# Weak and Dynamic GNSS Signal Tracking Strategies for Flight Missions in the Space Service Volume
## 1 Introduction  
The demand for reducing the burden of ground TT&C (Tracking, Telemetry and Command) stations and surveying vessels stimulates the development of precise orbit and attitude determination using GNSS. On the other hand, to take full advantage of the service capacity of GNSS, more flight missions from different space agencies equipped with onboard GNSS receiving terminals will utilize satellite navigation when operating in the space service volume (SSV) [1]. Nevertheless, the volume covered from a height of 3000 km to 36,000 km is difficult for GNSS applications. It should be noted that the altitude of 3000 km is defined as the boundary of the terrestrial service volume (TSV) and SSV, but the altitude (>20,000 km) above the GPS constellation is the most challenging environment for satellite navigation. A research satellite of the Max-Planck Institut fur Extraterrestrische Physik, Equator-S, equipped with a dual antenna Motorola Viceroy receiver was launched in December 1997 into a geostationary transfer orbit (GTO) by the German Space Agency (DLR). Its in-orbit experiment proved the reception of GPS signals above the GPS orbit, at an altitude of 34,000 km, is possible [2], but the quality of the physical signals and the data contents were not good enough for spacecraft in-orbit navigation. The main problems of navigation above the GPS constellation concentrate on two aspects: (1) insufficient signal availability and poor dilution of precision (DOP); and (2) weak signal processing with high dynamic stress and poor ranging accuracy. Both of them degrade the robustness andreliability of GNSS space service. The first problem is mainly related to signal visibility, while the second one is related to signal power. For the state of the art, the former can be improved by an interoperable SSV based on the development of multi-GNSSs interoperability [3], and we specified the GNSS SSV characterization and service performance in terms of four GNSS constellations in our previous research publication [4], but for the second problem, the technical matters are definitely more complicated, which will be the discussion topics in this work. In normal conditions, the sensitivity of a GNSS receiver and its dynamic performance interact with each other. Fortunately, there are few terrestrial GNSS terminal manufactures that claim both high receiver sensitivity and desirable dynamic performance simultaneously. However, for SSV users, the situation is quite different; herein, the issue about how to process weak GNSS signals with high dynamic stress have to be dealt with. Comparatively, the carrier tracking loop is more likely to lose lock than the code tracking loop in weak-signal and high-dynamic environments. Thus, a third-order phase-locked loop (PLL) is taken as the receiver reference assumption model (RRAM) for space applications. According to automatic control principle [5], the third-order loop is only sensitive to jerk rather than velocity and acceleration. Although the jerk for non-maneuvering space vehicle is quite small, the jerk for orbital maneuvering mission can be as high as 4 g/s (g = 9.8 m/s\({}^{2}\) is the Earth's acceleration of gravity) or more. It means that the performance of the SSV RRAM should be analyzed quantitatively. In order to keep the third-order loop stable, the coherent integration time (CIT) and loop noise bandwidth (LNBW) are designed with upper limitation. By calculating the loop measurement errors caused by thermal noise and dynamic stress respectively, the maximal bearable jerk under different carrier-to-noise density ratio (C/N\({}_{0}\)) can be determined. Obviously, the loop of SSV RRAM is likely to lose its lock in harsh environments, for instance, when the C/N\({}_{0}\) is lower than 30 dB-Hz and the jerk is over 4 m/s\({}^{3}\) at the same time. Owing to this reason, an adaptive four-state Kalman filter (KF)-based algorithm is presented with the intention of maximizing the signal processing performance of closed loop (CL) form.