# Radar Error Correction Method Based on Improved Sparrow Search Algorithm
## 4 Simulation Verification and Analysis  
The radar error correction method based on the ISSA is simulated and verified. The estimation effect of the KF algorithm [21], GLS [22], SSA [32], and ISSA on the systematic error is analyzed and compared under the same conditions. With reference to the simulation model parameters in references [22; 41], the simulation conditions set in this paper are shown in Table 1. Assume that the radar is located at (68.923\({}^{\circ}\), \(-\)137.259\({}^{\circ}\), 51.856 m), the range systematic error \(\Delta\tau\) is 1300 m, the azimuth systematic error \(\Delta\theta\) is 0.498\({}^{\circ}\), the elevation systematic error \(\Delta\eta\) is 0.544\({}^{\circ}\), the measurement noise follows Gaussian distribution, and the communication delay of the GNSS is set to 1 s. The starting position of the reference source is (69.014\({}^{\circ}\), \(-\)136.754\({}^{\circ}\), 10,000 m), and the end position is (69.535\({}^{\circ}\), \(-\)135.219\({}^{\circ}\), 10,000 m). The radar local coordinate system is used as the reference coordinate system to model the motion of the reference source using Equation (31) as follows:  
\[ \begin{cases}x_{LR}(k)=300k+20000\\ y_{LR}(k)=300k+10000\\ z_{LR}(k)=10000\end{cases}  \tag{31}\]  
Figure 3: ISSA flowchart. Based on the derived radar measurement error model, the GLS algorithm, KF algorithm, SSA, and ISSA are used to estimate the radar systematic error, and the convergence results of 200 observation points are taken. Table 2 shows the RMSE and the average calculation time of 100 Monte Carlo simulations, conducted using four algorithms under the same conditions. Among them, the RMSE is calculated using Equation (32). \(M\) is the number of simulations. The average time is the time taken to estimate the radar systematic error under the software and hardware conditions of the current PC. \[\left\{ \begin{aligned} \text{RMSE}(\Delta\hat{\eta})& =\sqrt{\frac{1}{M}\sum\limits_{i=1}^{M}\left(\Delta\hat{\eta}-\Delta \eta\right)^{2}}\\ \text{RMSE}(\Delta\hat{\theta})&=\sqrt{\frac{1}{M} \sum\limits_{i=1}^{M}\left(\Delta\hat{\theta}-\Delta\theta\right)^{2}}\\ \text{RMSE}(\Delta\hat{\eta})&=\sqrt{\frac{1}{M} \sum\limits_{i=1}^{M}\left(\Delta\hat{\eta}-\Delta\eta\right)^{2}}\\ \text{RMSE}(\Delta\hat{t})&=\sqrt{\frac{1}{M} \sum\limits_{i=1}^{M}\left(\Delta\hat{t}-\Delta t\right)^{2}}\\ \end{aligned} \right. \tag{32}\]  
It can be seen from Table 2 that the ISSA is the most accurate estimation of the systematic error, followed by the SSA, while the KF and GLS algorithms have close estimation results and poor effects. When compared with the KF algorithm, GLS algorithm, and SSA, the ISSA has improved the accuracy of the range systematic error estimation by 62%, 61%, and 48%. In the accuracy of the azimuth systematic error estimation, the ISSA improves by 79%, 79%, and 65%, respectively. In terms of the accuracy of the elevation systematic error estimation, the ISSA has improved by 79%, 78%, and 60%. When compared with the other three algorithms, the ISSA improves the accuracy of the GNSS communication delay estimation by 49%, 48%, and 4%. It can be seen that the ISSA and SSA are more accurate than the KF and GLS algorithms in estimating the systematic error, mainly because the former does not need to linearize the nonlinear equations to avoid the loss of accuracy in the process. However, high computational complexity and long computational time are common problems of group optimization algorithms. The solving time of the ISSA is