## 4 Establishing the Data Fusion Kalman Filter Equations
### Sports Vehicles Test Analysis  
In the car test discussed in this paper, the three SRINSs used employ laser gyroscopes and quartz flexible accelerometers. The parameters of the gyroscopes and accelerometers, as measured through laboratory static testing, are shown in Table 4 below:  
Three SRINSs were placed on an experiment vehicle. The installations of some instrumentation are shown in Figures 9 and 10. To better evaluate the navigation results after data filtering and fusion, we integrated a satellite navigation system. The position data measured by this equipment will not be used in the filtering and fusion calculation process. This position information is only used as a high-precision reference for calculating positioning errors. During the experiment, the data acquisition system continuously sent 1 PPS synchronization pulses to three RINSs and simultaneously collected raw gyroscope  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Item** & **SRINS1** & **SRINS2** & **SRINS3** \\ \hline Laser gyroscope bias & x-axis gyroscope & 0.0090\({}^{\circ}\)/h & 0.0084\({}^{\circ}\)/h & 0.0089\({}^{\circ}\)/h \\ Laser gyroscope bias & y-axis gyroscope & 0.0087\({}^{\circ}\)/h & 0.0086\({}^{\circ}\)/h & 0.0083\({}^{\circ}\)/h \\ stability (100-s smoothing) & z-axis gyroscope & 0.0081\({}^{\circ}\)/h & 0.0088\({}^{\circ}\)/h & 0.0074\({}^{\circ}\)/h \\ \hline Quartz flexible & x-axis accelerometer & 6.4591 ug & 8.3776 ug & 6.2241 ug \\ accelerometer bias stability & y-axis accelerometer & 9.3006 ug & 7.2004 ug & 6.2537 ug \\ (100-s smoothing) & z-axis accelerometer & 7.3542 ug & 6.4484 ug & 6.4292 ug \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of Laser Gyroscopes and Quartz Flexible Accelerometers.  
Figure 8: Structure Diagram of Data Acquisition Equipment.  
Figure 11: Route Map for the First Trial (location: Xiamen City, Fujian Province, China; starting point; latitude: 24.6120529175\({}^{\circ}\); starting point longitude: 118.0733718872\({}^{\circ}\); running time: approximately 2 h; and 13 min).  
Figure 12: Route Map for the Second Trial (Location: Xiamen City, Fujian Province, China; Starting Point Latitude: 24.6120529175\({}^{\circ}\); Starting Point Longitude: 118.0733718872\({}^{\circ}\); Running Time: approximately 3 h and 45 min).  
Figure 13: First Experiment Lever Arm Estimation Results.  
Figure 14: First Experiment Positioning Error.  
Figure 15: Second Experiment Lever Arm Estimation Results.  
Figure 16: Second Experiment Positioning Error.  
Table 5 shows the arm length estimation results of the two car tests. Due to the lack of precise distance measuring equipment, the actual distance between the SRINSs could not be measured, so the estimation error of the arm length cannot be accurately calculated. However, according to Table 5, the arm length estimation results of the two car tests differ by only a few centimeters, indicating high estimation accuracy. Based on the arm lengths obtained during the filtering process, the positions of multiple SRINSs can be constrained, thereby achieving a high-precision comprehensive position.  
Based on the position provided by GNSS, the position errors of three SRINSs during pure inertial navigation independently are compared with the position errors after applying the multi-inertial navigation data fusion method proposed in this paper, as shown in Figures 14 and 16. Table 6 shows the RMS values of the position error.  
From Table 6, it can be seen that the longitude error is reduced by approximately 8.4360%; the latitude error is reduced by approximately 6.9174%; and the overall positioning accuracy is improved by approximately 9.9492%. Therefore, the multi-INS data fusion method proposed in this paper can form a position reference, and the accuracy of this position reference is superior to the accuracy when the three sets of SRINSs perform navigation calculations independently.