Machine-learning-based navigation systems have become crucial for unmanned aerial vehicles (UAVs), particularly in environments affected by signal jamming and laser pointing. Traditional sensors such as global navigation satellite system sensors, lasers, and radar provide essential navigation data but have limitations, including the need for continuous pointing and vulnerability to interference. Advancements in imaging technology have rendered cameras a viable alternative. This article presents a real-time navigation solution for high-speed UAVs that minimize disruption from environmental dynamics. Key methodologies include (i) creating a virtual environment for model training, (ii) extracting UAV flight dynamics for simulation, (iii) applying and validating image-matching techniques, and (iv) developing a visual tracking algorithm for navigation between successive image-matching steps. The approach utilizes UAV-captured images alongside satellite images of the flight region. Experimental results and analyses demonstrate the effectiveness of various image-matching methods and visual tracking algorithms, showcasing the capabilities of the proposed solution compared with available techniques.
This study proposes an optimized, tightly coupled global navigation satellite sys-tem (GNSS)/inertial navigation system (INS) integration method for accurate smartphone positioning, developed and evaluated using data sets from the Google Smartphone Decimeter Challenge (GSDC) 2023-2024. In the GSDC literature, inertial measurement unit (IMU) data have been used in only a limited man-ner, primarily because of GNSS-IMU time misalignment between smartphone system clocks and GNSS time. To address this issue, we introduce a lightweight post-processing time synchronization scheme that selects a per-drive constant time offset by minimizing the root mean square of position corrections within a Kalman filter. The proposed method incorporates innovation-based adaptive measurement weighting to accommodate varying GNSS measurement qualities across smartphones and environments. Experimental results demonstrate that compared with conventional differential GNSS approaches, the proposed GNSS/ INS integration reduces the mean of the 50th and 95th percentile horizontal errors by up to 50 cm. The proposed method achieved submeter accuracy for the first time in a competition, securing first place at the GSDC 2023-2024 challenge.
A global navigation satellite system (GNSS) meta-signal is obtained by considering and processing components from different radio frequencies (RFs) as a single entity. While most research on GNSS meta-signals has considered components from only two frequencies, four and five open signals are currently provided by Galileo and the BeiDou satellite navigation system (BDS), respectively. In this paper, multidimensional GNSS meta-signals, with a number of components equal to a power of two, are introduced and described using multicomplex numbers, a multidimensional extension of complex numbers. In this way, single-frequency GNSS signal processing is generalized to the multidimensional case. A multicomplex cross ambiguity function is derived and used for the design of multifrequency acquisition and tracking algorithms. Theoretical results are supported by experiments in which four RF front-ends are used to capture Galileo and BDS signals from different frequencies. The four signals are then jointly processed using the algorithms developed.
In this work, the impact of state constraints in Kalman filters is analyzed. Such constraints are commonly used in integrated navigation systems to augment sensor measurements, for example, through zero-velocity updates in personal navigation systems. Constraints may be linear or nonlinear and may be posed as either equality or inequality constraints. It is shown that linear inequality constraints can introduce bias into the state estimate that is not reflected in the estimation error covariance matrix. Furthermore, for nonlinear equality and inequality constraints, projection-based methods that have been used in the design of integrated navigation systems can yield inconsistent estimates, in which the computed state estimation error covariance matrix is a poor proxy for the actual estimation error statistics.
The accuracy of global navigation satellite system (GNSS) signal reception is crucial for precise navigation and geodetic positioning. Signal interactions with objects near the receiving antenna can cause multipath errors and distort GNSS antenna group delays, thereby reducing the achievable positioning accuracy. To mitigate these effects, the distortions can be predicted in advance and subsequently reduced through a calibration approach. This approach is possible, for example, for static errors, such as those caused by interactions between the antenna and the installation platform, for instance, on a car. This paper addresses the accurate prediction of distortions caused by the installation of the antenna on a car in automotive scenarios. This work introduces a hybrid calibration approach that combines real-world data and simulations to enhance GNSS antenna performance predictions. This approach allows the simulation to reconstruct the effect of the mounting platform on the data of an individual antenna previously measured in an anechoic chamber, thereby predicting the final error of the installed antenna on the platform. This methodology is then validated and compared with a GNSS-based calibration of the antenna performed directly on a car, i.e., inherently including installation effects. The results show that approximately 48% of the sky plot region exhibits a code phase variation difference within +/- 25 cm, indicating a high level of accuracy and consistency.
X-ray pulsar navigation (XNAV) has the potential to provide autonomous navigation in deep space, but practical implementations are constrained, in part, by long signal integration times and single-pulsar observations. Under these conditions, navigation states (position, velocity, and clock error) are only partially observable, allowing the clock error to grow unchecked and potentially cause positioning, navigation, and timing algorithms to diverge. This work quantifies the impact of clock error on XNAV position and velocity estimates and identifies the oscillator performance required as a function of signal observation (integration) time. A maximum-likelihood estimator (MLE) is used to estimate phase and frequency from simulated pulsar observations corrupted by timing noise from oscillators of varying quality. The results demonstrate that typical temperature-controlled crystal oscillators are unsuitable for XNAV, whereas high-quality oven-controlled crystal oscillators or chip-scale atomic clocks provide sufficient stability to estimate and mitigate the clock error before clock noise dominates the MLE estimates.
This study introduces strategies for the establishment of a differential lunar nav-igation satellite system (DLNSS) on the Moon using a swarm of lunar rovers and provides a performance analysis. The proposed DLNSS can enhance user positioning accuracy by broadcasting differential correction messages gener-ated using raw measurements collected at multiple reference receivers with accurately known antenna coordinates. However, accurately determining the coordinates of reference receiver antennas presents a challenge, particularly in the absence of precise positioning methods on the Moon. In our proposed scheme for establishing a DLNSS on the Moon, we address this challenge by employing cooperative positioning techniques using a swarm of lunar rovers with a lunar navigation satellite system (LNSS) and ultra-wideband technology. Our simulations show that the proposed LNSS differential corrections achieve a three-dimensional user positioning accuracy that is better than a few meters with four or eight LNSS satellites.
The navigation signals of global navigation satellite systems have undergone development with limited consideration given to inherent payload and receiver constraints. The forthcoming satellite generation will be equipped with flexible, fully digital payloads and feature enhanced clock architectures, which may offer potential performance improvements for positioning, navigation, and timing (PNT) users. A significant challenge is to realize these performance improvements at the user level while addressing distortions in transmitter and receiver hardware that impair PNT performance. This study reviews previous signal design concepts and extends the multilevel coded spreading symbol optimization framework to account for nonlinear and linear payload distortions and receiver band limitations. The proposed comprehensive distortion-aware optimization methodology yields signal candidates with enhanced robustness by improving performance metrics such as mean tracking error jitter and differential range bias, consequently delivering greater user benefits than signal designs optimized for minimally distortion-affected signal propagation scenarios.
Global navigation satellite systems (GNSSs) are the only global, free, compre-hensive technology providing absolute and accurate positioning, navigation, and timing (PNT) services to users worldwide. These services have become an indispensable part of modern society, playing a critical role in many commer-cial, industrial, scientific, and safety-critical applications. Numerous applica-tions, including mass marketing, professional, and other applications linked to critical infrastructure, heavily depend on GNSSs, with increased expectations for more reliability, accuracy, and availability. However, in specific scenarios, the number of visible satellites can be low, even when all GNSS constellations are used: this is the case, for example, in urban environments or mountain terrain, where the position accuracy can be poor or position estimation may not even be possible. In such cases, the integration of a GNSS with other positioning tech-nologies, such as 5G, and the low Earth orbit (LEO)-PNT concept could improve results. Over the last years, LEO satellites have been put in orbit for several pur-poses such as telecommunication and Earth observation. Now, several private and institutional actors are considering the idea of designing and deploying LEO satellites for PNT services, by equipping these satellites with payloads able to transmit signals with a design that is interoperable with those already broad-casted by GNSS satellites. Therefore, the aim of this work is to assess the possi-ble integration of GNSS (and 5G) with LEO-PNT positioning signals. Real-life GNSS and 5G data are used from a previous experiment, conducted in the fall of 2023 in northern Italy. LEO-PNT orbits are generated and provided by the European Space Agency. LEO visibility tables and pseudorange observations are simulated for a given location and date. The measurements are combined and processed in a tightly coupled extended Kalman filter, and results are gener-ated for different configurations: 5G standalone, GNSS standalone, LEO-PNT standalone, LEO-PNT + 5G, and GNSS + LEO-PNT. Among these cases, the integrated GNSS + LEO-PNT solution provides the best results.
Global navigation satellite system (GNSS) positioning relies on accurate stochastic models for measurement errors to provide reliable position estimates and bounds. This paper presents a novel approach for modeling errors in GNSS measurements with Bayesian distributional regression, using variational inference to scale model complexity and data set size beyond typical computational limits. This methodology is applied to an automotive data set for GNSS pseudorange (multipath) errors, targeting a Student's t-distributed model to realistically characterize heavy-tailed data. The distribution is regressed on signal quality indicators from the GNSS receiver to segment different environmental effects on the measurements. Bayesian penalized tensor product splines are used to model nonlinear relationships based on the signal quality indicators. Detailed analyses of goodness-of-fit diagnostics show that the model is able to fit well to the data, and model uncertainty is quantified such that users may be aware of and compensate for inaccuracies in modeling.
To enable the use of global navigation satellite systems (GNSSs) for aircraft navigation, satellite-based augmentation systems have been implemented worldwide to guarantee the accuracy and integrity of aircraft position estimates derived from observations of GNSS signals. For over two decades, the United States' Wide Area Augmentation System (WAAS) has protected users of the Global Positioning System from threats to position accuracy posed by ionospheric disturbances over North America. A prior companion paper (Sparks et al., 2022) reviews how WAAS has protected users from the disruptive impact of moderate and extreme ionospheric storms. The present paper addresses the methodology adopted by WAAS to protect users from the influence of ionospheric disturbances that are more modest in magnitude, both those well-sampled and those poorly sampled. A subsequent companion paper traces in greater detail the evolution of the WAAS undersampled ionospheric irregularity threat model used to augment the integrity confidence bounds that quantify position accuracy.
Pulsars are spinning neutron stars that emit highly stable, periodic signals with periods on the order of milliseconds to seconds. This natural stability makes pulsars promising for forming an independent timing system for spacecraft navigation, especially in deep space. The North American Nanohertz Observatory for Gravitational Waves team has released 15 years of data for 68 millisecond pulsars. We analyze the stability of these pulsars and estimate their range positioning accuracy for autonomous navigation. Several pulsars enable sub-kilometer accuracy over averaging periods of 100 days to more than 15 years. We also demonstrate the feasibility of an onboard pulsar ensemble using a classical weighted algorithm, achieving stability levels of 10-16 over 10 years or more. Currently, no space-based atomic clock can provide these levels of stability over a 10-year period. Therefore, the exceptional natural stability of pulsars could be leveraged for deep-space missions. In addition, pulsars have extremely long lifespans, offering unprecedented reliability for space missions.
The use of low tracking loop bandwidths improves sensitivity and mitigates multipath. When applied to carrier-phase tracking, this method is analogous to using long coherent integration times. Based on this concept, we developed a receiver architecture capable of supporting phase-locked loop (PLL) bandwidth values as low as 0.1 Hz. This low bandwidth is achieved by leveraging external Doppler aiding from an inertial measurement unit (IMU) and incorporating a dedicated clock-locked loop. The IMU only needs to be stable over short time intervals. This method was analyzed via the z-transform and implemented for Global Positioning System C/A+L5Q and Galileo E1C+E5aQ signals. This approach was first tested with simulated signals and later with real-world data from the TEX-CUP measurement campaign. The results show a significant reduction in code/carrier-phase residuals and a roughly 50% improvement in positioning accuracy plus integrity compared with conventional delay-locked loop/PLL tracking when applied to a float real-time kinematic solution. Additionally, the ultra-low-bandwidth PLL observations enable the resolution of carrier-phase ambiguities for nearly 100% of epochs within the first 400 s of the TEX-CUP data sets, including those from urban areas. This paper also discusses various implementation considerations for operational deployment of this method.
This paper presents the first multi-year, nationwide diagnostic analysis of the precise point positioning (PPP) real-time kinematic (RTK) service, spanning the rise, peak (late 2024 to mid-2025), and initial decline of Solar Cycle 25. Using data from approximately 1,300 GNSS Earth Observation Network System (GEONET) stations, we validated our 30-s sampling methodology against official 1-Hz reports and analyzed nationwide performance trends. The analysis isolated two distinct degradation mechanisms: (1) unavoidable environmental stressors, such as plasma bubbles and medium-scale traveling ionospheric disturbances, driven by heightened solar activity, and (2) four structural vulnerabilities in the CLAS architecture that were exposed under stress. These vulnerabilities include persistent vertical bias from reference-frame misalignment (International Terrestrial Reference Frame [ITRF] 2014 vs. ITRF2020), error cross-contamination in bottom-up correction generation, user-level instability caused by ground facility (message generation facility) switching, and a single point of failure arising from dependence on continuous GEONET availability. We discuss the implications for system resilience and propose remedies for next-generation PPP/PPP-RTK services, including enhanced frame alignment and adaptive switching mechanisms.
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.
Previous studies using a physics-based global navigation satellite system scintillation simulator demonstrated that Global Positioning System-like L1 signals transmitted from low-Earth-orbit (LEO) satellites exhibit higher signal dynamics, resulting in more severe scintillation effects than those from medium-Earth-orbit satellites. This study extends these analyses from L-band to very high frequency, ultra-high frequency, and S-band, evaluating the effects of scintillation on LEO-transmitted signals across a broader range of frequency bands. Key scintillation characteristics, including fading time separation, duration, depth, and phase rate, are examined across frequencies and signal dynamics under different transmission scenarios. The results show that lower-frequency signals experience more frequent and deeper fades with greater phase fluctuations, particularly under higher dynamics of LEO transmissions. Quantitative analysis reveals that the ratios of mean scintillation characteristics (fading time separation, duration, and phase rate) between different signal dynamics cases remain consistent across frequencies. Rare fading overlaps among L-band frequencies suggest the potential for leveraging inter-frequency aiding to improve receiver tracking robustness for LEO transmissions.
This paper presents an experimental alternative positioning, navigation, and timing system for ground users, implemented at X-band, and demonstrated using a formation of four small unmanned aerial vehicles. The experimental system is designed to support stand-alone ground user positioning at the few-meter level within 30 s and to study the features and characteristics of X-band for this purpose. The payload that creates the X-band transmissions (8.52 GHz) and the user receiver are both based on commercial-off-the-shelf components and a software-defined radio architecture, enabling the study of various signal designs and receiver acquisition and tracking strategies. Horizontal positioning at a level of 1.5 m (root mean square) is demonstrated for both static and moving receivers. Examples of the tracking performance and multipath effects on individual signals highlight the effectiveness of the signal design and the payload and receiver implementations.
This article presents a comprehensive overview of the successful execution of the Lunar GNSS Receiver Experiment (LuGRE), the first known demonstration of global navigation satellite system (GNSS) signal acquisition, tracking, and navigation near and on the Moon. A general overview of the mission, payload, and ground system is provided. The as-flown mission profile is described in detail across the Earth-Moon transit, low lunar orbit, and lunar surface phases. A description of the high-level results of the mission is presented, including an evaluation of C/N-0, the quality of the pseudorange and carrier-phase measurements, the signal availability, the results of real-time least-squares position, velocity, and time estimation by the onboard receiver, and an evaluation of the in-phase and quadrature samples captured during the mission. Finally, key observations for future lunar GNSS users are discussed. The article also serves as a reference guide to the unique open data set released by the project.
We investigated the effects of the ionosphere on a very-high-frequency (VHF) signal transmitted from a polar orbiting National Oceanic and Atmospheric Administration (NOAA) weather satellite, NOAA-19, at an altitude of 861 km. NOAA-19 gathers cloud images and transmits reduced resolution images in the Automatic Picture Transmission format at 137.1 MHz. A software-defined VHF data collection system sampled the signal at Gakona, Alaska, during a high-frequency ionospheric heating experiment. A software algorithm was developed to extract the signal amplitude, frequency, and carrier phase, and the results were used to compute amplitude and phase scintillation indices as the signal traversed the artificially disturbed ionosphere. A strong response was observed in signal amplitude and phase due to the disturbances, in clear contrast to the mild disturbances experienced by global navigation satellite system signals traversing the ionosphere under similar conditions. The results demonstrate the frequency dependence of ionospheric effects on radio waves transmitted from low-Earth-orbit satellites. The study also reveals the deficiency in current ionospheric scintillation modeling in the VHF regime.
