## 1 Introduction  
The Chinese TH-2 satellite formation is the second microwave interferometric surveying satellite system in the world after TanDEM-X [1]. It is composed of two almost identical satellites, namely TH-2A and TH-2B. The primary goal of TH-2 is to generate a high-accuracy and -resolution digital elevation model (DEM) of the Earth. It is similar to the TanDEM-X mission; the essential requirement for achieving the expected DEM is to achieve millimeter-level relative orbit of two formation-flying satellites [2]. In order to achieve high-precision precise relative orbit determination (PROD) results, both TH-2A and TH-2B satellites are equipped with the same global navigation satellite system (GNSS) receiver, which tracks BDS2 and GPS satellites simultaneously. The collected pseudo-range and carrier phase observations onboard are used for PROD. The receivers contain many key technologies such as GNSS observation pre-processing, empirical forces modeling, maneuver parameterization and fixing double differenced (DD) integer ambiguities [3; 4]. Research results show that relative orbit determination at the millimeter to sub-millimeter level can be achieved through carrier-phase differential GNSS (CDGNSS) observations [5; 6]. BDS3 is independently developed and operated by China [7; 8]. At present, the third- generation BDS (BDS3) provides global positioning, navigation and timing service. Centimeter-level precision orbits of Tianping-1B [9] and Loujia-1A [10] were obtained by using only BDS measurements. With the rapid development of navigation satellite systems [11], multi-GNSS has become a hot research issue. Multi-GNSS improves the satellite numbers and geometric strength, which could further improve the accuracy of the LEO orbits. [PERSON] et al. showed that when GPS was jointed with BDS, the global geometric dilution of precision (GDOP) was increased by 50% on the basis of GPS [12]. [PERSON] et al. studied precise point positioning (PPP) based on GPS and BDS; the results showed that the ambiguity fixing rate within 10 min for GPS was only 17.6%; however, adding inclined geosynchronous orbit (IGSO) satellites and medium Earth orbit (MEO) satellites, the percentage improved significantly to 42.8% [13]. [PERSON] et al. used the FengYun-3C onboard BDS and GPS data of 2013, 2015, and 2017 to solve the precise orbit determination (POD) of FengYun-3C; the results showed that, without GEO satellites, the accuracy of BDS + GPS POD was slightly better than that of GPS-only POD [14]. In the past, the GNSS receivers carried by the LEO formation flying satellites could not receive BDS signals; research in multi-GNSS PROD was based on simulation data. Simulation experiments were carried out by [PERSON] et al. to show that BDS2 can realize the PROD of LEO formation flying satellites in global and the accuracy of the Asia-Pacific region can reach 3.4 mm [15]. [PERSON] and [PERSON] showed that GPS + BDS was more conducive to real-time relative orbit determination than GPS-only or BDS-only [16]. [PERSON] et al. found that the influence of GEOs' meter-level ephemeris errors on PROD of short-range formations could be ignored [17]. TH-2 is the first satellite formation system, which tracks both GPS and BDS2 signals. These GPS and BDS2 observations allow us to evaluate the PROD performances based on multi-GNSS. It is also the first time BDS has been applied to PROD of LEO satellites formation. The GRACE mission is equipped with a K-band ranging system, which enables a direct evaluation of the baseline precision [18]. However, for TanDEM-X and TH-2, no independent measurement system will be available to validate the PROD results. Therefore, how to check the accuracy of PROD becomes a problem. [PERSON] et al. [19] and [PERSON] et al. [20] discussed the TanDEM-X mission by using the GRACE as a reference case to illustrate the processing concept and expected accuracy. [PERSON] et al.