# A Phase Bias Compensation Method for Anti-Interference Antenna Arrays in RTK Positioning
## 1 Introduction
[PERSON] proposed a distortion-less pseudo-code tracking space-time PI algorithm by keeping the coefficients of the temporal taps as real values and imposing constraints on the weights of the antenna array [20]. In addition, this algorithm was only applicable to pseudo-code ranging systems and was not applicable to carrier phase measurements. [PERSON] adopted a robust phase compensation technique to reduce the phase distortion. The proposed technique operates in real time and causes no processing delay while requiring only a minor modification to existing GNSS receivers [21]. Moreover, the method reduces the computational complexity. Nevertheless, the estimate uses an observation sequence with a window size of L, which will influence the estimation accuracy and the dynamic performance. In addition, the estimated phase bias is limited by the phase lock loop discriminator. If the phase bias is beyond the detection range of the discriminator, the phase bias cannot be accurately estimated [22]. [PERSON] adopted blind adaptive beamforming based on direction lock loop. These algorithms can achieve similar effects to the MVDR algorithm by using the direction of arrival (DOA) estimation method without prior information. However, their complex hardware implementation restricts their application [23]. In conclusion, those methods require complex hardware implementation, which limits their application in low-cost general array receivers. The comparison of phase bias compensation algorithms is shown in Table 2. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Reference** & **Algorithm** & **Advantages** & **Disadvantages** & **Applicable Scenarios** \\ \hline \multirow{4}{*}{[PERSON] U. S. [17]} & \multirow{2}{*}{\begin{tabular}{c} Adds FIR filters after \\ each antenna to adjust \\ frequency \\ characteristics \\ \end{tabular} } & \begin{tabular}{c} Effectively adjusts \\ signal frequency \\ characteristics and \\ suppresses \\ measurement errors \\ \end{tabular} & \begin{tabular}{c} Ignores engineering \\ complexity; lacks \\ real-world positioning \\ tests; has incomplete \\ bias compensation \\ system \\ \end{tabular} & \begin{tabular}{c} Theoretical \\ validation \\ scenarios \\ \end{tabular} \\ \cline{1-1}  & \multirow{2}{*}{\begin{tabular}{c} Andreas \\ array weights to reduce \\ measurement bias \\ \end{tabular} } & \begin{tabular}{c} Constrains space-time \\ array weights to reduce \\ measurement bias \\ \end{tabular} & \begin{tabular}{c} Effective compensation \\ for carrier phase bias; \\ meets high-precision \\ requirements \\ \end{tabular} & \begin{tabular}{c} High computational \\ load; costly engineering \\ implementation \\ \end{tabular} & \begin{tabular}{c} High-precision \\ static/low-speed \\ dynamic scenarios \\ \end{tabular} \\ \cline{1-1}  & \multirow{2}{*}{\begin{tabular}{c} Combines reference \\ signal steering vector \\ estimation with \\ PI/MVDR algorithms \\ \end{tabular} } & \begin{tabular}{c} Achieves \(\leq\) 5 mm \\ carrier phase bias; \\ compatible with \\ multiple algorithm \\ frameworks \\ \end{tabular} & \
\begin{tabular}{c} Complex hardware \\ implementation; alters \\ receiver structure; has \\ poor real-time \\ performance \\ \end{tabular} &
\begin{tabular}{c} Static/quasi-static \\ high-precision \\ scenarios \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The comparison of phase bias compensation algorithms. The paper proposes an adaptive zeroing algorithm to compensate for the phase bias caused by the anti-interference algorithm of RTK. The algorithm consists of two steps. First, we present a rough bias compensation method based on array weighted-coefficient conjugation. Second, we propose fine bias compensation for the anti-interference output signal. The rough phase compensation is designed based on the PI algorithm, thus eliminating the need to obtain the satellite signal direction and reducing algorithm complexity compared to traditional phase bias compensation algorithms.