## 2 Multipath Error Principle and Mitigation Methods
### Multipath Error Mitigation Methods
[27] proposed a narrow spatial correlator technique to suppress multipath effects from the perspective of the receiver hardware. By improving the hardware of the receiver, the effect of alleviating the multipath effect in the middle- and long-band delays is better, but it cannot effectively weaken the impact of the short-band delay. [PERSON] et al. [28] proposed a multipath mitigation algorithm based on the steepest descent method and designed a new ranging code tracking loop, which has the advantages of a lower computational load and does not require external assistance. This algorithm is computationally more efficient than narrow-pitch correlation techniques. Table 1 summarizes multipath mitigation methods based on the antenna and receiver. By improving the antenna and receiver, the reflected multipath signal from the surrounding environment cannot be completely shielded, and the suppression effect on the multipath effect is limited. The approach to mitigating multipath errors through software data processing encompasses four key aspects. The first aspect is the multipath suppression method based on a stochastic model. In the second aspect, to leverage the frequency domain characteristics of multipath errors, filtering methods such as Vondrak filtering, empirical mode decomposition (EMD), and wavelet analysis are employed to extract the multipath error time series. These time series are then used to establish a multipath error correction model for post-processing correction. In the third aspect, based on the time domain repetition characteristics of multipath errors, time domain multipath error modeling methods based on the coordinate domain and the observation value domain are developed. The principal methods include sidereal filtering and advanced sidereal filtering (ASF). The fourth aspect is the modeling method based on the repeatability of the multipath spatial domain. The main methods include the multipath spherical harmonic model, multipath stacking (MPS), \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type** & **Method** & **Year** & **Scholar** \\ \hline \multirow{4}{*}{Antenna method} & Choke ring technology & 1998 & [PERSON] [18] \\  & Compression wheel antenna technology & 2001 & [PERSON] [20] \\  & Dual-polarized antenna technique & 2010 & [PERSON] [22] \\  & Cross-plate reflection planes & 2013 & [PERSON] [23] \\  & Single orthogonal dual-polarized GNSS antenna & 2017 & [PERSON] [24] \\ \hline \multirow{4}{*}{Receiver method} & Narrow spatial correlator technique & 1992 & [PERSON] [27] \\  & Multipath elimination delay-locked loop technology & 2002 & [PERSON] [25] \\  & Group-delay multiple amplitude phase-locked loop technology & 2013 & [PERSON] [26] \\ \cline{1-1}  & New ranging code tracking loop & 2022 & [PERSON] [28] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: A summary of hardware methods. and multipath hemispherical map. In a static environment, based on the time-spatial domain repetition characteristics of multipath errors, sidereal filtering and hemisphere map model can generate a multipath correction model for real-time GNSS data processing.