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Changjiang Geng Chenghe Fang Zhigang Hu Xiaoli Song Lei Chen Zhipeng Wang, Yilun Cui

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 × 10–5 level. Furthermore, a general discussion of Pconst and bnom is presented, with some recommendations.

Kaila M. Y. Coimbra, Marta Cortinovis, Tara Mina et al.

The National Aeronautics and Space Administration (NASA) Endurance rover mission concept is designed to enable the exploration and collection of samples along a 2000-km traverse within the Moon’s South Pole-Aitken (SPA) impact basin. Precise geotagging of these samples will be critical to the mission’s scientific objectives, which include characterizing the Solar System’s chronology and the Moon’s geological evolution. Concurrently, the European Space Agency (ESA) and Surrey Satellite Technology Ltd. (SSTL) are partnering to launch the Lunar Pathfinder satellite to provide communication services to lunar surface users, including the NASA Endurance rover. To enable precise absolute localization of the rover throughout its 2000-km traverse, we have investigated the achievable position estimation by opportunistically leveraging the Doppler shift observables from the Lunar Pathfinder’s downlink communication signals with no navigation payload. With only one satellite available, we accumulated Doppler shift measurements over time while the rover was stationary and refined the rover’s position estimate through a weighted batch filter framework. Through simulations, we modeled the effects of Doppler shift measurement uncertainty, which includes the frequency error of the rover clock as well as errors due to carrier tracking as a function of the carrier-to-noise ratio C/N0. The state estimation performance is evaluated at different key locations of the SPA basin under varying degrees of satellite ephemeris uncertainty and clock stability. With this framework of using the Doppler shift as the only navigation observable, we find that the Lunar Pathfinder is able to opportunistically localize the Endurance rover with sub-10-m accuracy, on average, within two orbital periods of the Lunar Pathfinder. To the best of the authors’ knowledge, this paper is the first to examine the achievable localization of a lunar surface asset using only a single satellite that is not equipped with a navigation payload.

William Konyk, Alex Smith, Bob Wong et al.

With the release of a new International Terrestrial Reference Frame (ITRF) in April 2022, the National Geospatial-Intelligence Agency (NGA) began the process of aligning the World Geodetic System 1984 Terrestrial Reference Frame (WGS 84 TRF) to the latest ITRF realization. The resulting realization, WGS 84 (G2296), represents the seventh such update using Global Positioning System measurements in 30 years. This work outlines the historical development of WGS 84, documents a new technique adopted by NGA in 2021 to maintain alignment between WGS 84 and the latest ITRF, provides transformation parameters between recent WGS 84 TRF realizations, and assesses the accuracy of WGS 84 TRF relative to the ITRF. We demonstrate that for high-accuracy users, the two frames have empirically remained within 3 cm of each other over the past decade.

Mathieu Joerger, Ali Hassani, Matthew Spenko et al.

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.

Junesol Song, Carl Milner, Heekwon No

Currently, surface movement, encompassing all operations on the airport surface prior to take-off and after landing, cannot be achieved under low-visibility conditions by an aircraft-guidance-only solution. In addition to surface movement radar and Automatic Dependent Surveillance–Broadcast, pilots also rely on signage, lighting and reports/commands from the airport traffic control tower, which are partly based on visual inspection of the airport, to aid in guidance from the runway to the gate. Therefore, low-visibility conditions caused by meteorological effects can significantly affect the continuity of operations on the airport surface. Global navigation satellite systems are considered to overcome these difficulties by enhancing guidance and situational awareness on the airport surface. This paper explores the feasibility of utilizing a ground-based augmentation system, which is potentially available at the airport, an inertial navigation system, and relative receiver autonomous integrity monitoring to support surface movement operations in low-visibility conditions. The paper provides results assessing the compliance of the proposed solution to accuracy and integrity requirements.

Hanjoon Shim, Changdon Kee

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.

Rong Yang, Jihong Huang, Xingqun Zhan

The collaborative efforts of multi-frequency receivers have proven to be a significant advantage in the challenging environments of global navigation satellite system carrier tracking. This paper delves into the exploration of multi-carrier hybrid tracking, employing both phase-locked loop and frequency-locked loop observations to maximize tracking capability. This hybrid approach conducts distributed phase tracking and centralized Doppler frequency tracking within decoupled local filters to accommodate the frequency dispersion and reduce dimensionality. Subsequently, global assimilation is performed to adjust filter weights for performance optimization. Theoretical analysis affirms that this hybrid design can achieve tracking performance close to optimality when compared with classic centralized estimation, significantly outperforming fully distributed approaches. Additionally, simulations of ionospheric scintillation validate the effectiveness of the proposed hybrid carrier tracking design.

Ali Hassani, Mathieu Joerger

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.

Hengwei Zhang, Yiping Jiang, Ling Yang

To support the operation of advanced receiver autonomous integrity monitoring (ARAIM), an integrity support message indicating a minimum performance level of satellite constellation is required for aircraft navigation. With BDS-3 providing worldwide service since July 2020, it is desirable to undertake a detailed study on its signal-in-space range error characteristics and prior fault probabilities for ARAIM. The latest accuracy criteria released by the China Satellite Navigation Office in May 2021 is validated by the 27 MEO and IGSO satellites in orbit from July 2020 to June 2021, in which 10 single satellite faults were identified and analyzed in detail with no constellation fault found. Based on this one-year data, the probability of single satellite faults and constellation faults can be initially set as 8x10^(-5) and 1x10^(-3), respectively, for BDS-3 in ARAIM.

Xuezhi Wang, Christopher Gilliam, Allison Kealy et al.

Robust aiding of inertial navigation systems in GNSS-denied environments is critical for the removal of accumulated navigation error caused by the drift and bias inherent in inertial sensors. One way to perform such an aiding uses matching of geophysical measurements, such as gravimetry, gravity gradiometry or magnetometry, with a known geo-referenced map. Although simple in concept, this map-matching procedure is challenging: The measurements themselves are noisy, their associated spatial location is uncertain, and the measurements may match multiple points within the map (i.e., non-unique solution). In this paper, we propose a probabilistic multiple-hypotheses tracker to solve the map-matching problem and allow robust inertial navigation aiding. Our approach addresses the problem both locally, via probabilistic data association, and temporally by incorporating the underlying platform kinematic constraints into the tracker. The estimated platform position from the output of map matching is then integrated into the navigation state using an unscented Kalman filter. Additionally, we present a statistical measure of local map information density — the map feature variability — and use it to weight the output covariance of the proposed algorithm. The effectiveness and robustness of the proposed algorithm are demonstrated using a navigation scenario involving gravitational map matching.

A. Khodabandeh, P.J.G. Teunissen

Carrier phase signals are considered among the key observations in global navigation satellite systems (GNSSs) and several other high-precision interferometric measurement systems. However, these ultra-precise measurements are not fully exploited when the integerness of their inherent ambiguities is discarded during the estimation process. Provided that the integer-estimable functions of their phase ambiguities are properly identified, integer ambiguity resolution (IAR) can be utilized to benefit their parameter solutions. For the GNSS code division multiple access systems with transmitters that broadcast carrier phase signals on identical frequencies, these integer-estimable functions have been characterized and are well-known as double differenced ambiguities. However, this is not the case with “frequency-varying” carrier phase signals that are broadcast by GLONASS satellites, Low-Earth-Orbiting communication satellites, or cellular long-term evolution (LTE) transmitters. This study aims to present full-rank models that can be used to identify integer-estimable ambiguity functions, thereby bringing the observation equations of frequency-varying carrier phase measurements into an IAR-applicable form. Our analytical results are supported by several numerical examples, including GNSS and terrestrial-based IAR as well as a new set of “inter-frequency” integer ambiguities that this study discovers in Galileo multi-frequency carrier phase signals.

Jiale Wang, Fu Zheng, Yong Hu et al.

The prevalence of inexpensive global navigation satellite system (GNSS) chips that facilitate the performance of carrier phase measurements has provided hardware that can be used as the foundation for implementing precise point positioning (PPP) of low-cost smartphones. However, because of the atmospheric delays and high measurement noise associated with low-quality patch antennae, the convergence time of smartphone PPP can increase from minutes to even hours. By establishing the Satellite-based Ionospheric Model (SIM) and Real-time Tropospheric Grid Point (RTGP) models, we aim to achieve instantaneous sub-meter level positioning for smartphone PPP. In both kinematic and static experiments, Xiaomi Mi8 and Huawei P40 smartphone signals can converge to sub-meter accuracy in the horizontal direction within one to six seconds when adopting multi-constellation and dual-frequency PPP solutions augmented by precise atmospheric corrections. The atmospheric augmentation PPP method effectively improves the convergence speed and positioning accuracy compared to what can be achieved using the conventional PPP algorithm, thereby satisfying smartphone users’ demand for rapid and high-accuracy positioning.

Randa Natras, Andreas Goss, Dzana Halilovic et al.

The ionospheric refraction of GNSS signals can have an impact on positioning accuracy, especially in cases of single-frequency observations. Ionosphere models that are broadcasted by the satellite systems (e.g., Klobuchar, NeQuick-G) do not include enough details to permit them to correct single-frequency observations with sufficient accuracy. To address this issue, regional ionosphere models (RIMs) have been developed in several countries in the western Balkans based on dense Continuous Operating Reference Stations (CORS) observations. Subsequently, a RIM for the western Balkans was built using an artificial neural network that combined regional ionosphere parameters estimated from the CORS data with spatiotemporal (latitude, longitude, hour of day), solar (F10.7) and geomagnetic (Kp, Dst) parameters. The RIMs were tested at the solar maximum (March 2014), a geomagnetic storm (March 2015), and the solar minimum (March 2018). The new RIMs mimic the integrated electron density much more effectively than the Klobuchar model. Furthermore, RIMs significantly reduce the ionospheric effects on single-frequency positioning, indicating their necessity for use in positioning applications.

Richard B. Langley

Welcome to the Summer 2023 issue of NAVIGATION. In this issue, we feature several articles on GNSS precise point positioning or PPP including its augmentation by additional sensors, articles on optimizing position estimation in environments with significant multipath, on the uncertainties in Coordinated Universal Time, on improving real-time ionospheric delay prediction, and much, much more.

Jef Bauwens

Xingya Zhao, Yixiong He, Liwen Huang et al.

Collision prevention is critical for navigational safety at sea, which has developed rapidly in the past decade and attracted a lot of attention. In this article, an improved velocity obstacle (IVO) algorithm for intelligent collision avoidance of ocean-going ships is proposed in various operating conditions, taking into count both a ship’s manoeuvrability and Convention on the International Regulations for Preventing Collisions at Sea (COLREGs). An integrated model combines a three-degree-of-freedom manoeuvring model with ship propeller characteristics to provide a precise prediction of ships in various manoeuvring circumstances. In the given case, what is different to present studies, this improved algorithm allows for decision-making in two ways: altering course and changing speed. The proposed technique is demonstrated in a variety of scenarios through simulation. The findings reveal that collision-avoidance decision-making can intelligently avoid collisions with the target ships (TSs) in multi-ship situations.

Yoav Baumgarten, Mark L. Psiaki, David L. Hysell

The performance of a proposed high-frequency (HF) navigation concept is analyzed using simulated data. The method relies on pseudorange and beat carrier-phase measurements of signals that propagate in the ionosphere along curved trajectories, where signals are refracted back downwards from the ionosphere. It has been demonstrated that the location of a receiver can be determined if several signals, broadcast from beacons at different locations, are received and processed at a user receiver. A challenge of determining exact signal paths is the uncertainty in the ionosphere’s electron density distribution. This is addressed by a batch filter that simultaneously estimates the receiver position along with corrections to a parametric model of the ionosphere. A previous paper developed the theory and batch filter for this concept. The present study examines its potential performance. Total horizontal position errors on the order of tens to hundreds of meters are achieved, depending on the case’s characteristics.

Sriramya Bhamidipati, Grace Gao

For robust GPS-vision navigation in urban areas, we propose an integrity-driven landmark attention (ILA) technique via stochastic reachability. Inspired by cognitive attention in humans, we perform convex optimization to select a subset of landmarks from GPS and vision measurements that maximizes integrity-driven performance. Given known measurement error bounds in non-faulty conditions, our ILA technique follows a unified approach to address both GPS and vision faults and is compatible with any off-the-shelf estimator. We analyze measurement deviation to estimate the stochastic reachable set of positions associated with each landmark, which is parameterized via probabilistic zonotope (p-zonotope). We apply set union to formulate a p-zonotopic cost that represents the size of position bounds based on landmark inclusion/exclusion. We jointly minimize the p-zonotopic cost and maximize the number of landmarks via convex relaxation. For an urban data set, we demonstrate improved localization accuracy and robust predicted availability for a pre-defined risk and alert limit.

Tobias Bamberg, Andriy Konovaltsev, Michael Meurer

Global navigation satellite systems (GNSSs) are the most significant service for global positioning and timing. The high relevance and wide spread of these systems contrast with the risk for interference or even manipulations of GNSS signals. One specific threat is GNSS spoofing. A spoofer counterfeits satellite signals to mislead the receiver to an erring position/time estimation. The technological progress enabling affordable and easy-to-use spoofer hardware further increases the relevance of this threat. To maintain the integrity of the position/time information, it is mandatory to be able to assess the errors induced by spoofing. The paper at hand derives a bound of the code tracking bias in relevant spoofing scenarios extending the well-known Multipath Error Envelope. These new bounds can be used as a tool to estimate the position/time error, especially but not exclusively for receivers that are collateral damage of a spoofing attack.

Chun Yang, Andrey Soloviev, Ananth Vadlamani et al.

A coherent combining and long coherent integration (CCLCI) scheme is presented for standalone direct acquisition of binary offset carrier (BOC) signals under strong radio frequency interference (RFI). To mitigate the ambiguity of BOC signals, a split-spectrum method extracts the upper and lower sidebands of a BOC signal, treats them separately as two binary phase shift keying (BPSK) signals, and finally combines the results to recover the loss due to splitting. The CCLCI scheme burns through strong interference by building up the desired weak signal while averaging out noise and interference. It exploits all information available (L1 and L2, upper and lower sidebands, odd and even chips, and I- and Q-components) by applying coherent combining across signal components and long coherent integration over time, followed by noncoherent accumulation if necessary. Issues and enabling techniques are described. The results of an embedded implementation in demonstration with a GPS RF simulator are analyzed.