# Radar Error Correction Method Based on Improved Sparrow Search Algorithm
## 1 Introduction  
Radar is the main means of the monitoring of and early warnings for non-cooperative targets at sea [1; 2]. The modern radar represented by phased arrays can detect and track multiple targets, such as ships, aircrafts, and missiles at the same time because of its fast beam control speed [3; 4]. However, due to the influence of mechanical structure deflection, installation platform tilt, the aging of internal electrical components, external electromagnetic interference, and other factors [5], radar measurements often have various forms of error (as shown in Figure 1), and the maximum error can even reach the magnitude of kilometers [6], therefore it is necessary to calibrate the radar regularly. In previous studies, radar observation errors were usually divided into random errors and systematic errors [7]. The random error can be eliminated using a filtering algorithm, and the impact on the subsequent measurement results is relatively small [8]. The systematic error is the fixed deviation generated by the characteristics of the radar system itself and the interaction with the external environment, which cannot be removed through the use of filtering, and needs to be estimated in advance to then be compensated for. This process is called radar calibration. Traditional land-based radar calibration usually uses fixed targets with known positions on the ground or establishes registration models, and solves them through measuring the same target in the common observation area of multiple radars [9; 10; 11; 12]. The calibration range of this method is limited, and it cannot be applied in the far sea area. To solve this problem, [PERSON] and [PERSON], respectively, proposed the idea of using AIS information to calibrate radars [13; 14]. However, this idea requires that the systematic error of the same radar is basically constant in a certain space-time range, and that the detection accuracy of the different targets is identical or similar. In this regard, references [8; 15; 16] analyzed a large number of measured data and found that the multi-target error samples in the radar coverage area were relatively concentrated, showing the characteristicsof correlation and normalizing distribution statistically; therefore, the systematic error could be regarded as a constant value within a certain time and region. The studies in references [17; 18] show that radar systematic errors are jointly determined by hardware design, manufacturing process, installation conditions, operation parameter setting, and environmental factors, while it does not depend on the specific attributes and states of the measured targets; that is, it will have a consistent impact on almost all targets' measurements. Therefore, it is feasible to use the self-reported position information of the moving target to carry out radar calibration. The method is favored by many experts and scholars because of its convenient and flexible selection of calibration sources and high positioning accuracy. Professor [PERSON]'s team took the AIS data as the true value in order to analyze the error distribution characteristics of the radar system, and they solved the problem of the low reliability of the error estimates under the assumption of uniform distribution through the use of the method of partition processing, but it did not establish a universal error model for the measured target, which was limited by the accumulation of error data in the database [15; 19; 20]. Considering that the error calibration of the three-coordinate radar needs to include three-dimensional position information, [PERSON] proposed a real-time radar error correction algorithm based on ADS-B data, derived the error observation model, and used Kalman filtering (KF) algorithm to solve it. It is more stable than the algorithm that uses the mean error as the systematic error to complete the calibration [21].