# A Phase Bias Compensation Method for Anti-Interference Antenna Arrays in RTK Positioning
## 4 Discussion  
In this section, we discuss the phase compensation performance based on the tracking process of the GNSS receiver. In Figure 11, we provide the carrier phase of the original satellite signal and the carrier phase after anti-interference algorithm processing. It can be observed that within one cycle, the phase bias from the original satellite signal is approximately 179.5\({}^{\circ}\). When the number of array elements is five or seven, the simulation results of the bias compensation method based on array weighted-coefficient conjugation are as follows. Figure 12a indicates the phase of the bias compensation method based on array weighted-coefficient conjugation when the number of antenna elements is five and Figure 12b indicates the phase bias compensation results when the number of antenna elements is seven. Only when the operating time is over 700 ms does the carrier phase approximate that of  
Figure 10: Anti-interference performance of bias compensation algorithm: (**a**) 7 elements; (**b**) 5 elements. the original desired signal. When the rough compensation can meet the phase measurement accuracy requirements, the user can adopt the results. However, when users have higher requirements for phase measurement accuracy and stability, they need to use fine compensation to increase the accuracy. In Figure 13, we provide the phase bias compensation results at the anti-interference output signal. The difference between the output signal and the original satellite signal is only 2\({}^{\circ}\). The simulation scenario of Figure 13 is established with the jammer-to-signal ratio (JSR) of 48 dB. Therefore, we analyze the effectiveness of the compensation algorithm at different JSR values. Simulation experiments are conducted with JSRs set to 51 dB and 54 dB. Figure 11: The carrier phase tracking results for antenna array. (**a**) The original phase of satellite signal. (**b**) The carrier phase after anti-interference algorithm processing. As shown in Figure 14a, with a JSR of 51 dB and a carrier-to-noise ratio (CNR) of 72 dB, the carrier phase of the original satellite signal is around 82\({}^{\circ}\), while the carrier phase of the output signal after anti-interference is approximately 91\({}^{\circ}\), introducing a deviation of about 9\({}^{\circ}\). After applying the compensation algorithm, the mean phase bias is reduced to 0.23\({}^{\circ}\), and the variance phase bias is 2.77\({}^{\circ}\). Figure 12: The phase of bias compensation method based on array weighted-coefficient conjugation: (a) 5 antenna elements; (b) 7 antenna elements. In Figure 14b, with a JSR of 54 dB, a CNR of 69 dB, and a jammer-to-noise ratio (JNR) of 50 dB, the situation is similar to that of a JSR of 51 dB. Anti-interference introduces a bias of 8.6\({}^{\circ}\), but the compensation algorithm can keep the mean phase bias within 0.04\({}^{\circ}\) and the variance phase bias within 2.41\({}^{\circ}\). In Figure 14c, with a JSR of 63 dB, CNR of 60 dB, and JNR of 50 dB, the compensation algorithm similarly achieves the desired compensation effect. After the phase bias compensation, the mean phase bias is reduced to 0.25\({}^{\circ}\), and the variance phase bias is 4.62\({}^{\circ}\). In Figure 14d, with a JSR of 73 dB, CNR of 50 dB, and JNR of 50 dB, it is impossible to achieve compensation with the anti-interference algorithm. Table 4 shows that the phase bias compensation consistently reduces the mean phase bias to near-zero levels across all JSR and CNR conditions, indicating effective compensation. However, the variance of phase bias generally increases after compensation, suggesting some variability in the compensation process, which may need further investigation or optimization. Moreover, with JSR increases and CNR decreases, the mean phase bias in the anti-interference stage increases, indicating higher interference levels. The compensation stage remains effective in reducing the mean phase bias, but the variance remains a concern.