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Recently, the Doppler shifts from Low Earth Orbit (LEO) satellites have been used to augment GNSS and provide navigation services. We propose a Doppler-only point-solution algorithm for GNSS-like navigation systems operated in LEO. The proposed algorithm can simultaneously estimate the receiver clock drift, position and velocity. Then, we analyze the main error sources in Doppler positioning. To achieve the meter-level positioning accuracy, the satellite position and velocity errors should be within several meters and several centimeters per second, respectively. The ionospheric delay rates of C-band signal will cause about 1 m error in Doppler positioning, which can be eliminated using the ionosphere-free combination. The Doppler positioning accuracy will deteriorate sharply by dozens of meters if there are no corrections for the tropospheric errors. Subsequently, we analyze the Doppler positioning performance. The undifferenced Doppler positioning accuracy is at meter level, which is comparable with the pseudorange-based positioning in GNSS. To ensure convergence in the LEO-based Doppler positioning, the initial receiver position error should be less than 300 km when the satellites orbit is at an altitude of 550 km.

The need for precise orbit determination (POD) has grown significantly due to the increased amount of space-based activities taking place at an accelerating pace. Accurate POD positively contributes to achieving the requirements of Low-Earth Orbit (LEO) satellite missions, including improved tracking, reliability and continuity. This research aims to systematically analyze the LEO–POD in four aspects: (i) data sources used; (ii) POD technique implemented; (iii) validation method applied; (iv) accuracy level obtained. We also present the most used GNSS systems, satellite missions, processing procedures and ephemeris. The review includes studies on LEO–POD algorithms/methods and software published in the last two decades (2000–2021). To this end, 137 primary studies relevant to achieving the objective of this research were identified. After the investigation of these primary studies, it was found that several types of POD techniques have been employed in the POD of LEO satellites, with a clear trend observed for techniques using reduced-dynamic model, least-squares solvers, dual-frequency signals with undifferenced phase and code observations in post-processing mode. This review provides an understanding of the various POD techniques, dataset utilized, validation techniques, and accuracy level of LEO satellites, which have interest to developers of small satellites, new researchers and practitioners.

Real-time, high-accuracy orbital products for low Earth orbit (LEO) satellites are essential for LEO-augmented real-time positioning, navigation and timing services. In particular, complete and continuous global navigation satellite system (GNSS) observations onboard tracked LEO satellites are necessary to guarantee precise orbit determination (POD) and generate short-term predicted orbits that can be fit with real-time ephemeris parameters. However, in practice, GNSS observations of LEO satellites often suffer from discontinuities due to tracking problems, data transmission problems, or downlinking strategies. Understanding the effect of these observation gaps on orbit accuracy is therefore essential for developing strategies to minimize accuracy degradation in real-time LEO satellite orbits. This study investigates trade-offs between two suites of strategies for addressing multi-hour observation data gaps followed by short segments of tail data during reduced-dynamic POD. The first strategy, EP, involves sacrificing the tail data and extending the prediction time. The second set of strategies retain the tail data but vary the POD strategies: the tested options include maintaining stochastic accelerations as estimable parameters (RP), not estimating stochastic accelerations (CP), or combining the RP-based orbits from the non-gap periods with the CP-based orbits during the gap (BP). Using real GNSS observations from the LEO satellite Sentinel-6A, we evaluated the accuracy and integrity of these strategies for 1-h orbital predictions with assumed gap lengths of 3, 5, 7, and 9 h and tail data lengths set to 15, 30, 45, and 60 min. Results show that the BP strategy achieves the highest prediction accuracy, with mean orbital user range errors (OUREs) of approximately 5.7 and 13.4 cm for a 3-h data gap followed by 60-min and 15-min tails, respectively. In contrast, the EP strategy demonstrates the highest integrity. For a 15-min tail, the 99.9% confidence level of the OURE for the EP strategy reaches approximately 3.1 and 8.7 dm for gap lengths of 3 h and 9 h, respectively. Overall, BP is the preferred strategy for maximizing prediction accuracy, while the EP strategy is preferable for short gaps and tails. The CP strategy provides a balanced approach, maintaining reasonably strong performance for both prediction accuracy and integrity.

Low Earth Orbit (LEO) satellites can augment the traditional GNSS-based positioning, navigation and timing services, which require real-time high-precision LEO satellite clock products. As the complicated systematic effects contained in the LEO satellite clock estimates limit their high-precision mid- to long-term prediction, high-frequency LEO satellite clocks need to be estimated within a Kalman filter, resulting in a short prediction time for real-time applications. Compared to the clock estimation using Batch Least-Squares (BLS) adjustment, filter-based clock estimation experiences a lower precision. Increasing the model strength by introducing external orbital information, thus, de-correlating the orbital and clock parameters, will benefit real-time clock precision. In this contribution, reduced-dynamic LEO satellite orbits are first estimated using BLS adjustment in near real-time and predicted in the short term. The predicted orbits are then constrained during the Kalman-filter-based clock estimation process. The variance–covariance matrix of the introduced orbital errors is tested for different sets of values in the radial, along-track and cross-track directions when constraining orbits of different prediction times. One week of GPS data from the Sentinel-3B satellite in 2018 was used for validation of the proposed method. When weakly constraining high-accuracy predicted orbits within a prediction time of 20 min, i.e., with a standard deviation of the constraint set to 2–3 dm in the radial and cross-track directions, and 4–6 dm in the along-track direction, the estimated clock accuracy can be improved from about 0.27 to 0.23 ns, with a 13.4% improvement. Depending on the prediction period of the introduced orbits, the Signal-In-Space Range Error (SISRE) of the LEO satellite to Earth can also be improved, from about 9.59 cm without constraints, to 7.38–8.07 cm after constraining the predicted orbits, with an improvement of 16–23%. The improvements in the SISRE also indicate a better consistency between the real-time clock and orbital estimates.

Low Earth orbit (LEO) signal of opportunity (SOP) positioning relies on the accumulation of epochs obtained through prolonged observation periods. The contribution of an LEO satellite single epoch to positioning accuracy is influenced by multi-level characteristics that are challenging for traditional models. To address this limitation, we propose an Agent-Weighted Recursive Least Squares (RLS) Positioning Framework (AWR-PF). This framework employs an agent to comprehensively analyze individual epoch characteristics, assess their credibility, and convert them into adaptive weights for RLS iterations. We developed a novel Markov Decision Process (MDP) model to assist the agent in addressing the epoch weighting problem and trained the agent utilizing the Double Deep Q-Network (DDQN) algorithm on 107 h of Iridium signal data. Experimental validation on a separate 28 h Iridium signal test set through 97 positioning trials demonstrated that AWR-PF achieves superior average positioning accuracy compared to both standard RLS and randomly weighted RLS throughout nearly the entire iterative process. In a single positioning trial, AWR-PF improves positioning accuracy by up to 45.15% over standard RLS. To the best of our knowledge, this work represents the first instance where an AI algorithm is used as the core decision-maker in LEO SOP positioning, establishing a groundbreaking paradigm for future research.

Low Earth orbit (LEO) satellites are considered as an augmentation to traditional global navigation satellite systems for positioning, navigation, and timing (PNT). To enable real-time LEO-augmented PNT services, particularly for stand-alone positioning, high-precision LEO satellite clock products are required in real time, which is a challenge owing to the high correlation between the clocks and orbits. This contribution introduces an approach for real-time LEO satellite clock estimation using a combination of low- and high-frequency clock solutions. This work introduces predicted clocks based on low-frequency batch least-squares (BLS) clock determination and properly constrains them to improve the next step of Kalman-filter-based high-frequency clock estimation. By using 6-day real onboard Global Positioning System observations of Sentinel-3B, the performance of the predicted clocks from the BLS adjustment is evaluated. These clocks are then introduced into the high-frequency clocks solutions, and the resulting real-time clock estimates are analyzed. The potential of introducing filter-based predicted clocks is also discussed. Results show that the predicted LEO satellite clocks based on the BLS adjustment exhibit a precision of 0.15, 0.22, 0.33, 0.44, and 0.56 ns for prediction windows of 0–3, 3–6, 6–9, 9–12, and 12–15 min, respectively. After properly constraining the introduced predicted clocks within the above-mentioned predicted windows, improvements of 46.38%, 39.33%, 31.77%, 25.62%, and 18.35% were observed in the high-frequency precision, respectively, reducing the clock precision from 0.24 to 0.13 ns for the short prediction window of 0–3 min. For the signal-in-space ranging error (SISRE), corresponding improvements at 34.73%, 26.48%, 18.58%, 13.55%, and 8.93% were achieved, reducing the SISRE from 0.09 to 0.06 m for a prediction window of 0–3 min.

Emerging low Earth orbit (LEO) satellites offer new opportunities for navigation augmentation. This paper investigates the potential of orthogonal frequency division multiplexing (OFDM) signals for LEO satellite navigation, focusing on challenges arising from carrier frequency offsets (CFOs) in low signal-to-noise ratio (SNR) environments. We comprehensively analyze the navigation properties of OFDM signals, assessing two synchronization sequence (SS) candidates for their resilience against CFOs. Our findings suggest that the m-sequence effectively mitigates integer CFOs while minimally impacting the receiver’s ranging estimation in the presence of fractional CFOs. Additionally, we introduce an SS detection architecture that integrates differential coherent accumulation (DCA) with a near-optimal likelihood ratio test (NOLRT). This DCA-NOLRT-based LEO receiver enhances detection reliability and sensitivity, effectively managing residual fractional CFOs and improving detection probabilities in low-SNR scenarios. Numerical simulations and terrestrial experiments validate the proposed framework’s capability to minimize CFO-induced ranging errors, even under demanding conditions in LEO navigation scenarios.

Satellite-based precipitation products (SPPs) have become a crucial source of quantitative global precipitation data. Geostationary Orbit (GEO) satellites provide high spatiotemporal resolution but tend to have lower accuracy, while Low Earth Orbit (LEO) satellites provide more precise precipitation estimates but suffer from lower temporal resolution due to their limited observation frequency. This study proposes an efficient algorithm for integrating and enhancing precipitation estimates from multiple satellite observations. The target domain includes the Full Disk (FD) and the extended East Asia (EA) regions, both of which are observable by GEO satellites, such as Himawari-8, serving as the GEO platform in this study. The algorithm involves four steps: pre-data preparation, LEO morphing, adjustment, and final merging. It produces Early and Late composite products with 10-min temporal and up to 2 km spatial resolution and significantly reduces latency compared to IMERG. Specifically, the Early and Late products can be generated with approximate latencies of 90 min and 270 min, respectively—much faster than Integrated Multi-satellite Retrievals for GPM (IMERG)’s Early (4-h) and Late (14-h) products. A key feature of the proposed method is the use of accuracy-based weighting derived from radar-based validation, enabling dynamic merging that reflects the reliability of each satellite observation. Statistical validation using Global Telecommunication System (GTS) precipitation data confirmed the positive impact of the proposed bias correction and merging method. In particular, the Late product achieved accuracy comparable to or higher than that of IMERG Early and IMERG Late, despite its significantly shorter latency. However, its accuracy was still lower than that of IMERG Final, which benefits from additional gauge-based correction but is released with a delay of several months.

The BeiDou-3 navigation satellite system (BDS-3) has officially provided positioning, navigation, and timing (PNT) services to global users since 31 July 2020. With the application of inter-satellite link technology, global integrity monitoring becomes possible. Nevertheless, the content of integrity monitoring is still limited by the communication capacity of inter-satellite links and the layout of ground monitoring stations. Low earth orbit (LEO) satellites have advantages in information-carrying rate and kinematic velocity and can be used as satellite-based monitoring stations for navigation satellites. Large numbers of LEO satellites can provide more monitoring data than ground monitoring stations and make it easier to obtain full-arc observation data. A new challenge of redundant data also arises. This study constructs multi-source observation links with satellite-to-ground, inter-satellite, and satellite-based observation data, proposes an integrity monitoring method with optimization of observation links, and verifies the performance of integrity monitoring with different observation links. The experimental results show four findings. (1) Based on the integrity status of BDS-3, the proposed system-level integrity mode can realize full-arc anomaly diagnosis in information and signals according to the observation conditions of the target satellite. Apart from basic navigation messages and satellite-based augmentation messages, autonomous messages and inter-satellite ranging data can be used to evaluate the state of the target satellite. (2) For a giant LEO constellation, only a small number of LEO satellites need to be selected to construct a minimum satellite-based observation unit that can realize multiple returns of navigation messages and reduce the redundancy of observation data. With the support of 12 and 30 LEO satellites, the minimum number of satellite-based observation links is 1 and 4, respectively, verifying that a small amount of LEO satellites could be used to construct a minimum satellite-based observation unit. (3) A small number of LEO satellites can effectively improve the observation geometry of the target satellite. An orbit determination observation unit, which consists of chosen satellite-to-ground and/or satellite-based observation links based on observation geometry, is proposed to carry out fast calculations of satellite orbit. If the orbit determination observation unit contains 6 satellite-to-ground monitoring links and 6/12/60 LEO satellites, the value of satellite position dilution of precision (SPDOP) is 38.37, 24.60, and 15.71, respectively, with a 92.95%, 95.49%, and 97.12% improvement than the results using 6 satellite-to-ground monitoring links only. (4) LEO satellites could not only expand the resolution of integrity parameters in real time but also augment the service accuracy of the navigation satellite system. As the number of LEO satellites increases, the area where UDRE parameters can be solved in real time is constantly expanding to a global area. The service accuracy is 0.93 m, 0.88 m, and 0.65 m, respectively, with augmentation of 6, 12, and 60 LEO satellites, which is an 8.9%, 13.7%, and 36.3% improvement compared with the results of regional service. LEO satellites have practical application values by improving the integrity monitoring of navigation satellites.

The vigorous development of Low Earth Orbit (LEO) satellite constellation programs imposes higher requirements for the accuracy of satellite orbit determination. Significant variations in atmospheric density within the operational region of LEO satellites are primary factors influencing their orbital decay and operational lifespan. This article first summarizes the research advancements in atmospheric density inversion utilizing LEO satellites, comparing and analyzing the principles of various algorithms, factors affecting accuracy, as well as the advantages and disadvantages associated with different acquisition methods. Subsequently, we introduce recent progress in enhancing atmospheric density inversion algorithms and data analysis applications based on LEO satellites. The SWARM-A satellite, equipped with a high-precision GPS receiver and accelerometer, was employed to invert atmospheric density using both semi-long axis attenuation and accelerometer methodologies. The inversion results were compared against empirical models to validate their reliability; specifically, the correlation coefficient between the semi-long axis attenuation method and nrlmsise00 reached 0.9158, while that between the accelerometer method and nrlmsise00 attained 0.9204. Notably, the inversion accuracy achieved by the accelerometer slightly surpasses that of the semi-long axis attenuation method. These findings provide valuable support for predicting large air tightness based on LEO satellite orbit data inversions and for adjusting operational orbits to ensure successful execution of satellite missions.