Search

Global navigation satellite systems have enabled significant improvements in aeronautical navigation. However, in recent years, a growing number of interference events have been reported by flight crews. In this paper, we first identify such events using crowd-sourced surveillance data collected between February and December 2022 for three different regions: the Baltic states, eastern Europe bordering the Black Sea, and the eastern Mediterranean. Then, we assess the extent and duration of these events to determine their impact on civil aviation. The analysis shows different characteristics, ranging from isolated events to regular large-scale and recurrent disruptions. Next, we identify aircraft types for the affected flights and evaluate flight plan data with respect to navigation equipment in order to identify flights that rely solely on satellite navigation and that might require assistance in the case of a loss of satellite navigation. Finally, we show the impact of radio frequency interference (RFI) on a selected passenger flight by analyzing automatic dependent surveillance-broadcast data as well as avionics data obtained from the airline’s flight data monitoring department for that specific flight and link the observations to the warnings triggered by the aircraft to alert the flight crew while encountering RFI.

Global navigation satellite system (GNSS) integrity monitoring (IM) has been introduced in aviation, but remains challenging for urban scenarios because of limited satellite visibility and strong multipath and non-line-of-sight effects. Consequently, factors such as limited measurement redundancy and inaccurate uncertainty modeling significantly compromise positioning and IM performance. To alleviate these issues, this paper proposes an integrity-constrained factor graph optimization model for GNSS positioning augmented by switch variables. In contrast to conventional IM methods, this method enhances redundancy through the factor graph structure. Instead of directly excluding measurements, the proposed method reweights the measurements by using switch variables to satisfy a chi-square test constraint within the optimization, ultimately yielding optimal positioning accuracy. Moreover, a proper protection level that conservatively bounds the positioning error can be derived by using the modified weighting matrix under a single-fault assumption. The effectiveness of the proposed method was verified based on data sets collected in open-sky and urban-canyon areas in Hong Kong.

This study addresses the practical challenges associated with real-time kinematic relative navigation for cube satellites (CubeSats) performing rendezvous missions in a low Earth orbit (LEO). Considering the limitations of CubeSats, we propose a method to achieve precise centimeter-level relative navigation using single-frequency Global Positioning System (GPS) measurements. By using GPS visibility and minimizing errors in the LEO, our approach eliminates the need for additional sensors. We employed range-domain differential GPS with a Hatch filter to enhance the pseudorange accuracy. Double-difference integer ambiguities were resolved epoch-by-epoch using the least-squares ambiguity decorrelation adjustment (LAMBDA) technique without filters, to ensure efficiency. The algorithm was applied to CubeSat hardware, integrating cycle-slip detection and CubeSat-tailored ground plane designs. Simulations validated the algorithm’s performance in LEO, and its real-world efficacy was evaluated through ground-based measurements in an open-sky environment. Considering hardware constraints, our method demonstrates the feasibility of achieving centimeter-level relative navigation for CubeSats, effectively and economically addressing a crucial need in autonomous space missions.

For low-Earth-orbit (LEO) satellites, high-precision clock estimation often depends on high-precision real-time global navigation satellite system (GNSS) products. Thus, service providers often choose to downlink observation data to the ground to achieve high accuracy. To relieve this burden for future LEO mega-constellations, this study investigates the performance of relative clocks and orbits determined between LEO satellites using the phase common-view (PCV) method. The PCV results are compared with results from three other single-satellite-based clock and orbit determination methods. Using real data from the Gravity Recovery and Climate Experiment (GRACE) Follow-On satellites and three different types of real-time GNSS products, the PCV method can deliver a relative clock precision below 0.2 ns and a relative orbital user range error of approximately 5 cm, even when using the broadcast ephemeris, whereas all three other methods encountered sharp degradations in their results when using degraded real-time GNSS products.

Network real-time kinematic (NRTK) coverage is defined as the area inside a station network. In conventional NRTK, the distance between stations is limited to 100 km, thus restricting the coverage of NRTK. In this study, we propose the utilization of an ionospheric-free combination and the application of a Kriging weighting model to mitigate tropospheric delay to extend the coverage of NRTK through network expansion. A network with station distances exceeding 100 km was constructed, and the residual errors, along with the success-fix rate of integer ambiguities, were analyzed on both sunny and rainy days to confirm the potential for network expansion using the proposed method. The results confirm that the success-fix rate increased by up to 44.3% on rainy days, compared with that of the traditional interpolation method. Furthermore, a high level of performance in integer ambiguity resolution can be maintained within the expanded network, regardless of the weather conditions.

An integral step in an ultra-wideband localization network installation is determining the positions of the fixed infrastructure nodes, the anchors. This process is time-consuming and usually requires specialized equipment. Additionally, it is difficult to achieve scalability, as any change or addition in the network requires a redetermination of the affected anchors. One can automate this process by utilizing the distance-measuring capabilities of the network infrastructure and employing a distributed position estimation algorithm, such as the consensus subgradient (CSG) algorithm. Yet, the CSG suffers from scalability issues due to high problem dimensionality and data-sharing bottlenecks in practical applications. Consequently, implementation in embedded devices is difficult. In this article, we propose a modification of this algorithm, the neighborhood CSG, which aims toward embedded implementation by local reduction of the problem dimensions without hindering the precision of the original CSG algorithm or its convergence rate.

Tightness remains the primary goal in all modern estimation bounds. For very weak signals, tightness is enabled by appropriately selecting the prior probability distribution and bound family. While current bounds in global navigation satellite systems (GNSSs) assess the performance of carrier frequency estimators under Gaussian or uniform assumptions, the circular nature of frequency is overlooked. Of all bounds in the Bayesian framework, the Weiss–Weinstein bound (WWB) stands out because it is free from regularity conditions or restrictions on the prior distribution. Therefore, the WWB is extended for the current frequency estimation problem. A divide-and-conquer type of hyperparameter tuning method is developed to mitigate issues of computational complexity for the WWB family while enhancing tightness. Synthetic results show that for a von Mises prior probability distribution, the WWB provides a bound up to 22.5% tighter than the Ziv–Zakaï bound when the signal-to-noise ratio varies between –3.5 dB and –20 dB, where the GNSS signal is deemed extremely weak.

Watermarking signal authentication is a technique in which a global navigation satellite system (GNSS) provider cryptographically perturbs the spreading code to allow for limited cryptographic authentication of a signal. Several proposals and studies have been presented or are underway to augment GNSS signals with this capability. This work reintroduces a generalized combinatorial watermarking function that affords a flexible pathway to cryptographically prove the authentication security of a signal with receiver observables under certain assumptions. The security levels are comparable to those of standard cryptographic security (e.g., 128-bit security) and require little or no additional use of the navigation data bandwidth. We show how our methods can be applied to signals of different designs and signal-to-noise ratios. With our receiver processing strategy, one can design a watermarking signal authentication scheme and the accompanying receiver to have high confidence in a signal’s authenticity.

This tutorial presents the factor graph, a recently introduced estimation framework that is a generalization of the Kalman filter. An approach for constructing a factor graph, with its associated optimization problem and efficient sparse linear algebra formulation, is described. A comparison with Kalman filters is presented, together with examples of the generality of factor graphs. A brief survey of previous applications of factor graphs to navigation problems is also presented. Source code for the extended Kalman filter comparison and for generating the graphs in this paper is available at https://github.com/cntaylor/factorGraph2DsatelliteExample.

This paper develops an asynchronous measurement processing technique for sequential filtering that effectively handles small errors in the measurement sampling epoch within a linearized framework. The derived method relaxes the assumption that sensing systems generate and communicate measurements instantaneously and suggests a linearized method for extracting information from latent measurements via a temporal measurement update that considers uncertainty in the measurement acquisition epoch. To investigate performance, numerical simulations are performed utilizing the consider/neglect extended Kalman filter framework applied to a lunar descent-to-landing scenario in which latent vision-based measurements with uncertain acquisition times are used to navigate the vehicle. Through Monte Carlo simulation and analysis, this paper shows that the presented approach can be used to maintain filter consistency for latent measurements with low measurement-time uncertainties. Furthermore, an error budget and sensitivity analysis are presented to provide insight into the impact of the measurement-time uncertainty on navigation performance.

The deterministic errors of an accelerometer comprise the prevailing i) bias, ii) scale factor, and iii) non-orthogonality. Together, these errors result in a nonlinear measurement model, which is conventionally solved via an iterative nonlinear least-squares method. In contrast to the conventional approach, we propose a novel method to transform the above nonlinear model into a system of linear equations, resulting in an exact, closed-form solution of the deterministic errors. The developed mathematical formulations are first verified in a simulation setting, followed by a real-time implementation using Robot Operating System for small micro-electromechanical inertial measurement units.

ION promotes the research of journal authors in a variety of ways including video abstracts hosted on the ION website. The latest video abstracts are documented below. You can find the video abstract for any recently published article under the article’s supplemental menu item on the journal’s website. ION also engages with the PNT community, through its webinar series, to highlight current topics of interest to the community. The most recent webinar is also documented below.

CubeSats hold promise for various applications, but their viability in demanding missions such as future low Earth orbiting position, navigation, and timing (LEO-PNT) systems hinges on higher orbital accuracy and reliable attitude information. To address these challenges, we present an array-aided combined precise orbit and attitude determination model with an optimal solution. In the estimation process, multi- and affine-constrained models are used to precisely determine the attitude, and then, highly precise observations for an antenna array are reconstructed based on fixed ambiguities and a decorrelation step. Validations confirm the significance of integer ambiguities in the model, highlighting the cost-effectiveness of this model compared with star trackers for attitude determination. The reconstructed observations outperform the original observations, leading to improved orbital components, with the three-dimensional root mean square (RMS) equal to 4.1 cm. The observation residuals are smoother, with an RMS of 6 mm, half of that obtained via a single antenna. The developed models offer great potential for CubeSats, advancing their orbit and attitude determination capabilities.

Distribution-to-distribution point cloud registration algorithms are fast and interpretable and perform well in unstructured environments. Unfortunately, existing strategies for predicting the solution error for these methods are overly optimistic, particularly in regions containing large or extended physical objects. In this paper, we introduce the iterative closest ellipsoidal transform (ICET), a novel three-dimensional (3D) lidar scan-matching algorithm that re-envisions the normal distributions transform (NDT) in order to provide robust accuracy prediction from first principles. Like NDT, ICET subdivides a lidar scan into voxels in order to analyze complex scenes by considering many smaller local point distributions; however, ICET assesses the voxel distribution to distinguish random noise from deterministic structure. ICET then uses a weighted least-squares formulation to incorporate this noise/structure distinction while computing a localization solution and predicting the solution-error covariance. To demonstrate the reasonableness of our accuracy predictions, we verify 3D ICET in three lidar tests involving real-world automotive data, high-fidelity simulated trajectories, and simulated corner-case scenes. For each test, ICET consistently performs scan matching with sub-centimeter accuracy. With this level of accuracy, combined with the fact that the algorithm is fully interpretable, this algorithm is well suited for safety-critical transportation applications. Code is available at https://github.com/mcdermatt/ICET.

Reference stations constitute important elements within the global navigation satellite system (GNSS) infrastructure, as they provide valuable measurements for performance monitoring. For high-quality measurements from such stations, local error sources should be properly characterized and compensated for or minimized. Multipath remains a major contributor to these errors. In severe occurrences, multipath can cause critical errors in sensitive systems such as those utilized for code-dependent applications. This paper discusses a method for GNSS multipath characterization in challenging installation scenarios, based on a dual-polarization antenna and its integration in a hybrid measurement–simulation framework. A dedicated dual-polarized probe, which houses both an effective geodetic antenna and a multipath-susceptible antenna, was designed, manufactured, and assessed. The dual-sensing nature of the probe allows auxiliary information to be acquired about multipath generated by nearby objects and can be used to infer a plausible range of expected multipath-induced code error at a GNSS sensor station. In addition, a ray-tracing method is discussed, in which antenna measurements are integrated into digital-twin simulations of installations for characterizing multipath conditions. Finally, this study demonstrates that by combining the DPA with digital-twin simulations, it is possible to predict multipath error bounds at an installation in advance. This combined technique presents a flexible tool that is useful for planning system performance with respect to multipath, site layout/selection, and even optimal receiving antenna placement at a given installation. The proposed simulative method is validated through field experiments, and tests with commercial geodetic-grade antennas are presented to confirm the capability of this method to predict their performance ranges.

We argue the merits of having a simplified method to simulate equatorial plasma bubble (EPB) plume structures for practical usage. The capability to realistically model EPB plume structures in simulations would be advantageous when assessing the severity of ionospheric threats. Such advantages would arise because a realistic model of EPB plume structures could allow nonstationary scintillation signals to be simulated. Although EPB plume structures can be modeled via first-principle physics-based models, these models tend to be computationally demanding. High-performance computing facilities might be able to offer some remedy, but serious handicaps would remain for those without access to such advanced facilities. We investigated multiple options that utilize the diffusion-limited aggregation (DLA) fractal process to generate bifurcating structures that resemble typical EPB plume structures. We combined the DLA algorithm with the International Reference Ionosphere model to simulate EPBs in three dimensions. Initial tests of this modeling approach indicate promising results.

With advancements in the broadcast ephemeris accuracy of global navigation satellite systems (GNSSs), precise point positioning based on broadcast ephemeris (BE-PPP) is gradually showing promising prospects. However, the periodic updates of GNSS ephemeris result in discontinuities in the satellite orbit and clock offset during handovers. These discontinuities can significantly impact positioning accuracy. In this study, we calculate the combined ephemeris discontinuities, which indicate a linear combination of satellite radial orbit and clock discontinuities. We then compensate for the combined ephemeris discontinuities in the subsequent satellite clocks prior to positioning. For BeiDou Navigation Satellite System 3 (BDS-3) and the Global Positioning System (GPS), the three-dimensional (3D) position accuracy in kinematic mode is improved by 30–50 cm, reaching 33.9 cm. For GPS/Galileo/BDS-3 triple-constellation kinematic solutions, the accuracy reaches 23.2 cm. In static mode, the 3D position accuracy is 14.6 cm for BDS-3-only positioning and 15.1 cm for GPS. For GPS/Galileo/BDS-3 triple-constellation static BE-PPP solutions, the 3D position accuracy improves to 8 cm.

A ground-based augmentation system (GBAS) is a critical component in civil aviation that augments the Global Positioning System (GPS) in providing precision approach and landing capabilities with guaranteed accuracy and integrity. The GBAS ground facility broadcasts a parameter known as svig to the aircraft, which is used to compute vertical protection levels for evaluating navigation integrity. svig represents the standard deviation of the vertical ionospheric gradients, which bounds the spatial gradients under nominal conditions. Although the time-step method has been widely utilized to estimate ionospheric spatial gradients, this strategy suffers from temporal effects. In this paper, an improved time-step method is developed for separating temporal gradients from spatial gradients using observation data collected from the Hong Kong Satellite Positioning Reference Station Network. We investigated two parameters: stg, which bounds the standard deviation of temporal gradients, and svig. The results show that a constant value of 5.5 mm/km can serve as an upper bound for all stg values. However, the results of svig vary seasonally, with maximum and minimum values occurring at the equinoxes and summer, respectively. To reflect this seasonality, quadratic polynomial expressions, given as functions of the day of the year, were derived to provide an upper bound for all svig values.

Interference events, both intentional and unintentional, are significant threats to global navigation satellite system (GNSS) service continuity. In the presence of interference, it can be difficult for GNSS receivers to maintain continuous tracking of carrier phase and frequency. To address this issue, in place of a traditional phase-locked loop (PLL), we develop and validate a new estimation-based approach to allow GNSS receivers to correctly estimate carrier phase and frequency under conditions of low carrier-to-noise power. An adaptive Kalman filter forms the core of the estimator, with a multiple-model algorithm to account for discrete navigation data bit transitions. The performance of the estimator in the presence of wideband interference is validated through simulation and experiment, showing performance markedly superior to that of a PLL.

As time goes on, quantum computing has become more of a reality, bringing several cybersecurity challenges. Modern cryptography is based on the computational complexity of specific mathematical problems; however, as new quantum-based computers are developed, classical methods might not be sufficient to secure communications. In this paper, we analyze the state of the Galileo open service navigation message authentication (OSNMA) to overcome these new threats. This analysis and its assessment have been performed using OSNMA documentation, where we have reviewed the available post-quantum cryptography (PQC) algorithms competing in the National Institute of Standards and Technology standardization process and assessed the possibility of OSNMA implementation in the Galileo service. The main barrier to adopting PQC approaches is the size of both the signature and the key. This analysis shows that OSNMA is not yet capable of facing quantum threats and that significant changes are required. This work concludes by assessing different transitory countermeasures that can be implemented to sustain the system’s integrity in the short term.

Utilizing broadband low Earth orbit satellite signals in an opportunistic manner for navigation is becoming increasingly popular. This paper deals with a particularly useful approach for navigation based on satellite signals of opportunity, which uses carrier Doppler-shift observables. We provide analytically derived and simplified formulas for the Jacobian involved in the numerical computation of the navigation solution and derive a global navigation satellite system-like dilution-of-precision metric that can be used to assess accuracy. A numerical study provides preliminary computational results.

This paper presents an innovative approach aimed at enhancing satellite position determination accuracy within a geostationary equatorial orbit (GEO) by integrating a regional navigation satellite system (RNSS) with a global navigation satellite system (GNSS). In a GEO, incoming GNSS signals are typically constrained to a specific direction on the other side of the Earth, resulting in a significant dilution of precision (DOP) and, consequently, a significant radial error. By incorporating an RNSS, signals from more diverse directions are available, improving observability and enhancing navigation precision. Taking the quasi-zenith satellite system (QZSS) as a representative RNSS, this paper demonstrates the feasibility of receiving signals from GEO satellites across a substantial range. Link budget analyses were conducted using the precise side-lobe patterns of the QZSS, revealing that QZSS signals can be consistently observed across most arcs in a GEO. Two comprehensive simulations were conducted: a point solution and an extended Kalman filter-based orbit determination. The results affirm the anticipated improvement in navigation precision indicated by the DOP analysis. It is essential to note that whereas RNSS signals can be received from any longitude in a GEO, enhanced navigation precision relies on the distance from the satellite to the RNSS. Considering the availability of multiple RNSS options, the concept presented in this research can be adapted to any longitude within a GEO, thereby promoting stable, high-precision navigation.

This paper presents a constant-envelope modulation scheme, based on a synthesized binary offset carrier (SBOC), for a global navigation satellite system (GNSS) that combines three signals in a nonlinear fashion with unequal amplitudes. The proposed SBOC modulation meets the power spectral density criteria of multiplexed binary offset carrier (MBOC) modulation used in the L1 frequency band (1575.42 MHz) open civilian service interoperable signals for GNSS. This SBOC modulation also allows for the selection of an arbitrary power-sharing ratio between the data and pilot signals. This approach provides better performance than various MBOC(6, 1, 1/11) modulations for narrowband receivers.

To protect civilian Global Positioning System (GPS) users from spoofing, the Air Force Research Lab has developed the chips-message robust authentication (Chimera) signal enhancement for the GPS L1C signal. With Chimera, standalone receivers that only have access to the GPS signal will be able to authenticate their received measurements once every 3 min, whereas users with access to an out-of-band source will be able to perform authentication once every 1.5 or 6 s. However, moving receivers typically rely on much faster real-time GPS update rates of 1–20 Hz. In this work, we design a spoofing-resilient filter framework that provides continuous and secure state estimation between Chimera authentication times. By leveraging self-contained sensors on-board the vehicle, such as an inertial measurement unit or wheel encoder, as well as the periodic Chimera authentication, our proposed filter determines how much to rely on the received unauthenticated GPS measurements for state estimation. In this respect, our filter relies more extensively on GPS measurements in order to improve real-time navigation performance and reduce localization errors when GPS signals are authentic, while successfully mitigating spoofing-induced errors during an experienced attack. We experimentally validate our proposed spoofing-resilient filter in a simulated test environment for a ground vehicle model with access to the 3-min Chimera channel, under various simulated spoofing attack scenarios. To the best of the authors’ knowledge, this is the first adaptive filter proposed for Chimera that continuously leverages real-time GPS measurements in a spoofing-resilient manner.

Vertical navigation is crucial for safe aircraft separation and has been traditionally based on the pressure altitude provided by barometric altimeters. New aviation operations require robust determination of geodetic altitude and are expected to primarily rely on a global navigation satellite system (GNSS). Because deviations between pressure and geodetic altitudes can reach hundreds of meters, an altitude harmonization is needed to use barometers in combination with GNSS. In this paper, we first present a methodology to compute an accurate geodetic altitude from barometer and external weather data. Secondly, we derive error and threat models of this geodetic altitude. Finally, we employ these models within a GNSS integrity monitoring algorithm augmented with the derived altitude. We assess our methodologies against flight test measurements and availability simulations of localizer performance with vertical guidance operations. These analyses illustrate the potential benefits of employing barometers as augmentation or stand-alone systems for geodetic altitude navigation.

The concept of the signal-in-space (SIS) root-mean-square (RMS) user range error (URE) is used to evaluate the performance of multiple global navigation satellite systems (GNSSs); however, a complete analytical derivation has not been published. This article describes the instantaneous SIS URE and the instantaneous SIS RMS URE, explains the role of the instantaneous SIS RMS URE in evaluating the statistical accuracy of GNSS signals, and provides an analytical derivation of the instantaneous SIS RMS URE. This derivation is then compared to the equations found in various papers and performance standards to illustrate how the equations, although appearing different, actually measure the same quantity with differing constraints.

This paper proposes a strategy for improving ionospheric detection of threatening conditions, motivated by issues with ground-based augmentation systems (GBASs) at low latitudes. A methodology is developed for a real-time alerting system that monitors the ionosphere state using surrounding ground stations and sends alerts to differential global navigation satellite systems services when threatening conditions are detected. The method is based on time-step gradients and data gap analysis to detect ionospheric disturbances and to declare periods for affected satellite signals to be unavailable. Validation was performed with real data using the largest observed gradients from the Brazilian ionospheric threat model. The results demonstrate that the method is effective, detecting the vast majority of previously known threatening gradients. An availability assessment was also performed to assess for a loss of availability resulting from the implementation of this technique. Applications of the developed technique include the improvement of low-latitude nighttime GBAS availability.

We introduce an algorithm that provides robust three-dimensional orientation of a smartphone for pedestrian indoor localization. The algorithm focuses on integration of the magnetometer and a reformulated observation model such that the influence of magnetic anomalies is mitigated. The methodological novelty of this approach lies in the use of an extended Kalman filter (EKF), based on a state vector that contains only the slow-varying systematic deviation components of the magnetometer. We apply a statistical test to the EKF residuals to detect the presence of magnetic anomalies and update the absolute heading when beneficial conditions prevail. Otherwise, the heading is propagated based on gyroscope observations. We investigate the properties of the proposed algorithm by using simulated smartphone sensor observations with different scenarios of systematic deviations. In experiments with very accurate ground truth, the proposed algorithm achieves a root mean square error of 17.4° for the computed heading, outperforming state-of-the-art algorithms by at least 40%.

This paper quantifies an error source that limits the accuracy of lidar scan matching, particularly for voxel-based methods. Lidar scan matching, which is used in dead reckoning (also known as lidar odometry) and mapping, computes the rotation and translation that best align a pair of point clouds. Perspective errors occur when a scene is viewed from different angles, with different surfaces becoming visible or occluded from each viewpoint. To explain perspective anomalies observed in data, this paper models perspective errors for two objects representative of urban landscapes: a cylindrical column and a dual-wall corner. For each object, we provide an analytical model of the perspective error for voxel-based lidar scan matching. We then analyze how perspective errors accumulate as a lidar-equipped vehicle moves past these objects.

Taking the work conducted by the global navigation satellite system (GNSS) software-defined radio (SDR) working group during the last decade as a seed, this contribution summarizes, for the first time, the history of GNSS SDR development. This report highlights selected SDR implementations and achievements that are available to the public or that influenced the general development of SDR. Aspects related to the standardization process of intermediate-frequency sample data and metadata are discussed, and an update of the Institute of Navigation SDR Standard is proposed. This work focuses on GNSS SDR implementations in general-purpose processors and leaves aside developments conducted on field programmable gate array and application-specific integrated circuit platforms. Data collection systems (i.e., front-ends) have always been of paramount importance for GNSS SDRs and are thus partly covered in this work. This report represents the knowledge of the authors but is not meant as a complete description of SDR history.

This paper presents estimates of surface reflectivity (SR) over time of global navigation satellite system (GNSS) signals scattered from a partially frozen lake surface. A portable ground-based GNSS reflectometry sensor system that collects both scattered global positioning system L1 signals and independent validation data (lidar and camera) was deployed on the Lake Michigan waterfront in Chicago at a time when the lake surface was a mixture of ice and water. Lidar surface scans were merged with camera images and mapped, along with estimated reflection zones. For three satellites whose reflection points scan across ice and water over time, the relative SR and mean red intensity (differentiating ice from water) of camera pixels inside the first Fresnel zone were computed and shown to be correlated. This system concept will be used in the future for more complete mapping of phase changes of snow and ice in the cryosphere.

This paper proposes a visual map-based position and heading estimation system that is invariant to image rotation and consistent over time, which is achieved by exploiting the radial and azimuthal distributions of semantic segments. To characterize the specific position and heading, a novel concept termed “visual semantic context” is applied, which collects semantics in a polar-coordinated fashion in collaboration with measures of discrepancy. The system then matches visual semantic contexts: one from a semantically segmented aerial image aided by deep learning technology and others from a semantics-labeled database. Two-stage minimization alleviates the expensive computation of an exhaustive search. The first stage marginalizes the heading and coarsely searches for positions. At the same time, the Kolmogorov–Smirnov test significantly reduces the search domain by rejecting unlikely candidates, and the second stage refines the estimates. Numerical experiments show that the proposed algorithm fixes the position and heading, is invariant to image rotation, and is also robust to imprecise scale information.

This paper investigates how global navigation satellite systems (GNSSs) and inertial navigation systems (INSs), when appropriately augmented by ranging from local landmarks, can safely navigate vehicles through a real-world urban environment. We begin by considering safety requirements for driverless vehicles under fault-free assumptions and developing measurement models for multi-sensor integrated navigation systems using an extended Kalman filter. The critical elements of urban navigation are then discussed, including individual INS noise parameter specifications, vehicle speed, and the effect of velocity updates. Covariance analyses performed along a 9-km-long urban transect in downtown Chicago show that velocity updates measured by wheel speed sensors, vehicle kinematic constraints, and zero-velocity updates can extend navigation continuity by bridging intermittent GNSS signal availability. However, position reference updates at intervals between 15 and 35 m, based on light detection and ranging data from local landmarks in our case, are needed to achieve full navigation availability through the transect.

This study investigates the impact of antenna group delay variation (AGDV)-induced error on advanced receiver autonomous integrity monitoring. We model the AGDV error contribution not only as a measurement bias but also as a random process sigma term in protection-level computations by using AGDV errors analyzed within the European Dual Frequency Multipath Model for Aviation (DUFMAN) project. We also apply the new multipath and AGDV error models developed for aviation use to assess the availability of localizer performance with vertical guidance down to 200 feet. The results show that the fraction of users with =99.5% availability increases by approximately 5% when the newly derived DUFMAN models are used. In contrast, considering the AGDV effect alone as the worst-case bias has a weaker impact at the current user range accuracy standard.

In this article, we describe a new method for detecting global navigation satellite system (GNSS) spoofing using an inertial navigation system. We specifically address the most difficult-to-detect scenario, in which a spoofer replicates the authentic GNSS signal with only additive errors due to the spoofer’s uncertainty in knowledge of the target’s position. We derive an optimal monitor to detect the anomalous temporal structure of the spoofed measurements caused by the spoofer’s target tracking errors. This new monitor uses accumulated Kalman filter innovations projected into the position state domain. We demonstrate how the monitor window length can be set to achieve any required missed detection probability, and we evaluate the performance of the monitor for both white and colored tracking error. Finally, we present a complementary solution separation monitoring concept to detect rapid-onset spoofing and to achieve protection levels in real time.

The Iris software radio has been updated to collect one-way Doppler and range data for potential use with deep space autonomous navigation. One-way radiometric data have found limited use because a typical radio oscillator is not sufficiently stable for use in navigation. However, Iris has been paired with a chip-scale atomic clock (CSAC) via an input signal of one pulse per second. With superior stability relative to a typical oscillator, the CSAC has the potential to provide onboard tracking data with sufficient accuracy to support a small satellite mission with modest navigation requirements. In this paper, we develop models of the Iris radio one-way Doppler and range data and analyze their performance in lab testing prior to a future inflight test on NASA’s CAPSTONE mission to the Moon. The test results confirm theoretical predictions for range precision measured between 0.38 m and 2.21 m with a range rate of 11 mm/s at 60 s.

There is a growing interest in the use of legacy terrestrial Global Positioning System (GPS) signals to determine the precise positioning and timing onboard a lunar satellite. Unlike prior works that utilize pseudoranges with meter-level accuracy, we propose a precise positioning and timekeeping technique that leverages carrier-phase measurements with millimeter-level accuracy (when integer ambiguities are correctly fixed). We design an extended Kalman filter framework that harnesses the intermittently available terrestrial GPS time-differenced carrier-phase (TDCP) values and gravitational accelerations predicted by the orbital filter. To estimate the process noise covariance, we implement an adaptive state noise compensation algorithm that adapts to the challenging lunar environment with weak gravity and strong third-body perturbations. Additionally, we perform measurement residual analysis to discard TDCP measurements corrupted by cycle slips and increased measurement noise. We present Monte-Carlo simulations of a lunar satellite in an elliptical lunar frozen orbit and quasi-frozen low lunar orbit, wherein we showcase higher positioning and timing accuracy as compared with the pseudorange-only navigation solution.

This paper investigates the application of a vector tracking approach to carrier phase tracking for improved tracking in degraded signal environments. In contrast to many vector-based carrier phase tracking approaches, the algorithms described in this paper do not rely on local loop filters to maintain phase lock. A relative position vector estimate, fixed-integer carrier ambiguities, and measurements from the base station are used to drive the carrier replica. To test carrier phase tracking approaches, Monte Carlo simulations were performed to compare the performance of a real-time kinematic (RTK) vector phase-locked loop (VPLL) approach with the performance obtained by scalar tracking. In these simulations, the RTK-VPLL maintains phase lock at carrier-to-noise density ratios 4 to 7 dB-Hz lower than the scalar tracking receiver. The proposed algorithms were tested using live sky data, and the RTK-VPLL performance was compared with the performance of a commercial global positioning system receiver. Significant reductions in carrier cycle slips and loss of lock were observed in moderate-foliage environments.

The issue of user privacy in the context of collaborative positioning is addressed in this work, wherein information is passed between and processed by multiple cooperative agents, with the goal of achieving high levels of positioning accuracy. In particular, this paper discusses three privacy-preserving schemes in the context of differential global navigation satellite system (GNSS)-based and GNSS-based cooperative positioning methods. The discussed architectures provide the same positioning results, while yielding different levels of privacy to the cooperative users. These architectures also involve increased complexity as privacy grows and as non-encrypted, encrypted, and homomorphically encrypted solutions are implemented. The latter scheme is the most computationally demanding; however, it provides the highest level of privacy by employing homomorphic encryption, whereby addition and multiplication operations may be performed on encrypted data to produce encrypted outputs, without revealing information about the collaborative agent’s location. The proposed privacy-preserving cooperative position schemes are shown to provide the same results as their non-privacy-preserving counterparts, while providing privacy guarantees. Based on this analysis, some of the proposed solutions can be considered for real-time applications, while homomorphic encryption is a valid solution for latency-tolerant applications. Advances in computing power will increase their overall usability in the near future.

Smartphone receivers comprise approximately 1.5 billion global navigation satellite system receivers currently manufactured worldwide. Smartphone receivers provide measurements with lower signal levels and higher noise than commercial receivers. Because of constraints on size, weight, power consumption, and cost, it is challenging to achieve accurate positioning with these receivers, particularly in urban environments. Traditionally, global positioning system measurements are processed via model-based approaches, such as weighted least-squares and Kalman filtering approaches. While model-based approaches can provide meter-level positioning accuracy in a postprocessing manner, these approaches require strong assumptions on the corresponding noise models and require manual tuning of parameters such as covariances. In contrast, learning-based approaches have been proposed that make fewer assumptions about the data structure and can accurately model environment-specific errors. However, these approaches provide lower accuracy than model-based methods and are sensitive to initialization. In this paper, we propose a hybrid framework for learning position correction, which corresponds to the offset between the true receiver position and the estimated position. For a learning-based approach, we propose a graph convolution neural network (GCNN) that can learn different graph structures with multi-constellation and multi-frequency signals. For better initialization of the GCNN, we use a Kalman filter to estimate a coarse receiver position. We then use this coarse receiver position to condition the input features to the graph. We test our proposed approach on real-world data sets from the Google Smartphone Decimeter Challenge and show improved positioning performance over model-based methods such as the weighted least-squares and Kalman filter methods.

This paper describes the design, analysis, and experimental evaluation of a new landmark-based localization method that integrates light detection and ranging (lidar) with an inertial measurement unit (IMU). We develop a tight IMU/lidar integration scheme that exploits the complementary properties of the two sensors to facilitate safety risk evaluation. Lidar localization updates limit the IMU error drift over time while IMU data improve lidar position and orientation (or pose) prediction, thereby reducing the risk of incorrectly associating perceived features with mapped landmarks. In addition, lidar return-light intensity measurements are incorporated to better distinguish landmarks and to further reduce the risk of incorrect associations. We analyze the integrity performance of the localization algorithm using an automated testbed that generates analytical and empirical pose estimation error distributions.

Global navigation satellite system (GNSS) signal reflection over buildings degrades positioning performance in urban canyons. Different three-dimensional (3D) mapping-aided (3DMA) GNSS algorithms have been proposed, which utilize 3D building models to aid in positioning. Recently, the candidate-based 3DMA GNSS framework has been applied to examine evenly spaced distributed particles. The particles that best match the observed measurements, that is, with the minimum cost, are identified as the receiver location. However, such particle sampling approaches incur a high computational load and are not robust. In this study, a Kriging-based interpolation method is applied to model the cost function of a 3DMA GNSS based on sampled particles, and the modeled cost function is then integrated with Doppler measurements through factor graph optimization. The regressed model can reduce the computational load by sparsely distributing the particles. Designed experiments with smartphone and commercial-level GNSS receivers demonstrate that the positioning performance can achieve a root mean square error of less than 10 m in Hong Kong and New York City urban canyons.

To protect civilian global positioning system (GPS) users from spoofing attacks, the U.S. Air Force Research Lab has proposed the chips-message robust authentication (Chimera) enhancement for the L1C signal. In particular, the Chimera fast channel allows users to authenticate the received GPS signal once every 1.5 or 6 s, depending on the out-of-band source utilized for receiving the fast channel marker keys. However, for many moving receiver applications, receivers often use much higher GPS measurement rates, at 5–20 Hz. In this work, we derive a stochastic reachability (SR)-based detector to perform continuous GPS signal verification and state estimation between Chimera authentications. Our SR detector validates the received GPS measurement against any self-contained sensor, such as an inertial measurement unit, in the presence of bounded biases in the sensor error distributions. We demonstrate via Monte Carlo simulations that our detector satisfies a user-defined false alarm requirement during nominal conditions, while successfully detecting a simulated spoofing attack. We further demonstrate that our SR state estimation filter successfully bounds the true state during both authentic and spoofed conditions.

This paper focuses on a heterogeneous redundant inertial navigation system (INS) that consists of one three-axis rotation-modulation fiber optic gyroscope (FOG) INS and one strapdown ring laser gyroscope (RLG) INS. A novel co-calibration method is proposed to estimate the FOG scale factor instability and RLG bias instability error in real time, in which the geometric constraints of the FOG-INS rotating axis are deployed to establish the observation equation without external reference information. In addition, the proposed method has a global navigation capability, which is achieved by using the normal vector of the earth ellipsoid and the state transformation extended Kalman filter to predict positioning errors. An output position error compensation method is used without disturbing the original INSs. Simulation and physical experiment results show that the positioning error of the heterogeneous redundant marine INS is reduced by more than 30% over 300 h of navigation.

Generalized binary offset carrier (BOC) modulations and global navigation satellite system (GNSS) meta-signals require advanced processing algorithms to overcome problems associated with their multi-peaked correlation functions. In this paper, bicomplex numbers are introduced for GNSS signal representation and for algorithm development. Bicomplex numbers generalize complex numbers and are characterized by four real components. These numbers have the potential to represent multicomponent signals, such as GNSS meta-signals, leading to a compact notation that allows effective derivations and algorithm development. Moreover, bicomplex numbers allow one to express a meta-signal as the product of a code, a carrier, and a subcarrier component: this representation leads to acquisition and tracking algorithms that are capable of effectively processing GNSS meta-signals, thus solving the code ambiguity problem. Theoretical developments are demonstrated using real data collected using software-defined radio front-ends for the Galileo alternative BOC modulation and the BeiDou B1I/B1C meta-signal.

Radio frequency interference (RFI) in global navigation satellite system (GNSS) frequencies can endanger human life and safety by preventing the use of these signals for navigation and positioning, in addition to degrading measurements for science applications. Here, we use data from the Cyclone GNSS (CYGNSS) constellation to map GNSS RFI from 2017 to 2022, identify the location of several potential sources of RFI, and quantify the duration of transmission. Although our method of RFI detection can only provide a rough approximation of transmitter positions, it is possible that advanced data processing techniques could better pinpoint their locations, once guided by these observations. We find that, since the launch of CYGNSS, GNSS jammers have proliferated across the world and are often associated with the beginnings of geopolitical unrest. Our results agree well with previous studies that have also used satellite observations to map ground-based RFI transmission.

This study introduces a navigation integrity and continuity algorithm against an inertial measurement unit (IMU) sensor fault within a Kalman filter (KF) that ensures a high level of safety for IMU-integrated safety-critical navigation applications. A representative example of an IMU integrated navigation system is a global navigation satellite system (GNSS)/IMU system. Most previous studies have focused on GNSS faults when evaluating the integrity and continuity of a KF-based GNSS/IMU navigation system, leaving the IMU fault hypothesis unaddressed. Unlike GNSS, which is applied in the measurement update step within the KF, IMU measurements are applied in the state prediction step, which results in different fault propagation characteristics in the user state error compared with those in GNSS. This paper analytically derives the sequential IMU fault impacts on user state errors. Based on this investigation, a KF innovation-based fault detector and protection-level equations are developed, which can safely bound user state errors against sequential IMU fault impacts.

There has been a growing interest in using small satellites (SmallSats) for a future lunar navigation and communication satellite system (LNCSS). We conceptualize the design of a SmallSat-based LNCSS with Earth-global positioning system (GPS) time transfer that provides navigation and communication services near the lunar south pole. A hybrid constellation design is formulated, wherein all satellites provide navigation services while only a fraction are communication-enabled. Using Systems Tool Kit software, we examine various LNCSS case studies based on an elliptical lunar frozen orbit with a lower-grade chip-scale atomic clock. Case studies are evaluated in terms of (1) navigation considerations, including position and timing accuracy, lunar user equivalent ranging error, and dilution of precision, (2) communication considerations, including data volume, availability, and data rate, and (3) SmallSat factors, including cost, size, weight, and power. We performed a trade-off analysis for satisfying the criteria outlined by international space agencies while designing low-cost, low-SWaP lunar constellations.

In this paper, we present a spatiotemporal deep learning (STDL) network to conduct binary phase scintillation forecasting at a high-latitude global navigation satellite systems (GNSS) station. Historical measurements from the target and surrounding GNSS stations are utilized. In addition, external features such as solar wind parameters and geomagnetic activity indices are also included. The results show that the STDL network can adaptively incorporate spatiotemporal and external information to achieve the best performance by outperforming a naive method, three conventional machine learning algorithms (logistic regression, gradient boosting decision tree, and fully connected neural network) and a machine learning algorithm known as long short-term memory that incorporates temporal information.

Accurate positioning in urban canyons remains a challenging problem. To facilitate the research and development of reliable and precise positioning methods using multiple sensors in urban canyons, we built a multisensory dataset, UrbanNav, collected in diverse, challenging urban scenarios in Hong Kong. The dataset provides multi-sensor data, including data from multi-frequency global navigation satellite system (GNSS) receivers, an inertial measurement unit (IMU), multiple light detection and ranging (lidar) units, and cameras. Meanwhile, the ground truth of the positioning (with centimeter-level accuracy) is postprocessed by commercial software from NovAtel using an integrated GNSS real-time kinematic and fiber optics gyroscope inertial system. In this paper, the sensor systems, spatial and temporal calibration, data formats, and scenario descriptions are presented in detail. Meanwhile, the benchmark performance of several existing positioning methods is provided as a baseline. Based on the evaluations, we conclude that GNSS can provide satisfactory results in a middle-class urban canyon if an appropriate receiver and algorithms are applied. Both visual and lidar odometry are satisfactory in deep urban canyons, whereas tunnels are still a major challenge. Multisensory integration with the aid of an IMU is a promising solution for achieving seamless positioning in cities. The dataset in its entirety can be found on GitHub at https://github.com/IPNL-POLYU/UrbanNavDataset.