# Radar Error Correction Method Based on Improved Sparrow Search Algorithm
## 4 Simulation Verification and Analysis
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Simulation Parameter** & **Symbol** & **Value** \\ \hline Radar geographic coordinates & \((L_{s},\lambda_{s},H_{s})\) & \((68.923^{\circ},-137.259^{\circ},51.856\text{ m})\) \\ Range systematic error & \(\Delta\tau\) & 1300 m \\ Azimuth systematic error & \(\Delta\theta\) & 0.498\({}^{\circ}\) \\ Elevation systematic error & \(\Delta\eta\) & 0.544\({}^{\circ}\) \\ Communication delay & \(\Delta t\) & 1 s \\ Measurement noise of range & \(nr_{m}\) & 80 m \\ Measurement noise of & \(n\theta_{m}\) & 0.2\({}^{\circ}\) \\ azimuth & \(n\eta_{m}\) & 0.2\({}^{\circ}\) \\ Measurement noise of & \(n\eta_{m}\) & 0.2\({}^{\circ}\) \\ elevation & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation conditions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Evaluation Index** & \multicolumn{4}{c}{**Error Estimation Algorithm**} \\ \cline{3-5}  & **KF** & **GLS** & **SSA** & **ISSA** \\ \hline \(\Delta\hat{\eta}\) (m) & RMSE & 204.49 & 198.62 & 148.11 & 77.44 \\ \(\Delta\hat{\theta}\) (\({}^{\circ}\)) & RMSE & 0.0364 & 0.0352 & 0.0216 & 0.0075 \\ \(\Delta\hat{\eta}\) (\({}^{\circ}\)) & RMSE & 0.0463 & 0.0450 & 0.0243 & 0.0098 \\ \(\Delta\hat{t}\) (s) & RMSE & 0.9195 & 0.8973 & 0.4844 & 0.4667 \\ \hline Average time consuming(s) & 0.0072 & 0.0111 & 0.8206 & 0.4687 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison of different algorithms. nearly half of that of the SSA, which indicates that the research in this paper reduces the computational complexity of the SSA, accelerates the algorithm convergence, and improves the real-time performance by integrating multiple strategies. Figure 4 shows the estimation effect of four algorithms on the radar systematic error when different measurement points are taken, showing the convergence of the algorithms. As can be seen from Figure 4, with the increase in measurement points, the accuracy of the systematic error estimation is gradually improved. Under the simulation conditions in this paper, the ISSA can use about 40 measurement points of the reference source target movement to converge the radar systematic error estimate to the true value, while the other three algorithms need more measurement values, which indicates the good convergence and solution accuracy of the ISSA. In addition, it can be seen from Figure 4a that the solution results of the SSA fluctuate greatly, which is most likely the result of the local optimal stagnation of the solution. In comparison, the fluctuation of the ISSA is small, indicating that the algorithm has a strong ability to jump out of the local optimal and that the solution results are more stable. The estimated value of the systematic error was used to correct the radar observation results, and the target track comparison before and after correction was shown in Figure 5.  
Figure 4: The RMSE of the radar systematic error estimation under different measurement points. (**a**) Range systematic error; (**b**) Azimuth systematic error; (**c**) Elevation systematic error; (**d**) Communication delay. Obviously, the corrected radar measurement track is closer to the real track, but, due to the existence of measurement noise, there is still a certain difference between the radar observation track and the real track, which can be reduced through subsequent data processing (filtering, etc.). Figure 6 compares the radar observation errors before and after correction in the _xyz_ triaxial direction. Here, 200 radar measurement values are taken along the triaxial direction, and the RMSE before and after correction is calculated as follows: the _x_-axis direction decreases from 1037.1 m before correction to 172.2 m after correction. The _y_-axis direction decreased from 1044.4 m before correction to 235.2 m; the _z_-axis direction decreased from 995.1 m to 222.5 m. It can be further calculated that the measurement accuracy of the corrected radar along the _xyz_ axis is improved by 83%, 77%, and 78%, respectively.