## 2 Multipath Error Principle and Mitigation Methods  
### Generation Principle of Multipath Errors  
During the propagation process of the GNSS satellite signal from the satellite to the receiver, the signal reflected by the reflector enters the receiver and interferes with the direct signal, causing the time and phase delays of the satellite signal, making the GNSS observation value deviate from the true value. The interference delay effect caused by the superposition and propagation of satellite signals from different paths is called multipath effect, and the deviation of the GNSS observation value caused by it is called multipath error. There are multipath effects from both the satellite side and the station side. The satellite-side pseudo-range multipath error mostly occurs in BeiDou inclined geosynchronous orbit (IGSO) and middle earth orbit (MEO) satellite pseudo-range observations, and is related to the satellite elevation and belongs to a special systematic error, which is not discussed in this article. The multipath error from the station side is affected by the surrounding environment of the station and cannot be eliminated using the double-difference method. Figure 1a is a schematic diagram of the multipath effect of horizontal ground signal reflection and Figure 1b is a schematic diagram of the multipath effect of vertical building signal reflection. There is a phase delay \(\theta\) between the reflected wave and the direct wave. In the case of horizontal ground signal reflection, \(\theta\) can be expressed as:  
\[\theta=\frac{4\pi H\sin z}{\lambda} \tag{1}\]  
where \(H\) is the height from the antenna to the ground, \(\lambda\) is the carrier wavelength, and \(z\) is the incident angle of the reflected signal. In the case of vertical building signal reflection, \(\theta\) can be expressed as:  
\[\theta=\frac{4\pi L\cos z}{\lambda} \tag{2}\]  
where \(L\) is the horizontal distance between the antenna and the building reflector. Figure 1: Two types of multipath effect schematic diagrams: (**a**) schematic diagram of the multipath effect of horizontal ground signal reflection; and (**b**) schematic diagram of the multipath effect of vertical building signal reflection. The multipath error in the carrier-phase measurement can be expressed as [14]:  
\[\varphi=\frac{\lambda}{2\pi}\arctan\frac{\alpha\sin\theta}{1+\alpha\cos\theta} \tag{3}\]  
where \(\alpha\) is the reflection coefficient of the reflector. According to the above formula, the size of the multipath error is affected by factors such as the reflection coefficient of the reflector, the incident angle of the reflected signal, and the spatial relationship between the reflector and the receiver. Since satellite signals are reflected by water bodies, trees, slopes, buildings, and other reflectors, the reflection coefficients are different, resulting in different multipath effects. The theoretical upper limit of the multipath error, denoted as \(\varphi\), is interconnected with \(\alpha\). In the case of horizontal ground reflection signals, when the incident angle and its rate of change are constant, the frequency of the multipath error is positively correlated with the receiver instrument height. In the case of vertical building reflection signals, when the incident angle and its rate of change are constant, the frequency of multipath errors is positively correlated with the horizontal distance from the instrument to the building. The multipath errors produced by carrier signals of different wavelengths are also different. Under conditions where the station receiver's position and its surrounding environment remain stable, with unaltered reflection coefficients and positional relationships between the reflector and the receiver, the incident angle of the reflected signal undergoes regular changes due to the periodic movement of the satellite in a fixed orbit. Due to the periodic repeatability of the GNSS satellite orbital motion, multipath errors have repetitive characteristics in the time domain and spatial domain.