## 4 Velocity Tracing Method for DVL Based on Motion Constraint  
### Analysis of the Relationship between the DVL Error and SINS Navigation Accuracy  
With the above integrated navigation scheme, the errors in DVL, MCP, and PS introduce estimation errors in both the subsystems and the main filter, and navigation errors of the estimation are fed-back to SINS. In SINS/DVL/MCP/PS, because there is no external position-aided information, the accuracy of the level position is mainly determined by the accuracy of DVL.  
In the integration of SINS/DVL, constant error in the aided velocity leads to constant error in the measurement vector through velocity matching. Moreover, the constant error in measurement vector leads to estimation error in the velocity, _i.e._, error in the SINS velocity. Then, the velocity error generates constant errors in misalignment and constant errors in attitude, which cause analytical errors in the specific force. With integration, errors in the specific force cause velocity and position errors. Due to the lack of aided position information, the position errors cannot be corrected.  
Due to the significantly negative role of the constant errors in DVL, they should be effectively compensated in engineering. For the specific working conditions shown in Figure 3, taking the work-mode against the seafloor of DVL as an example, the following scenarios exist: (1) when the AUV sails across the seafloor gully, the velocity from the DVL suddenly changes to zero because the distance between the AUV and the seafloor exceeds the measuring range; (2) when the AUV sails across a fish population, the velocity from DVL suddenly changes from the relative velocity between the AUV and the seafloor to that between the AUV and the fish. Unfortunately, these sudden changes cannot be predicted. As explained above, the sudden changes in DVL velocity cause position errors that cannot be corrected. How to judge and compensate these sudden changes plays an important role in increasing the positioning accuracy. In engineering, these sudden changes are considered as faults, and fault diagnosis based on \(\chi^{2}\) rules can be adopted to evaluate them. However, when these sudden changes are identified and isolated, finding a substitution to data fusion becomes a new problem.  
Figure 2: Federated data fusion of SINS/DVL/MCP/PS.  
Similarly to constant errors, random errors in DVL have also attracted significant attention. Several self-adaptive filters have been presented from the aspects of error parameter modeling. Optimal estimation can be obtained only when the model and statistical parameters are consistent with actual ones [3; 4; 5; 6; 12; 14]. However, how to restrain random noise with mathematical methods has received little attention. The random noise in DVL can be treated as a constant error lasting for a short time, which also introduces errors in the SINS attitude, velocity, and position. Due to the short duration, the random noise with positive and negative changes is smoothed with integrated operation; thus, the position error caused by random noise is small. However, the errors in attitude and velocity caused by DVL random noise cannot be smoothed. Therefore, the variances of the SINS attitude and the velocity errors are partly determined by the variances of the DVL random noise. When SINS/DVL acts as an attitude reference system, random noise in DVL decreases its accuracy.  
Similar analysis can be performed with MCP and PS. For the purposes of this paper, the constant errors in MCP and PS are assumed to be fully compensated, the random errors are well modeled, and the static parameters are effective.  
To solve the problems of sudden changes and random noise in DVL, a velocity tracing algorithm is proposed based on the moving characteristics of the AUV in the next section.