# A Phase Bias Compensation Method for Anti-Interference Antenna Arrays in RTK Positioning
## 1 Introduction  
Real-time kinematic (RTK) positioning technology has been developed to address both errors in the global navigation satellite system (GNSS) positioning process, such as those caused by ionospheric and tropospheric delays, as well as atomic clock synchronization issues [1, 2]. This technology significantly enhances positioning accuracy by processing differential carrier phase observations between a reference station and a moving station in real time [3]. For unmanned aerial vehicles (UAVs), RTK positioning technology is particularly critical for applications requiring high precision, such as aerial mapping, precision agriculture, and autonomous navigation. However, the GNSS signals received by RTK systems are extremely weak, typically below \(-130\) dBm, making them highly susceptible to interference [4]. This underscores the importance of robust anti-interference solutions to ensure reliable and precise positioning for UAV operations in challenging conditions. In most cases, the noise power in GNSS signals is higher than the desired GNSS signal but lower than interference levels, posing a significant challenge for UAV operations that rely on precise positioning. Additionally, the direction of incoming satellite signals is often unknown to the GNSS receiver, further complicating the task of signal acquisition and interference mitigation [5]. Therefore, the primary challenge for GNSS receiver anti-interferencetechnology lies in suppressing interference signals while ensuring that the gain of the useful GNSS signal is not compromised. To address this optimization problem, researchers have proposed the power inversion (PI) criterion. This criterion requires minimizing the output signal power after processing by an anti-interference algorithm, effectively filtering out interference while preserving the integrity of the useful GNSS signals [6]. Due to its straightforward implementation and proven effectiveness in interference suppression, the PI criterion has become the most widely adopted approach in UAV GNSS systems [7]. Other advanced criteria, such as the minimum mean square error (MMSE) criterion, maximum signal-to-interference plus noise ratio (MSINR) criterion, and minimum variance distortionless response (MVDR) criterion, have also been developed to enhance antenna anti-interference capabilities [8; 9; 10]. A comparative analysis of these anti-interference criteria is presented in Table 1, highlighting their respective advantages and suitability for UAV applications in challenging environments. To address interference challenges in UAV operations, space array processing (SAP) and space-time array processing (STAP) have been developed based on established anti-interference criteria [11; 12]. These techniques utilize antenna arrays to generate adaptive weights through anti-interference algorithms, which are applied to incoming signals to reduce interference power. However, the inherent characteristics of phased-array antennas and the weighting effects of adaptive anti-interference algorithms can compromise signal integrity, introducing measurement biases that are particularly critical for high-precision positioning systems like RTK systems. These biases arise from factors such as mutual coupling between array elements [13], amplitude and phase deviations among array units [14], inconsistencies in array RF channels [15], and phase biases directly or indirectly introduced by anti-interference algorithms [16]. Unlike common errors, these biases cannot be easily eliminated, posing significant challenges for UAV applications requiring centimeter-level accuracy, such as precision agriculture, aerial surveying, and autonomous navigation. Addressing these biases is essential to ensure reliable and precise RTK positioning in interference-prone environments. To compensate for the deviations introduced by the anti-interference of array antennas, [PERSON].