# Radar Error Correction Method Based on Improved Sparrow Search Algorithm
## 2 Radar Measurement Error Model  
The key of radar calibration is to estimate the systematic error accurately. This paper deduces the radar observation error model from the radar calibration principle based on the cooperative target. The method of radar calibration, based on the cooperative target, consists of detecting the cooperative target, which is equipped with a global navigation satellite system (GNSS) and can transmit its position to us in real time through a data link (the cooperative targets mentioned above all refer to cooperative aircraft in this paper), and use it as the reference source. After the position data of the reference source measured by the GNSS are associated with the radar measurement data, time registration, and coordinate transformation, the difference between the two is used to estimate the radar systematic error, so as to achieve radar calibration. The basic principle is shown in Figure 2.  
The correlation between the GNSS and radar measurement data is the primary link of radar calibration, which can be realized by the nearest neighbor (NN) association algorithm [25], joint probability data association (JPDA) [26], and other algorithms. There are many relevant studies and the technology is relatively mature, so this paper will not go into detail. Through time registration, the GNSS information received can be extrapolated in order to keep time synchronization with the radar positioning data. However, there is a delay in data link communication, and the sending time of the GNSS positioning data is deviated from the radar measurement time (this deviation is referred to as the communication delay in the paper), during which the aircraft will still fly forward for a certain distance. Due to the high speed of the aircraft when moving, the position error caused by the communication delay cannot be ignored. The GNSS data transmission period of the cooperation target is set as \(T_{G}\), the radar measurement period as \(T_{R}\), the GNSS data transmission time is successively \(t_{1}^{G},t_{2}^{G}\ldots t_{N_{A}}^{G}\) the radar measurement time is \(t_{1}^{R},t_{2}^{R}\ldots t_{N_{R}}^{R}\), and the time deviation between  
Figure 2: Calibration principle of the radar system based on the cooperative target. the two is, in turn, \(\Delta t_{1}=t_{1}^{R}-t_{1}^{G}>0,\Delta t_{2}=t_{2}^{R}-t_{2}^{G}>0\ldots\Delta t _{n}=t_{n}^{R}-t_{n}^{G}>0\). The following relationships can be obtained:  
\[\Delta t_{2}+T_{G}=T_{R}+\Delta t_{1} \tag{1}\]  
Through smoothing and interpolation algorithms [27; 28], the position-sending period of the cooperative target is reconstructed so that \(T_{G}=T_{R}\), which can be obtained via \(\Delta t_{2}=\Delta t_{1}\triangleq\Delta t\); that is, the communication delay is a constant value \(\Delta t\). After estimating this value, the position deviation caused by the communication delay can be corrected via combining it with the aircraft speed. The cooperative target points obtained by the GNSS are represented by the longitude, latitude, and altitude in the WGS-84 coordinate system, while the radar measurement track is in the radar-centered polar coordinate system, and the two must be unified. Because the common least square method and Kalman filter are the linear estimation algorithms, they are transformed to the Cartesian coordinate system. In this paper, the Earth-centered, Earth-fixed (ECEF) coordinate system is used as a unified coordinate system, cooperative targets that can be self-located through the GNSS within the radar detection range are used as reference sources, and the positioning errors of the GNSS are ignored. The integrated error model of these radar is established considering the position deviation caused by the systematic error of range, azimuth and elevation, measurement noise, and communication delay. The position data sent by the cooperative target through the datalink are measured using the onboard GNSS.