# Precise Orbit Determination for GNSS Maneuvering Satellite with the Constraint of a Predicted Clock
## 1 Introduction  
A satellite in space tends to drift gradually from its designed orbit because of various perturbations. When the deviation from the designed orbit is larger than the tolerance, the satellite needs to be maneuvered correspondingly to keep its optimal orbit. Two kinds of maneuvers, i.e., in-plane maneuver and out-of-plane maneuver, are usually employed to maintain satellite orbits. An in-plane maneuver is generally implemented by a thrust force in the along-track direction, while the out-of-plane maneuver is applied in the cross-track direction [1; 2]. The maneuver frequency depends largely on orbit characteristics, especially the orbit period [3]. The American global positioning system (GPS) consists of 32 Median Earth orbit (MEO) satellites with a revolution period of half a sidereal day. With one satellite of Block III in checkout, there are 31 GPS satellites available ([[https://www.gps.gov/systems/gps/space/](https://www.gps.gov/systems/gps/space/)]([https://www.gps.gov/systems/gps/space/](https://www.gps.gov/systems/gps/space/))). Each GPS satellite has to be maneuvered about once a year to maintain a regular satellite constellation [4; 5]. The Chinese Beidou navigation satellite system (BDS) is rather sophisticated in that it includes five satellites in the geostationary orbit (GEO), five in the inclined geosynchronous orbit (IGSO) and four in the MEO. [PERSON] et al. showed that BDS GEO satellites needed east-west (along-track direction) station-keeping maneuvers every 25-35 days and north-south (cross-track direction) maneuvers about every 2 years [6]. [PERSON] et al. showed that the regular maneuver cycle of BDS IGSO satellites is about half a year [5]. Maneuver may reduce the availability of a global navigation satellite system (GNSS) and degrade the navigation and positioning performance. As early warning information, the approximate repositioning epochs of a maneuvering satellite are published in the notice advisory to navstar users (NANU) message ([[https://www.navcen.uscg.gov](https://www.navcen.uscg.gov)]([https://www.navcen.uscg.gov](https://www.navcen.uscg.gov))). In addition, this satellite is also flagged as unhealthy in the broadcast ephemeris. However, the published maneuvering epochs are so rough that many normal observations may be discarded. What is more, the unhealthy flags in the broadcast ephemeris are sometimes wrong or missing, which is unreliable and will mislead real-time users [7]. Consequently, some efforts have been made to detect satellite maneuvers. The classical maneuver detection strategy is based on the closest approach of two arcs calculated separately before and after the maneuvering, in which the instantaneous velocity change is determined as the difference between these two arcs at this point [4; 8]. This method is adopted by the Center for Orbit Determination in Europe (CODE) to generate the precise orbit products for the International GNSS Services (IGS). [PERSON] et al. detected BDS satellite maneuvers using the triple-differenced phase residuals from ground monitoring stations [9]. [PERSON] et al. and [PERSON] et al. have used the orbit mutual differences of broadcast ephemeris to detect BDS orbit anomalies and maneuvers [10; 11]. Furthermore, [PERSON] et al. proposed a robust maneuver detection method by using the code residuals from reference stations that can be used in real-time [7; 12]. In addition to maneuver detection, a maneuver handling operation is necessary to avoid orbit discontinuities or precision degradation during and around maneuvering periods, so that the rather precise orbit products are available. The common approach is introducing pseudo-stochastic parameters to model maneuvers in precise orbit determination (POD), e.g., instantaneous velocity changes at specific maneuvering epochs [13], piecewise constant accelerations over a processing interval [14] or piecewise linear and continuous accelerations at each epoch [15].