. Numerous fusion algorithms for SINS/DVL are available in the literature, including non-linear filtering, online error calibration, and DVL-aided alignment [9; 10; 11; 12; 13; 14; 15]. In contrast to the above problems, this paper focuses on how to address the random and sudden noise in DVL. The velocity-matching mode is used in SINS/DVL [4; 5; 6; 10; 12]. With velocity matching, random noise in the level attitudes and velocities is introduced by the random noise in the DVL measurement, and sudden errors in level attitudes are generated by the sudden change in DVL. Errors in specific forces are generated, which will be accumulated as velocity and position errors with integrated operation [4]. To solve the random noise and sudden changes in DVL, in this paper, a constant velocity motion model is introduced to trace the measured velocity of the DVL based on the assumption of gentle motion of the AUV underwater, and a fault diagnosis method based on \(\chi^{2}\) rules is introduced to judge the sudden change from innovations [16; 17; 18; 19]. When sudden changes occur, the time update of velocity from tracing model is used to perform data fusion instead of the velocity from DVL. In the integration of SINS/DVL, due to the low observability of yaw misalignment caused by velocity matching, a magnetic compass (MCP) is always used to provide aided yaw information.