# Integrated Precise Orbit Determination of Multi-Gnss and Large LEO Constellations
## 1 Introduction  
The precise orbit and clock products of global navigation satellite system (GNSS) are of great importance for GNSS applications, such as precise point positioning (PPP), GNSS meteorology etc. Currently, the precise GNSS orbit and clock products provided by the international GNSS service (IGS) are generated from the global ground stations. Using ground observations, GPS and GLONASS orbits present a 1D accuracy which is better than 3 cm ([[http://www.igs.org/article/official-igs-citation-updated](http://www.igs.org/article/official-igs-citation-updated)]([http://www.igs.org/article/official-igs-citation-updated](http://www.igs.org/article/official-igs-citation-updated))). However, compared with GPS and GLONASS, the orbit accuracy of the new GNSS constellation (such as BDS) is relatively poor [1]. In the case of BDS constellation, this poor quality mainly results from: (1) special attitude control mode [2], (2) inaccurate solar radiation pressure (SRP) modeling [3; 4], (3) relatively few, unevenly distributed station networks, and (4) unfavorable geometry conditions [5]. In particular, the worst orbit accuracy of 3-4 m can be found for BDS GEO satellites because of their stationary characteristics [3; 6], which leads to a weak tracking geometry. Ideally, a globally well-distributed tracking station network is needed to ensure adequate observation strengths for all satellites at every epoch in the GNSS orbit determination. Meanwhile, relative motion between the satellite and ground stations is also necessary to yield a changeable tracking geometry. However, these conditions are not fully available for the BDS constellation due to the limited ground stations and special constellation design of the BDS. Fortunately, the weakness in observability and tracking geometry can be overcome by introducing low earth orbiters (LEO) as moving stations. LEO satellites have become a very important platform in earth observing and communication over the past two decades. Along with the proposing of many large LEO constellation projects, such as Iridium, SpaceX, OneWeb, and Hongyan etc., LEO satellites have been recently gaining widespread attention for the prospect of a LEO-augmented global navigation satellite systems (GNSSs). The constellation, with a large number of LEO satellites, is expected to enhance the positioning service of GNSS, notably reducing the long convergence time of the precise point positioning technique [7]. Many studies on the availability, design, and performance of LEO-augmented GNSS positioning have been conducted by many researchers [8; 9; 10; 11; 12; 13]. The aforementioned LEO constellations (such as Hongyan), which aim to provide augmented navigation services, usually carry a state-of-the-art GNSS receiver to obtain the precise knowledge of LEO orbits. These abundant onboard GNSS observations from hundreds (or even thousands) of LEO satellites can be used to improve the orbit accuracy of GNSS satellites through integrated processing with ground observations. The fast motion of LEO can greatly improve the observation geometry of GNSS satellites. Furthermore, the strong algebraic correlations between LEO orbit, GNSS orbits, and the ground reference frame will be introduced in the process of integrated POD. The integrated precise orbit determination (also called the one-step method) refers to simultaneously estimating the GNSS and LEO orbit parameters as well as other parameters (for example, earth rotation parameters, etc.) using the onboard and ground observations in one parameter estimation process. This method was first validated and investigated by [PERSON] et al. [14] using CHAMP and GRACE onboard GPS data. The integrated POD of GPS and LEO satellites have also been reported and analyzed in many other papers. [PERSON] and [PERSON] [15] developed a double-differenced, integrated algorithm based on CHAMP and Jason satellites. [PERSON] et al. [16] integrated GPS ground observations with CHAMP, GRACE, and SAC-C data to estimate the orbits and the Earth system parameters simultaneously.