# Research on the SSUKF Integrated Navigation Algorithm Based on Adaptive Factors
## 4 Simulation Experiment  
To validate the algorithm proposed in this paper, a trajectory is designed that includes various typical operating states, such as straight driving, acceleration, slow turns, sharp turns, and circular motion. The total duration of the trajectory is 1066 s, and the actual trajectory is shown in Figure 1's trajectory chart, with the starting point marked by a red star. To ensure comprehensive validation, the designed trajectory covers various commonnavigation scenarios. At 300 s, GNSS data is corrupted with a 10 s error and 2 times the measurement variance, and at 500 s, GNSS data is corrupted with a 50 s error and 3 times the measurement variance. This is intended to test the algorithm's robustness and accuracy in different dynamic environments. The algorithm in this paper uses the \"East-North-Up\" (ENU) coordinate system. The initial position is 39.96\({}^{\circ}\) (N), 116.35\({}^{\circ}\) (E), and 45 m; the initial pitch, roll, heading angles, and velocity are all 0. The inertial navigation data frequency is 100 Hz, and the GNSS observation frequency is 1 Hz. The initial three-dimensional position errors are 2 m, 2 m, and 5 m, and the three-dimensional attitude angle errors are [1\({}^{\circ}\), 1\({}^{\circ}\), 10\({}^{\circ}\)]. The three-dimensional velocity error is 0.1 m/s, and the GNSS measurement variance is [1, 1, 3]. The parameters of the inertial measurement unit are shown in Table 1.  
Under the same simulation conditions, the same set of IMU and GNSS simulation data are selected to perform simulations for the Unscented Kalman Filter (UKF), the Simplified Spherical Unscented Kalman Filter (SSUKF), and the Adaptive Simplified Spherical Unscented Kalman Filter (ASSUKF) proposed in this paper. The algorithms' running times are compared, and corresponding comparison curves of attitude error, velocity error, and position error are plotted. As can be seen from Figures 2-10, in terms of attitude, velocity, and position, ASSUKF exhibits smaller errors and more stable fluctuations, with overall performance superior to the other two methods. Different measurement errors were set at 300 s and 500 s, causing fluctuations at these specific time points for all three methods. Among them, the attitude error shows relatively minor fluctuations, while the three-axis velocity error fluctuates at 300 s and 500 s but gradually converges, with ASSUKF showing significantly smaller fluctuations and faster convergence. The larger fluctuations in velocity errors during the remaining time are due to filtering errors caused by the measurement data. From \begin{table}
\begin{tabular}{c c c} \hline
**Sensor** & **Bias** & **Random Walk** \\ \hline Gyroscope & 0.3\({}^{\circ}\)/h & 0.01\({}^{\circ}\)/\(\sqrt{\mathrm{h}}\) \\ Accelerometer & 100 \(\mathrm{\SIUnitSymbolMicro g}\) & 5 \(\mathrm{\SIUnitSymbolMicro g}\)/\(\sqrt{\mathrm{Hz}}\) \\ \hline \end{tabular}
\end{table} 
Table 1: Main sensor parameters. Figure 1: Trajectory chart. these points, it can also be observed that ASSUKF effectively identifies and corrects these errors, ensuring the accuracy of the filtering process. Similar fluctuations are seen in the position error, but ASSUKF provides a smoother result with smaller errors, indicating that ASSUKF can maintain stable estimation results in complex dynamic environments and significantly reduce the error magnitude. Compared to the standard UKF, ASSUKF demonstrates stronger adaptability and robustness. The standard UKF, due to its lack of noise estimation capability, cannot promptly and accurately perceive changes in GNSS measurement noise, leading to significant deviations in the filter's estimation results when such changes occur. In contrast, ASSUKF, by introducing an adaptive noise estimation mechanism, can continuously monitor and precisely estimate changes in GNSS measurement noise. The adaptive factor enables ASSUKF to dynamically adjust the noise covariance matrix based on real-time observational data, thereby better adapting to different noise environments.