## 3 Signal Performance  
The pseudorange code bias found in BeiDou-2 signals has already been verified, analyzed, and corrected [4; 6; 21; 22]. The bias has been shown to be most probably caused by satellite components other than the receiver surroundings. Variations in the code observations were first detected using the multipath (MP) combination. This combination, which is both geometry-free and ionosphere-free, was presented by [PERSON] and [PERSON] [23] and applied in the TEQC tool. The combination is defined as:  
\[MP_{i}=P_{i}-\frac{f_{i}^{2}+f_{j}^{2}}{f_{i}^{2}-f_{j}^{2}}\lambda_{i}\varphi_ {i}+\frac{2f_{j}^{2}}{f_{i}^{2}-f_{j}^{2}}\lambda_{j}\varphi_{j}-B_{i},i\
eq j \tag{1}\]  
where \(f\) is frequency, \(P\) and \(\varphi\) represent the code range and carrier phase observables, respectively, and \(\lambda\) represents wavelength of carrier phase, whereas the subscripts \(i\) and \(j\) are used to denote different number of frequencies. The bias term \(B_{i}\) mainly contains the linear combination of the phase ambiguities and the constant part of the hardware delays. In general, the carrier phase MP is much lower than the pseudorange MP and can be neglected in the MP combination. If no cycle slip occurs during successive epochs, the bias \(B_{i}\) is assumed to be constant and should be replaced by the average MP. As GEOs remain nearly stationary relative to ground stations, and the surroundings of the stations also remain the same, the relation between elevation angle and MP is not analyzed in this paper. In addition, as only IGSOs and MEOs are presented in the BeiDou-3e constellation, we demonstrate the B1 frequency MP (MP1) and B3 frequency MP (MP3) characteristics for representative BeiDou-2 and BeiDou-3e satellites using the B1I and B3I signals of IGSOs and MEOs. The behavior of MP combinations for BeiDou and GPS satellites versus elevation is shown in Figure 2. In this paper, BeiDou-2 IGSO (PRN C10) and MEO (PRN C14), BeiDou-3e IGSO (PRN C31) and MEO (PRN C34), and GPS Block IIF (PRN G32) are selected as representative examples. Figure 1: Stations used for precise orbit determination (POD) of BeiDou satellites. The green diamonds represent iGMAS stations and the black circles represent GA tracking stations. The blue and red lines indicate the trajectories of the BeiDou-2 and BeiDou-3e satellites, respectively. The data shown in Figure 2 were collected from all the stations distributed in Asia-Pacific region, which is indicated in Figure 1. The blue and red dots correspond to the B1I and B3I frequencies, respectively. As mentioned in [6], the MP bias is satellite-induced and linearly dependent on the elevation of the satellite. As seen in Figure 2, the MP values for the BeiDou-2 satellites are not uniformly distributed near zero but display an obvious tendency with elevation from positive values (low elevation) to negative values (high elevation), in which the slope for the B1I signal is greater than that for the B3I signal, and the slope for MEOs is greater than that for IGSOs. This phenomenon is related to the BeiDou satellite types and can be clustered into IGSO and MEO groups, and the maximum bias in the B1I signal for MEOs is over 1 m, close to the zenith. For BeiDou-3e satellites, no obvious variations in signals as a function of elevation can be found. Obviously, the satellite-induced MP bias is almost eliminated, and the MP values for BeiDou-3e satellites fluctuate slightly to the same extent as those for GPS satellites. After detrending the MP series, the fluctuation in MP values for IGSOs is larger than that for MEOs. This may be related to the satellite altitude: IGSOs are in geosynchronous orbit at an altitude of 36,000 km, which is much higher than the orbit of MEOs (22,000 km), and the carrier-to-noise density ratio for IGSOs is lower than that for MEOs. Moreover, the MP for the B3I signal is smaller than that for the B1I signal and the noise in the B3I signal is also smaller than that in the B1I signal, which may be related to the precision of the code element.