In this paper, we develop and evaluate two new methods to derive high-integrity models of measurement error time correlation from experimental data. These models enable the determination of sequential estimation error variance bounds in safety-critical navigation applications such as aircraft localization based on global navigation satellite systems and inertial navigation systems. We achieve tight bounding models from empirical data based on lagged product distributions instead of autocorrelation functions in the time domain and based on scaled periodogram distributions instead of power spectra in the frequency domain. We bound these distributions using first-order Gauss-Markov process (FOGMP) models, which provide a means to account for error time correlation and can be easily incorporated in linear estimators. To determine bounding models, we identify theoretical probability density functions of lagged products and derive the cumulative distribution function of scaled periodograms for FOGMPs. We implement and evaluate these two methods using simulated samples and experimental Global Positioning System data collected in a mild multipath environment.
The robust interference mitigation (RIM) framework offers a promising solution to jamming attacks on global navigation satellite system (GNSS) receivers. By identifying interfered samples as outliers in the selected transform domain, RIM operates without relying on jamming waveform assumptions. This paper adapts RIM for GNSS snapshot architectures, assessing the impact of low-bit quantization on receiver performance under continuous wave (CW) and chirp interference. Using simulated data, snapshot RIM demonstrates significant improvements, achieving gains of 10, 20, and 35 dB in detected satellites for 2-, 4-, and 8-bit quantization in the presence of CW jamming. We also analyze the effect of quantization on the effective jammer-to-noise ratio, waveform distortion, and robust variance estimation. An experiment with realistic recordings shows that snapshot RIM achieves a 20-dB gain in the carrier-to-noise ratio over a professional receiver. Finally, a 24-h specifications test supports the feasibility of RIM integration in snapshot receivers with a maximum time-to-first-fix increase of 0.31 s.
This paper proposes and evaluates a novel approach for wide area multilateration (WAM) airspace surveillance based on time difference of arrival (TDOA) navigation. Unlike commercial Automatic Dependent Surveillance-Broadcast (ADS-B)-based WAM solutions, which require high-grade clock synchronization, the framework proposed here achieves airspace surveillance without the need for highly stable clocks or time synchronization between ground stations. In the proposed approach, aircraft 3D positions and velocities and the relative clock offsets of the receivers are estimated consistently using an extended Kalman filter (EKF). The accuracy of the 3D aircraft position estimates was tested using simulated ADS-B messages across a variety of different ground station network configurations.
Modern global navigation satellite system L5/E5a code families offer improved correlation properties, with lower auto-correlation sidelobes and cross-correlations, compared with legacy Global Positioning System L1 coarse/ acquisition (C/A) codes. However, these codes encounter unique L5/E5a interference environments, particularly those including interference due to pulses from distance-measuring equipment and tactical air navigation systems. In civil aviation, temporal blanking is the assumed countermeasure. In temporal blanking, incoming samples are set to zero when the peak envelope power exceeds a threshold, blanking the codes within the sampled signals and affecting their correlation with non-blanked replicas. Through extensive simulations, this study analyzes L5/E5a code properties under blanking duty cycle (bdc) values of 0%-75% over a 1-ms integration time. Results indicate reduced auto-correlation and cross-correlation protections, although these effects remain superior to those of L1 C/A codes until bdc reaches approximately 60%. Further increases in bdc to 75%, likely due to increasing air traffic, diminish these advantages. Additionally, simulations show that Doppler residuals have a minimal impact on L5/E5a correlation properties.
cations, including precise navigation during aircraft approach and landing. However, signal interference near airports can severely impair operational availability and integrity, and traditional methods for interference detection are generally costly and time-consuming to implement over large areas. In this paper, we develop a novel algorithm that uses Automatic Dependent Surveillance- Broadcast (ADS-B) reports, which are routinely transmitted by aircraft and publicly available, to estimate interference power and the geographic location of a GNSS interference source. We then test the algorithm on recorded ADS-B transmissions from a 2022 interference event at Denver International Airport (KDEN). Results show that the algorithm successfully detects interference and localizes the source within a 0.1-degree error margin in latitude and longitude. Unlike previous interference detection methods, our algorithm also quantifies uncertainty through error bounds and probability heatmaps, enhancing the reliability and interpretability of the results. Overall, this algorithm can help narrow the ground search area and support the physical shutdown of GNSS interference sources.
The realization of the advanced receiver autonomous integrity monitoring (ARAIM) algorithm relies on integrity support data (ISD). To support the use of the BeiDou Navigation Satellite System (BDS) in ARAIM applications, the ISD parameters for BDS are analyzed. Global averages and worst-case signal-in-space ranging errors (SISREs) are computed using data from July 2020 to July 2022. The data cover three open signals: B1I, B1C, and B2a, which are committed for civilian aviation uses. The complementary Gaussian cumulative distribution function is used to bound the SISREs of different signals for all satellites. The results show that the global SISRE values are less than 0.6 m (root mean square) for B1I, B1C, and B2a signals, and the worst-case SISRE can be bounded by a zero-mean Gaussian distribution with a standard deviation of 4.0 m at the 4.0 x 10-5 level. Furthermore, a general discussion of Pconst and bnom is presented, with some recommendations.
Several organizations, including NASA and the European Space Agency, have initiated plans for establishing lunar navigation satellite systems (LNSSs). This effort is driven by surging interest in the Moon as a platform for scientific discovery and staging area for future missions beyond Earth orbit. Near-Earth missions benefit from GNSSs, which have been refined over decades and are capable of real-time, sub-meter level positioning. For GNSS systems, the navigation community and managing organizations, such as the U.S. Department of Defense (in the case of GPS), have precisely characterized the error sources inherent in pseudorange and range-rate measurements in Earth’s vicinity. Here, we draw parallels between errors in current GNSSs and those expected in future cislunar navigation systems. We identify key differences between the terrestrial and lunar environments and propose methods to accurately quantify the resulting measurement errors. Specifically, we develop techniques for constructing a time-varying error budget for pseudorange and pseudorange-rate measurements near the Moon and then test these techniques using arbitrary system and signal configurations.
This paper develops a navigation accuracy metric for magnetic navigation when adapted to civil aviation. Metrics that are currently used may not directly apply to magnetic navigation because the assumptions behind these metrics are based on the statistics of more conventional navigation modalities where the uncertainty distribution in the horizontal plane is typically radially symmetric. Magnetic navigation challenges these assumptions. New standard deviation limits based on the probability of exceedance of radial error are derived. Use is made of quadratic forms over random variables, specifically the Hoyt distribution and its associated probability density function and cumulative density function. Although the density functions lack closed-form solutions, new approximations for this distribution are utilized in order to make rapid computation possible, enabling their use for navigation purposes. When used in conjunction with robust numerical methods, the new approach accurately calculates the bounds on error distributions that would meet the requirements associated with Performance Based Navigation.
The time-differenced carrier phase can be computed from measurements recorded by a multi-global navigation satellite system software-defined radio receiver such as PyChips, from which the user displacement and receiver clock drift can be solved. PyChips is able to simultaneously track authentic and inauthentic signals in separate channels, which makes it possible to observe both types of measurements with corresponding navigation data. A random sample consensus algorithm has been introduced to assess the consistency between the measurements and data. This algorithm successfully separated authentic channels from inauthentic channels when they are broadcast simultaneously.
Accurate estimations of differential code biases (DCBs) are critical for producing absolute ionospheric measurements using global navigation satellite system observables. DCB estimation generally requires translating slant total electronic content (TEC) measurements to the vertical domain using a mapping function. Analyzing DCB estimates from regional modeling and global ionospheric maps (GIMs) over 4.5 years reveals significant DCB differences across different mapping functions, varying by a few nanoseconds. Decompositions of receiver DCB estimates show that for some mapping functions, such as the Jet Propulsion Lab extended slab function and the 350-km thin shell function, variations in DCB estimate over time can be largely accounted for by temperature and ionospheric activity. In contrast, other mapping functions, such as the 450-km thin shell function, exhibit significantly less variation over time. Our computational and analytical results suggest the importance of selecting an appropriate mapping function for accurate DCB and TEC estimation from GIMs and shell-based spatiotemporal models.
Although the issue of global navigation satellite system (GNSS) interference has been addressed in the community of satellite navigation, the extent of GNSS interference in the past couple of years has raised serious concerns for air and marine transportation. This paper assesses GNSS interference based on observations of the TRITON GNSS reflectometry (GNSS-R) payload. The TRITON GNSS-R payload contains a navigation unit and a science unit that are designed to receive direct line-of-sight and scattered GNSS signals, respectively. In the presence of radio-frequency interference, these two units experience different phenomena, including navigation disruptions, spoofed localization, and degradation of GNSS-R performance. This paper describes the effects of interference, analyzes the observation data, and elucidates the interference characteristics. Analyses of GNSS interference based on space data are believed to be instrumental for providing information concerning the frequency, location, and severity of interference and for developing interference-resistant techniques.
As a step toward founding the new field of lidar integrity, this paper compiles a list of lidar faults, threats, anomalies, and challenges – which we collectively label adversities. Engineers will eventually need to characterize and mitigate these adversities for rigorous quantification of lidar integrity. Lidar adversities manifest at the intersection of environment, hardware, and algorithms. By extension, the specific design approach or architecture of a lidar system, as well as its application, must be specified to define a complete set of adversities and resulting measurement-error distributions, including operationally hazardous errors. To this end, we focus on the application of absolute positioning for high-integrity roadway operations and identify three promising lidar architectures for that application. In comparing and contrasting these architectures, we review the broader literature to identify associated lidar adversities, and we provide a perspective on how those adversities might be mitigated in the future.
This paper presents a new data association method for bounding the integrity risk in landmark-based localization in ground transportation applications. Data association is the process of assigning currently-sensed landmark features to features that were previously observed or mapped. Most association methods use a nearest-neighbor criterion based on the normalized innovation squared (NIS). In contrast, we derive a new, closed-form, compact association criterion based on projections of the extended Kalman filter’s innovation vector. These innovation projections (IP) capture the impact of wrong associations on both the magnitude and direction of the innovation vector. We evaluate our newly derived IP method using simulated and experimental data for inertial-aided LiDAR localization in both indoor and outdoor environments. Compared to NIS, the proposed IP method (a) reduces the risk of wrong associations and (b) tightens the bound on predicted integrity risk.
Unmanned aerial vehicles often rely on the Global Positioning System (GPS) for navigation. GPS signals, however, are very low in power and can be easily jammed or otherwise disrupted. This paper presents a method for estimating the navigation errors present at the beginning of a GPS-denied period using data from a synthetic aperture radar (SAR) system. These errors are estimated by comparing an online-generated SAR image with a reference image obtained a priori. The distortions relative to the reference image are exploited by a convolutional neural network to learn the initial navigation errors, which can be used to recover the true flight trajectory throughout the synthetic aperture. The proposed neural network approach is able to learn to predict the initial errors on both simulated and real SAR image data.
This paper presents CoNaV, a comprehensive framework for creating a multi-vehicle cooperative localization (CL) testbed designed to support the benchmarking, development, and deployment of cooperative navigation algorithms. Given the essential role of CL in improving localization accuracy for both defense and civilian applications, CoNaV provides a robust environment for rigorously validating algorithms under real-world conditions. By establishing a benchmark for CL algorithms, CoNaV lays a foundation for advancing research into more sophisticated and distributed CL solutions. This framework highlights the potential of cooperative navigation to enhance multi-vehicle operations and offers a scalable, practical approach for future developments in CL technology.
Combinatorial watermarking can help establish trust in global navigation satellite system (GNSS) signals. In combinatorial watermarking, the GNSS provider elects to secretly invert a subset of ranging code chips and then later distributes those inversions to receivers. From these ranging code perturbations, receivers can use signal statistics to determine the authenticity of the signal. In previous work, we demonstrated how one can design combinatorial watermarking schemes and derive the distributions of receiver statistics to ensure low probabilities of missed detection and false alarm, assuming that an adversary does not attempt to estimate the watermarked chips and replay. In this work, we extend the analysis of combinatorial watermarking to adversaries capable of engaging in security code estimation and replay (SCER) attacks. We derive the distributions of our statistics for defense against SCER-capable adversaries. Provided a bound on the estimation capability of the SCER-capable adversary, one can use this work to design a combinatorial watermarking scheme that meets security requirements.
Rotation modulation technology in inertial navigation systems (INS) can effectively suppress the divergence of navigation errors, thereby enhancing long-endurance navigation accuracy. However, established INS calibration methods do not fully account for non-orthogonality between the dual rotation axes, which may couple with other errors and degrade overall navigation performance. To address this issue, this paper develops a mathematical model that accounts for axis non-orthogonality and analyzes its effects on system behavior. Based on this model, the paper proposes a calibration scheme that mitigates the effect of non-orthogonality without the need for special alignment procedures. Simulation-based and experimental results demonstrate that the proposed approach effectively reduces attitude and velocity errors under both static and rotation modulation conditions. The proposed method thus represents a significant improvement in long-term navigation accuracy compared to traditional calibration methods.
In the context of global navigation satellite systems (GNSSs), synchronization is crucial for successfully decoding the navigation message and accurately estimating pseudoranges. Synchronization of each received GNSS signal typically involves at least two tracking loops: a delay lock loop (DLL) and a phase lock loop (PLL). The reception of a spoofed signal disrupts the synchronization process, potentially leading to erroneous pseudorange estimation or loss of service. This paper investigates the impact of spoofing on code, carrier phase, and frequency tracking estimates and proposes a transformation-based strategy to characterize the joint DLL and PLL under spoofing, focusing on the system’s stable equilibria (SE), linearity and interdependence, transient response, and noise impact. The study reveals the nonlinearity and interdependence of the tracking loops (i.e., the PLL and DLL cannot be considered separately) and shows the emergence of multiple SE, leading to potential chaotic behavior and bifurcation.
This paper presents a novel concept for orbit determination and time synchronization of a lunar radio navigation system. The proposed approach is based on small ground antennas that simultaneously track the entire constellation using K-band frequency links, implementing the concept of multiple spacecraft per aperture. This configuration ensures sufficient data rates and provides high accuracy in Doppler, range, and single-beam interferometry observables, enabling a precise orbit determination. We assess the achieved time transfer accuracies using both the standard asynchronous two-way satellite time and frequency transfer and a novel time transfer method that leverages onboard code epoch time-stamping and precise spacecraft range information. We propose a structure for the navigation message as well as a reference frame and associated time scale for user positioning. We complete the analysis by estimating the attainable accuracies of the signal-in-space error.
In the BDS-3 constellation, only the B3I signal is used to compute the broadcast clock offset. However, because advanced receiver autonomous integrity monitoring (ARAIM) uses dual-frequency measurements, the time group delay (TGD) must be considered in BDS-3-based ARAIM applications. The existing BDS-3 error model is therefore not sufficient to describe the actual TGD error encountered by aviation users. Specifically, the estimated signal-in-space error underestimates the actual error, which cannot be bounded by the estimated user range accuracy and nominal bias. This inaccuracy results in a loss of integrity. To avoid this risk, this paper develops a separated Gaussian model to bound the TGD error for BDS-3 in ARAIM. Using a one-year data set, this paper characterizes and bounds the TGD error for different signal combinations. Of the tested combinations, the B1C/B2a signal combination resulted in the smallest standard deviation of 0.78 m and a corresponding bias component of 0.71 m. We suggest that this signal combination be adopted for use in ARAIM.
