Advancing Positioning, Navigation, and Timing (PNT) Service Using Satellite Navigation Technology

1. Introduction

As a pivotal spatiotemporal infrastructure in the modern information society, satellite navigation provides global users with high-precision, all-weather, and round-the-clock Positioning, Navigation, and Timing (PNT) services. It constitutes an indispensable spatial infrastructure for today’s national economic development and defense construction. Satellite navigation systems have found widespread applications across various sectors, including transportation, surveying and mapping, geographical information, meteorology, land and resources surveys, precision agriculture, and seismology, permeating every facet of the national economy.

Currently, four Global Navigation Satellite Systems (GNSSs) have fully completed their satellite constellation deployments, while two regional navigation satellite systems (RNSSs) and several satellite-based augmentation systems have also been largely established, with other satellite navigation systems are under planning. The discipline of satellite navigation emerged from the interdisciplinary convergence of geometry, electromagnetism, mechanics, and geodesy. With the expansion of its application domains and an increase in its significance, it has evolved into a relatively independent discipline. Looking ahead, the emergence of perception methods based on new physical principles is expected to give rise to new disciplines.

PNT serves as crucial foundational information for economic development and national defense advancement, as well as vital supporting information for the development of an intelligent society. PNT has permeated every aspect of our lives, from daily commuting to national security, and from scientific research to engineering applications, underscoring its indispensable status and role. With the increasing complexity of spatiotemporal measurement methods, PNT technology has gradually demonstrated a trend of multidisciplinary integration. In particular, with the emergence of satellite navigation being a colossal and complex system, the interdisciplinary characteristics of the PNT field have become even more pronounced. However, relying solely on any single PNT technology cannot meet the PNT needs of arbitrary users in any scenario. It is imperative to construct a PNT infrastructure network that provides full-domain coverage and integrates multiple physical principle-based information sources, forming a PNT application and service system characterized by multi-source data fusion and complementary advantages of multiple technologies. This not only represents an inevitable trend in the development of the international PNT system but also serves as the necessary path to promote PNT applications and enhance PNT service performance.

Currently, integrated PNT addresses the issue of PNT information sources, resilient PNT focuses on the optimal combination of PNT information sources, and micro-PNT tackles the challenges of miniaturization and low power consumption in PNT terminals. For the vast number of PNT users, having PNT infrastructure and resilient guidelines is not sufficient. It is also essential to address the issue of intelligent applications.

The Special Issue is dedicated to exploring the wide-ranging PNT technologies based on satellite navigation. We invite original research articles and reviews that delve into various aspects including, but not limited to, constellations, signals, orbit determination, PNT theory, algorithms, models, and their applications in engineering and Earth sciences, as well as multi-sensor integration. Topics of interest for this Special Issue include, but are not limited to, integrated PNT, resilient PNT, micro PNT, secure PNT, GNSS Precise Point Positioning (PPP) and PPP-Real-Time Kinematic (PPP-RTK), GNSS timing, GNSS orbiting determination and modeling, GNSS atmospheric sensing, GNSS ionosphere and space weather, integrated navigation and smart applications, satellite navigation countermeasure, future Low Earth Orbit (LEO) PNT, and broadband PNT constellations using signal of opportunity.

The Special Issue received a total of 38 submissions and ultimately published 9 research papers, all of which have undergone a rigorous review process. The objective of this Editorial is to provide an overview of the contributions from the studies in this Special Issue. Section 2 summarizes the individual articles hosted in the Special Issue in alphabetical order based on the publication time and article type, and Section 3 outlines some concluding remarks.

2. Overview of Contributions

Jiao et al. (Contribution 1) introduced a novel undifferenced model integrated with satellite clock offsets, which further transforms the inter-frequency clock bias (IFCB) into time-variant mixed observable-specific signal biases (OSBs) for both code and phase measurements. This innovation addresses the limitations inherent in traditional approaches while streamlining the bias correction process for multi-frequency PPP. The proposed model not only enhances the accuracy of mixed OSBs but also eliminates the adverse effects of receiver-dependent time-varying biases on satellite-based mixed OSB estimation. Quantitative evaluations demonstrate significant improvements, where the standard deviation (STD) and root mean square (RMS) of original OSBs are reduced by 7.5–60.9% and 9.4–66.1%, respectively, while those of epoch-differenced (ED) OSBs are improved by 50.0–87.5% and 60.0–88.9% for STD and RMS. Furthermore, PPP solutions utilizing the new mixed OSBs outperform those relying on conventional IFCB products. The findings validate the reliability, practicality, and efficacy of the proposed time-variant mixed OSB framework and the undifferenced model with integrated satellite clock offsets for multi-frequency PPP applications.

Tao et al. (Contribution 2) proposed a modified Multipath Hemispherical Map (MHM) approach to mitigate the multipath for single-frequency multi-GNSS tightly combined positioning. The method partitions the hemispherical space into a 36 × 9 grid with 10° × 10° angular resolution, then utilizes elevation and azimuth angles as search parameters to determine the multipath correction value from the nearest grid point. To enhance computational efficiency without compromising accuracy, a k-dimensional tree structure is implemented for rapid nearest-neighbor searches. Experimental results demonstrate that the modified MHM improves mean positioning accuracy by 10.20%, 10.77%, and 9.29% for Global Positioning System (GPS), BeiDou Navigation Satellite System (BDS), and Galileo single-difference residuals, respectively, compared to conventional advanced sidereal filtering-based corrections. Precision enhancements reach 32.82%, 40.65%, and 31.97% in the east, north, and up components, respectively. The modified MHM exhibits superior performance and more consistent error mitigation across different satellite systems.

Zhao and Wei (Contribution 3) conducted a performance assessment of short-duration PPP using PPP-B2b correction products and introduced a backward smoothing technique to improve positioning accuracy during the initial convergence phase. The analysis revealed that the orbit and clock precision of BDS PPP-B2b products outperform those of GPS, with BDS achieving radial, along-track, and cross-track orbit accuracies of 0.059 m, 0.178 m, and 0.186 m, respectively, and clock synchronization accuracy within 0.13 ns. For hourly static PPP solutions, 50% of test sessions reached horizontal and vertical accuracy of 0.5 m and 0.1 m after convergence times of 4.5 min and 25 min, respectively. However, 7.07% to 23.79% of sessions failed to achieve 0.1 m accuracy due to insufficient GPS and BDS correction availability at specific stations. Simulated kinematic PPP required an additional 1–4 min to attain comparable accuracy to static PPP. The implementation of backward smoothing significantly enhanced positioning precision, achieving north, east, and up direction accuracies of 0.024 m, 0.046 m, and 0.053 m, respectively. In vehicle-based applications, forward PPP attained horizontal accuracy better than 0.5 m within 4 min, though errors could exceed 1.5 m and 3.0 m for east and up components during convergence. With smoothing applied, horizontal accuracy improved to better than 0.2 m, while vertical accuracy reached sub-0.3 m levels.

Chen et al. (Contribution 4) introduced an adaptive robust filtering algorithm featuring an optimized fading factor to address the divergence issues of traditional Kalman filters under severe heave motion and anomalous observation conditions. A multi-source information fusion framework was developed by integrating four key indicators, including satellite Positioning Dilution Of Precision (PDOP), solution quality metric (Q-value), effective satellite observation count (Satnum), and residual vector analysis. A dynamic weight adjustment mechanism was designed to enable real-time optimization of the fading factor, while a dual robust mechanism was constructed through the synergistic integration of robust estimation theory and adaptive filtering, employing a sequential update strategy. During the measurement update phase, observation weights were dynamically adjusted based on innovation covariance, and a fading memory factor was introduced in the time update phase to mitigate model error accumulation. Experimental evaluations demonstrated significant accuracy improvements compared to conventional Extended Kalman Filter (EKF), Sage-Husa adaptive filtering, and basic robust filtering approaches. In high-maneuver vehicle scenarios, three-dimensional positioning accuracy increased by 47.12%, 35.26%, and 9.58%, respectively, while shipborne heave motion scenarios showed corresponding improvements of 19.44%, 10.47%, and 8.28%. These findings provide an effective anti-interference solution for navigation systems operating in highly dynamic and complex environments.

Deng et al. (Contribution 5) proposed an orthogonal frequency division multiplexing (OFDM)-based LEO navigation system and conducted a detailed performance analysis. Leveraging 5G New Radio (NR) as the satellite transmission signal, the study identified NR signal components suitable for navigation services while introducing a novel zero-padding correlation (ZPC) receiver design. This ZPC technique effectively eliminates cyclic prefix (CP) and inter-carrier interference (ICI), significantly enhancing signal tracking precision. The power spectral density (PSD) of the NR navigation signal was mathematically derived, followed by a comprehensive evaluation of tracking accuracy under varying NR configurations, including bandwidth, spectral allocation, and signal composition parameters. An extended Kalman filter (EKF) was implemented to integrate pseudorange and pseudorange rate measurements for real-time positioning solutions. Simulation results revealed substantial improvements over conventional receivers, with ranging precision enhanced by 80% and positioning accuracy improved by 88.3%. The proposed ZPC receiver demonstrated centimeter-level navigation capabilities. This research provides a systematic analysis of LEO NR system navigation performance and offers valuable insights for the design of future LEO-based PNT architectures.

Wu et al. (Contribution 6) introduced a robust approach that leverages narrow-lane ambiguity resolution to compensate for receiver clock discontinuities, coupled with an adaptive sliding-window weighting strategy that optimally utilizes multi-epoch observational data. The methodology effectively addresses day-boundary jumps by implementing dynamic thresholding for error detection and minimizing the impact of incorrect ambiguity fixing. Experimental evaluations demonstrated that at an averaging interval of 76,800 s, the frequency stability for GPS, Galileo, and BDS integer precise point positioning (IPPP) solutions reached 4.838 × 10⁻¹⁶, 4.707 × 10⁻¹⁶, and 5.403 × 10⁻¹⁶, respectively. For zero-baseline time transfer applications, GPS IPPP achieved stability at the 10⁻¹⁷ level, outperforming optical fiber time transfer in long-term differential comparisons. Across both short- and long-baseline scenarios, IPPP consistently surpassed conventional PPP float solutions and International GNSS Service (IGS) final products. Specifically, at a 307,200 s averaging interval, IPPP improved average frequency stability by approximately 29.3% relative to PPP and 32.6% compared to IGS final products.

Zheng et al. (Contribution 7) conducted a thorough evaluation of the Adaptive Stochastic Model (ASM) and its effect on PPP. The study first detailed the implementation of ASM using Variance Component Estimation (VCE) techniques. Experimental results revealed that ASM effectively captures varying observation conditions through dynamically estimated variance components, thereby enhancing both PPP float and fixed solutions particularly when predefined stochastic models prove insufficient. The approach also improved cycle-slip detection performance by tightening the stochastic constraints, reducing the missed detection rate from 19% to 8%. Furthermore, ASM accelerated both direct reconvergence and re-initialization processes following data interruptions, with reconvergence times shortened by 18% and re-initialization times by 55%, respectively.

Fan et al. (Contribution 8) introduced a tightly coupled integration model combining Pseudolite System (PLS) and GNSS at the observation level, where ambiguity resolution strategy plays a critical role in augmentation performance. The study proposes a novel ambiguity resolution approach that leverages the rapid convergence characteristics of PLS by independently fixing PLS ambiguities first, followed by cascading resolution of GNSS wide-lane and L1 ambiguities. The fixed ambiguities are subsequently incorporated as constraints in the filtering process to enhance solution robustness. Experimental evaluations demonstrated significant improvements in ambiguity fixing rates, particularly for short-duration augmentation scenarios, where the proposed method outperformed conventional approaches.

Lv et al. (Contribution 9) developed comprehensive modeling frameworks for both traditional and Artificial Intelligence (AI) approaches in GNSS PNT. The study systematically reviewed classical mathematical models, including polynomial, gray, Kalman filter, and time series methods, alongside AI-based techniques such as machine learning (ML), multilayer perceptron (MLP), recurrent neural networks (RNNs), and Transformer architectures. The technical attributes, practical applications, and inherent limitations of each model type were analyzed in depth. While AI-based models exhibited superior adaptability and performance in complex environments compared to classical methods, they demanded larger training datasets and significant computational resources. The research concluded with a comparative summary of strengths, weaknesses, and future development trajectories, providing actionable insights for advancing real-time, high-precision GNSS PNT solutions.

3. Concluding Remarks

The papers included in this Special Issue collectively demonstrate that field of PNT technology encompasses multiple disciplines and involves complex technical challenges. The advancement of PNT technology necessitates proactive integration with cutting-edge technologies such as big data and AI. It also requires research into multi-technology fusion development models and active exploration of PNT sensing technologies based on novel physical principles. Some studies in this Special Issue have proposed improvements to PNT technologies from the perspective of technical algorithms, while others have focused on enhancements through the adoption of novel technologies.

Based on the insights from this Special Issue, multiple promising avenues for future research become apparent as follows:

• Research on challenges in spatiotemporal reference framework construction under strong interference conditions. The research primarily focuses on the anti-jamming capabilities of navigation systems, addressing adaptability issues in satellite constellations, signal architectures, and receiver performance, as well as the applicability of navigation systems under complex operational conditions [1,2].
• Research on integrated PNT system technologies. Key research areas include deep-space PNT technologies, design and deployment of Lagrangian constellations, LEO-augmented PNT solutions, integrated navigation combining network communication technologies with GNSS, hybrid navigation approaches integrating inertial, celestial, gravimetric and magnetic, and terrain-matching navigation, along with underwater PNT systems [3,4,5].
• Research on resilient PNT theories and methodologies. The research encompasses resilient integration techniques for multi-source PNT information, development of resilient functional and stochastic models for PNT data under complex environments, and establishment of fusion criteria, models, and algorithms for multi-source PNT information resilience [6,7,8].
• Key theories and technologies for intelligent PNT service systems. Research priorities include PNT intelligent perception theories and sensor technologies, intelligent fusion of multi-source PNT information, and service architecture development for intelligent PNT systems adapted to diverse environmental conditions [9,10].

It is evident that PNT technology research remains in its nascent stage, with substantial efforts still required in satellite navigation-based PNT studies to enhance the continuity, availability, robustness, and reliability of PNT services.