Accurate orbit prediction (OP) of space debris is vital in Space Situation Awareness (SSA) related tasks, like space collision warnings. However, due to the sparse and low precision observations, unknown geometrical and physical features of debris, and effects of incomplete force models, OP based on the orbital mechanics theory or physics-based OP of space debris suffers from rapid error growth over a long duration, limiting the period of validity of debris OP for precise space applications. Considering that the tracking arcs of a debris object over a single station often share a similar temporal and spatial distribution in the inertial space, the resultant OP errors possibly have a coherent relationship with the temporal and spatial distribution of tracking arcs. This paper proposes a machine learning (ML)-based approach to model the underlying pattern of debris OP errors from historical observations and apply it to modify the future physics-based OP results. The approach includes three steps: constructing a historical OP error set, training a ML model to fit the historical OP error set, and correcting the future physics-based OP with ML-predicted orbital errors. The ensemble learning algorithm of boosting tree (BT) is studied as the primary ML method for the error modeling and predicting process. Experiments with three low-Earth-orbit (LEO) objects, tracked by a single radar station, demonstrate that the trained ML models can capture more than 80% of the underlying pattern of the historical OP errors. More importantly, the errors of physics-based OP over the future 7 days reduce from thousands of meters to hundreds or even tens of meters through the error correction with the learned error pattern, achieving at least 50% accuracy improvement. Such dramatic OP improvements show the promising potential of ML for enhanced SSA capability.

Satellite remote sensing systems require accurate, autonomous and real-time orbit determinations (RTOD) for geo-referencing. Onboard Global Positioning System (GPS) has widely been used to undertake such tasks. In this paper, a novel RTOD method achieving decimeter precision using GPS carrier phases, required by China’s HY2A and ZY3 missions, is presented. A key to the algorithm success is the introduction of a new parameter, termed pseudo-ambiguity. This parameter combines the phase ambiguity, the orbit, and clock offset errors of the GPS broadcast ephemeris together to absorb a large part of the combined error. Based on the analysis of the characteristics of the orbit and clock offset errors, the pseudo-ambiguity can be modeled as a random walk, and estimated in an extended Kalman filter. Experiments of processing real data from HY2A and ZY3, simulating onboard operational scenarios of these two missions, are performed using the developed software SATODS. Results have demonstrated that the position and velocity accuracy (3D RMS) of 0.2–0.4 m and 0.2–0.4 mm/s, respectively, are achieved using dual-frequency carrier phases for HY2A, and slightly worse results for ZY3. These results show it is feasible to obtain orbit accuracy at decimeter level of 3–5 dm for position and 0.3–0.5 mm/s for velocity with this RTOD method.

Achieving continuous and high-precision positioning services via smartphone under a Global Navigation Satellite System (GNSS)-degraded environment is urgently demanded by the mass market. In 2018, Xiaomi launched the world’s first dual-frequency GNSS smartphone, Xiaomi Mi 8. The newly added L5/E5 signals are more precise and less prone to distortions from multipath reflections. This paper discusses the characteristics of raw dual-frequency GNSS observations from Xiaomi Mi 8 in urban environments; they are characterized by high pseudorange noise and frequent signal interruption. The traditional dual-frequency ionosphere-free combination is not suitable for Xiaomi Mi 8 raw GNSS data processing, since the noise of the combined measurements is much larger than the influence of the ionospheric delay. Therefore, in order to reasonably utilize the high precision carrier phase observations, a time differenced positioning filter is presented in this paper to deliver continuous and smooth navigation results in urban environments. The filter first estimates the inter-epoch position variation (IEPV) with time differenced uncombined L1/E1 and L5/E5 carrier phase observations and constructs the state equation with IEPV to accurately describe the user’s movement. Secondly, the observation equations are formed with uncombined L1/E1 and L5/E5 pseudorange observations. Then, kinematic experiments in open-sky and GNSS-degraded environments are carried out, and the proposed filter is assessed in terms of the positioning accuracy and solution availability. The result in an open-sky environment shows that, assisted with L5/E5 observations, the root mean square (RMS) of the stand-alone horizontal and vertical positioning errors are about 1.22 m and 1.94 m, respectively, with a 97.8% navigation availability. Encouragingly, even in a GNSS-degraded environment, smooth navigation services with accuracies of 1.61 m and 2.16 m in the horizontal and vertical directions are obtained by using multi-GNSS and L5/E5 observations.

The advancements of Earth observations, remote sensing, communications and navigation augmentation based on low Earth orbit (LEO) platforms present strong requirements for accurate, real-time and autonomous navigation of LEO satellites. Precise onboard real-time orbit determination (RTOD) using the space-borne data of multiple global navigation satellite systems (multi-GNSS) becomes practicable along with the availability of multi-GNSS. We study the onboard RTOD algorithm and experiments by using America’s Global Positioning System (GPS) and China’s regional BeiDou Navigation Satellite System (BDS-2) space-borne data of the FengYun-3C satellite. A new pseudo-ambiguity parameter, which combines the constant phase ambiguity, the orbit and clock offset error of the GPS/BDS broadcast ephemeris in the line-of-sight (LOS), is defined and estimated in order to reduce the negative effect of the LOS error on onboard RTOD. The analyses on the variation of the LOS error in the GPS/BDS broadcast ephemeris indicate that the pseudo-ambiguity parameter could be modeled as a random walk, and the setting of the power spectral density in the random walk model decides whether the pseudo-ambiguity can be estimated reasonably and the LOS error could be reduced or not. For different types of GPS/BDS satellites, the LOS errors show different variation characteristics, so the power spectral density should be set separately and differently. A numerical search approach is presented in this paper to find the optimal setting of the power spectral density for each type of GPS/BDS satellite by a series of tests. Based on the optimal stochastic model, a 3-dimensional (3D) real-time orbit accuracy of 0.7–2.0 m for position and 0.7–1.7 mm/s for velocity could be achieved only with dual-frequency BDS measurements and the broadcast ephemeris, while a notably superior orbit accuracy of 0.3–0.5 m for position and 0.3–0.5 mm/s for velocity is achievable using dual-frequency GPS/BDS measurements, due to the absorption effect of the estimated pseudo-ambiguity on the LOS error of the GPS/BDS broadcast ephemeris. Compared to using GPS-alone data, the GPS/BDS fusion only marginally improves the onboard RTOD orbit accuracy by about 1–3 cm, but the inclusion of BDS satellites increases the number of the tracked GNSS satellites and thus speeds up the convergence of the filter. Furthermore, the GPS/BDS fusion could help suppress the local orbit errors, ensure the orbit accuracy and improve the reliability and availability of the onboard RTOD when fewer GPS satellites are tracked in some anomalous arcs.