# A Phase Bias Compensation Method for Anti-Interference Antenna Arrays in RTK Positioning
## 1 Introduction
[PERSON] adjusted the frequency characteristics of the signal by adding a finite impulse response (FIR) filter after each antenna element and suppressed measurement errors in the antenna array by trying to adjust the filter coefficients [17]. However, since the complexity  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criteria** & **PI** & **MMSE** & **MSINR** & **MVDR** \\ \hline \hline Cost Function & \( \begin{cases}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{s}=1\end{cases} \) & \(\min E[\mathbf{d}(n)-\mathbf{w}^{H}\mathbf{x}(n)]^{2}\) & \(\max_{\mathbf{w}^{H}\mathbf{R}_{x}\mathbf{w}}{\mathbf{w}^{H}\mathbf{R}_{(a)(i) +\mathbf{w}}}\) & \( \begin{cases}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases} \) \\ Optimal Weights & \(\mathbf{w}_{opt}\)=\(\frac{\mathbf{R}_{x}^{-1}\mathbf{s}}{\mathbf{s}^{H}\mathbf{R}_{x}^{-1}\mathbf{s}}\) & \(\mathbf{w}_{opt}=\mathbf{R}_{x}^{-1}\mathbf{r}_{xd}\) & \( \begin{cases}\mathbf{R}_{x}\mathbf{w}_{opt}=\\ \lambda_{\max}\mathbf{R}_{n+1}\mathbf{w}_{opt}\end{cases} \) & \(\mathbf{w}_{opt}=\frac{\mathbf{R}_{x}^{-1}\mathbf{a}(\theta_{0})}{\mathbf{a}( \theta_{0})^{H}\mathbf{R}_{x}^{-1}\mathbf{a}(\theta_{0})}\) \\ \multicolumn{2}{c}{Has simple} & Improves signal & Obtains the \\ Advantage & implementation and does not require the signal direction & reception accuracy & maximum signal-to-interference plus \\ & \(\begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases}\) & \( \begin{cases}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases} \) \\ \multicolumn{2}{c}{Has higher} & \(\begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases}\) \\ Disadvantage & requirements in some complex interference environments & \( \begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}_{opt}=\mathbf{R}_{x}^{-1}\mathbf{r}_{xd}\end{array} \) & \( \begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{array} \) \\ Computational & \( \begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{array} \) & \( \begin{cases}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases} \) \\ \multicolumn{2}{c}{Has higher} & \(\begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases}\) \\ \multicolumn{2}{c}{Has higher} & \(\begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{cases}\) \\ \multicolumn{2}{c}{Has higher} & \( \begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^{H}\mathbf{a}(\theta_{0})=1\end{array} \) \\ \multicolumn{2}{c}{Has higher} & \(\begin{array}{c}\min:P=\mathbf{w}^{H}\mathbf{R}_{xx}\mathbf{w}\\ \mathbf{w}^of actual engineering implementation was not taken into account and real positioning performance tests needed to be conducted, the measurement bias system needed to be improved. [PERSON] reduced the measurement bias introduced by the entire antenna array system by constraining the weights of the space-time array [18]. The simulation results indicate that this method has a good compensation effect on the carrier phase bias and meets the requirements of high-precision applications. However, the computational load is too large, and the cost in terms of engineering implementation remains too high. [PERSON] improved carrier phase estimation accuracy based on reference signal steering vector estimation combined with PI and MVDR algorithms [19]. The simulation experiments showed that a carrier phase bias of within 5 mm could be achieved. However, the hardware implementation was highly complex, significantly altered the existing receiver structure, and lacked real-time usability.