Advanced Receiver Autonomous Integrity Monitoring Research Articles

Improved protection level for the solution-separation ARAIM based on worst-case fault bias searching

The aviation community is actively pursuing advanced receiver autonomous integrity monitoring (ARAIM) to enhance the safety of aircraft navigation services. Protection level calculation is a crucial task in the solution separation-based ARAIM as it determines the availability of the ARAIM. Accurately determining the worst-case fault bias (WCFB) is beneficial in improving the bounding tightness of protection level on positioning error. Unfortunately, the WCFB determination is a challenging task that requires a time-consuming searching procedure, especially when dealing with the multi-satellite faults. The traditional ARAIM protection level is achieved by constructing a conservative worst-case positioning error bound to avoid the unacceptable time-consumption of the brute-force searching for multi-satellite WCFBs. However, this approach comes at the cost of losing the tightness of the protection level and the availability of the ARAIM. The ARAIM milestone reports have pointed out that the availability of the baseline ARAIM needs to be continuously improved in order to satisfy the worldwide localizer precision vertical 200 (LPV-200) requirements. In response, this paper proposes a novel multi-satellite WCFBs searching method for the ARAIM to improve the tightness of protection level. The method consists of determining the worst-case fault direction and constructing an efficient WCFBs searching procedure. GPS/Galileo dual-constellation simulation result demonstrates that the proposed method not only can improve the availability of ARAIM up to 9.33% when compared with the baseline ARAIM algorithm, but also achieves comparable computation efficiency.

Impact Analysis of Satellite Geometry Variation on ARAIM Integrity Risk over Exposure Interval

Accurate integrity risk evaluation is of significance in ensuring that aviation navigation applications satisfy the predefined integrity requirement. The integrity risk evaluation method over a specified exposure interval has been proposed in previous works for the development of advanced receiver autonomous integrity monitoring (ARAIM) (ARAIM technical subgroup reference airborne algorithm description document v4.1, 2022). However, this method typically relies on an underlying optimistic assumption that the satellite geometry remains constant throughout the exposure interval. The variation in satellite geometry due to potential satellite outages undermines the widely-used geometry constant assumption. Thus, we investigate the influence of satellite geometry variations throughout the exposure interval on the integrity performance by introducing a geometry-sensitive risk-evaluation model. The findings demonstrate that, under the nominal situation, the region where the ARAIM fails to meet predefined integrity requirement could expand by a maximum of 2.93% when accounting for satellite geometry variations. Furthermore, in the situation of a single satellite outage, this hazardous region has significantly expanded from 13.12% of the global coverage to 66.82%. Based on these findings, we recommend that the ARAIM should consider satellite outages as a critical factor in real-time integrity risk evaluation.

Effect of User Antenna Group Delay Variation Error on Advanced RAIM

Effect of User Antenna Group Delay Variation Error on Advanced RAIM

An Improved Adaptive Simulated Annealing Particle Swarm Optimization Algorithm for ARAIM Availability

Civil aviation transportation equipment is more convenient and faster than other transportation tools and is an essential part of intelligent transportation. It is significant to study the reliability of positioning information and enhance traffic safety. Advanced receiver autonomous integrity monitoring (ARAIM) can provide vertical guidance during the different navigation stages in civil aviation fields. The traditional multiple hypothesis solution separation (MHSS) algorithm distributes the probability of hazardous misleading information (PHMI) and probability of false alarm (PFA) uniformly over all visible satellites resulting in reduced global availability of ARAIM. Aiming at this problem, we proposed an adaptive simulated annealing particle swarm optimization (ASAPSO) algorithm to redistribute integrity and continuity risks and establish a protection level optimization model. Based on the real BeiDou navigation satellite system/global positioning system (BDS/GPS) data, the experimental results show that the optimized algorithm can reduce the vertical protection level (VPL), and the ARAIM global availability of BDS/GPS is improved by 1.73%∼2.73%. The optimized algorithm can improve the availability of integrity monitoring at different stages of the navigation system and provide a basis for ensuring the reliability of the positioning results.

Opportunistic Autonomous Integrity Monitoring for Enhanced UAV Safety

An opportunistic advanced receiver autonomous integrity monitoring (OARAIM) algorithm for unmanned aerial vehicle (UAV) navigation is developed. This algorithm fuses ambient terrestrial signals of opportunity (SOPs) with global navigation satellite system (GNSS) signals to improve the capability of detecting GNSS and SOP measurement faults and provide tight protection level (PL) bounds. A receiver is assumed to make pseudorange measurements on multiple GNSS satellites and terrestrial SOPs. Experimental tests are presented injecting simulated faults into the OARAIM algorithm, which successfully detects the faults in GPS satellites and SOPs. Moreover, the OARAIM algorithm and the inclusion of the SOPs reduces the vertical and horizontal PLs by more than 55% and 70%, respectively, compared to only using GNSS measurements.

Integrity monitoring scheme for single-epoch GNSS PPP-RTK positioning

Integrity monitoring for precise point positioning is critical for safety-related applications. With the increasing demands of high-accuracy autonomous navigation for unmanned ground and aerial vehicles, the integrity monitoring method of high-precision positioning has become an essential requirement. While high precision Global Navigation Satellite Systems (GNSS) positioning is widely used in such applications, there are still many difficulties in the integrity monitoring method for the multi-frequency multi-GNSS undifferenced and uncombined Precise Point Positioning (PPP). The main difficulties are caused by using the measurements of multiple epochs in PPP. Based on the baseline Multiple Hypothesis Solution Separation (MHSS) Advanced Receiver Autonomous Integrity Monitoring (ARAIM) algorithm, this paper discusses the feasibility of the pseudorange-based baseline ARAIM method on the single-epoch PPP based on Real-Time Kinematic (RTK) networks (PPP-RTK) framework to overcome these difficulties. In addition, a new scheme is proposed to transfer the conventional PPP process into the single-epoch PPP-RTK framework. The simulation results using the proposed model are analyzed in this study. The Protection Levels (PLs) estimated by PPP Wide-lane Ambiguity Resolution (PPP-WAR) model with regional corrections can reach the meter level and the PLs estimated by PPP Ambiguity Resolution (PPP-AR) and PPP-RTK models are usually the sub-meter level. Given a horizontal Alert Limit (AL) of 1.5 m, the global coverage of availability above 99.9% for PPP-WAR, PPP-AR, and PPP-RTK can reach 92.6%, 99.4%, and 99.7% respectively. The results using real kinematic data also show that tight PLs can be achieved when the observation conditions are good.

Integrity monitoring scheme for undifferenced and uncombined multi-frequency multi-constellation PPP-RTK

The precise point positioning (PPP)-based real-time-kinematic (RTK) method attracts increasing attention from both academia and industry because of its potential for high accuracy positioning with a shorter convergence time compared to the traditional PPP. Besides high accuracy, integrity monitoring (IM) is indispensable for safety–critical real-time land vehicle and aviation applications. As the traditional advanced receiver autonomous integrity monitoring (ARAIM) method is designed for (smoothed) pseudorange-based positioning, the complexity of multi-frequency multi-constellation PPP-RTK using carrier phase measurements has not been given sufficient consideration. This study proposes an IM scheme for multi-frequency multi-constellation uncombined PPP-RTK applying the ARAIM theory, with a new comprehensive threat model to accommodate not only pseudorange measurements, but also carrier phase measurements, and other fault events arising from the network corrections that support PPP-RTK. Characteristics of different types of faults are analyzed with the aid of numerical experiments. In addition, the impact of ambiguity-fixed solutions on PPP-RTK integrity performance is investigated. The authors have also conducted case studies, including static and real-kinematic positioning experiments. Experiments have demonstrated that fast convergence in accuracy and the position error bounds, or protection levels, with a given integrity risk, in horizontal position components of PPP-RTK could be achieved. For the open sky environments on a highway, the protection levels estimated by PPP-RTK solutions have the potential to meet the alert limit requirement for road transportation using ambiguity-fixed PPP-RTK positioning under the assumption that the risks of wrong ambiguity fixing are very small and can be ignored.

Implementation and analysis of fault grouping for multi-constellation advanced RAIM

The aviation community is pursuing multi-constellation Advanced Receiver Autonomous Integrity Monitoring (ARAIM) to offer safe aircraft navigation services. The computational issue of ARAIM becomes critical when multiple constellations are involved and Fault Exclusion (FE) is enabled. This paper proposes an implementation of fault grouping to improve the efficiency of multi-constellation ARAIM and to benefit navigation performance. To potentially accommodate most ARAIM services, we consider both ARAIM Fault Detection (FD) and ARAIM Fault Detection and Exclusion (FDE) scenarios. In addition, given the difference between Vertical ARAIM (V-ARAIM) and Horizontal ARAIM (H-ARAIM), the implementation steps of fault grouping for V-ARAIM and H-ARAIM are respectively described. More importantly, unlike most of the prior approaches that were limited to dual-constellation scenarios, our implementation can support up to four constellations. The implementation of fault grouping is evaluated using multiple sets of simulations, which are carried out as a function of the number of constellations, prior fault probabilities, error models, and operational services. The results suggest that in most cases, the proposed implementation of fault grouping can effectively reduce the ARAIM computational load while benefiting or maintaining the navigation performance.

Sequential advanced receiver autonomous integrity monitoring method considering the optimal sample size

The integrity monitoring performance of Receiver Autonomous Integrity Monitoring (RAIM) degrades when insufficient satellites are visible, which may cause RAIM to fail to support the approach procedure with vertical guidance service. We propose a sequential advanced receiver autonomous integrity monitoring (S-ARAIM) method to improve the integrity monitoring capability and availability. We first introduce a sample size to a dominant snapshot technique, advanced RAIM (ARAIM), to formulate cumulative test statistics for fault detection. The sample size is then determined to maximize the fault detection capability, including the response speed and sensitivity to minor faults. Meanwhile, the optimal sample size minimizes the undetected fault magnitude bound when no fault is declared. In this manner, S-ARAIM combines the advantage of snapshot RAIM and sequential RAIM in detecting severe pulse and small persistent faults. Additionally, we derive a protection level to envelop the estimate error under the constraints of continuity and integrity requirements. Experiments validate the fault detection performance under single-satellite-fault and dual-satellite-fault scenarios. Compared with least square residual RAIM and ARAIM, S-ARAIM improves the integrity availability by 45.91% and 5.64%, respectively.

Preliminary Analysis of BDS-3 Performance for ARAIM

<h3>Abstract</h3> 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 8 × 10⁻⁵ and 1 × 10⁻³, respectively, for BDS-3 in ARAIM.

RAIM Fault Detection and Exclusion with Spatial Correlation for Integrity Monitoring

For safety-of-life applications used together with global navigation satellite systems, such as in civil aviation and autonomous driving, integrity is of paramount importance. Integrity monitoring protects the user safety based on two general approaches: mitigating large signal failures and bounding the residual errors. The fault detection and exclusion (FDE) of faulty satellites is part of the former approach. In the classical integrity monitoring algorithms in civil aviation, the use of test statistics based on least squares residuals relies on the assumption that the observations from different satellites are independent. When applied to urban environments with spatial correlation introduced by large multipath errors, a review of the FDE method is needed. With the optimal FDE method defined as the one with minimized integrity risk, we propose two optimization criteria for use in fault detection and fault exclusion. The optimal test statistics were obtained by analytical derivation for cases with and without correlations among different satellites. This method was theoretically compared with another commonly used test statistic using the minimum detectable bias, and it was numerically compared using the horizontal protection level under the scenario of advanced receiver autonomous integrity monitoring. The optimal test produces less conservative protection level results, and its advantage is especially obvious when the geometries are weak, or when the correlation coefficients among the satellites are high.

ARAIM Stochastic Model Refinements for GNSS Positioning Applications in Support of Critical Vehicle Applications.

Integrity monitoring (IM) is essential if GNSS positioning technologies are to be fully trusted by future intelligent transport systems. A tighter and conservative stochastic model can shrink protection levels in the position domain and therefore enhance the user-level integrity. In this study, the stochastic models for vehicle-based GNSS positioning are refined in three respects: (1) Gaussian bounds of precise orbit and clock error products from the International GNSS Service are used; (2) a variable standard deviation to characterize the residual tropospheric delay after model correction is adopted; and (3) an elevation-dependent model describing the receiver-related errors is adaptively refined using least-squares variance component estimation. The refined stochastic models are used for positioning and IM under the Advanced Receiver Autonomous Integrity Monitoring (ARAIM) framework, which is considered the basis for multi-constellation GNSS navigation to support air navigation in the future. These refinements are assessed via global simulations and real data experiments. Different schemes are designed and tested to evaluate the corresponding enhancements on ARAIM availability for both aviation and ground vehicle-based positioning applications.

Nonparametric estimation-based five-layer neural network RAIM with improved availability

The monitoring performance of receiver autonomous integrity monitoring (RAIM) is restricted when visible satellites are limited in challenging environments. For that, artificial neural network-based RAIM methods have been investigated to improve the detection efficacy. Nevertheless, their corresponding fault exclusion and protection level algorithms are hardly provided for integrity assessments. In this regard, a nonparametric estimation-based RAIM method (NE-RAIM) is investigated to support fault detection, exclusion, and protection level calculation in this paper, boosting the declined monitoring capacity caused by the decrease of visible satellites. We propose a classification variable and a dynamic sampling method based on the variance inflation theory and then obtain the regression of the classification variable using nonparametric estimation. In this way, a five-layer NE-RAIM neural network is constructed to enhance the detection capability further. We also provide a NE-RAIM-based fault exclusion strategy by analyzing the detection result vector. Meanwhile, a protection level algorithm is proposed to enable direct integrity and availability evaluation based on searching the worst-case scenario where the missed detection risk is maximized. Results show that NE-RAIM requires a minimum pseudorange bias of 35 m to realize 100% detection rates under all single-faulty-satellite modes. Compared with least-square RAIM and advanced RAIM, NE-RAIM improves overall 24 h availability by 59.30% and 4.52%, respectively.

Bayesian fault-tolerant protection level for multi-constellation navigation from integrity perspective

The multi-constellation is anticipated to enhance navigation performance by providing abundant satellites in view. However, with this comes the necessity of considering simultaneous fault events in integrity risk assessment when applying the receiver autonomous integrity monitoring. Meanwhile, the integrity monitoring efficacy remains vulnerable to the uncertainty of prior fault probability in multi-constellation navigation. In this regard, this paper proposes a Bayesian approach for the multi-constellation navigation at the user segment to strengthen the evaluation robustness of integrity risk. We bound the Bayesian posterior probability of fault hypotheses that comprise multiple concurrent faults (satellite or constellation faults) without assuming an optimistic prior fault distribution. This posterior probability bound leads to an associated Bayesian integrity risk. Following that, a fault-tolerant estimate accounting for multiple faults and nominal biases is derived to minimize the Bayesian integrity risk. Finally, we establish a Bayesian fault-tolerant protection level to bound the position estimate error and assess the integrity availability, resisting the uncertainty in the prior fault probability. Results validate the robustness improvement the proposed Bayesian approach fulfills compared with the advanced receiver autonomous integrity monitoring in four cases. In addition, the Bayesian approach can lower the protection level at the cost of an offset from the least-square estimate while maintaining the same position accuracy.

Implementation and Performance Analysis of Constellation Dynamic Selection in Multi-Constellation RAIM.

Global navigation satellite system (GNSS) plays a crucial role in many fields, such as aerospace and transportation. Integrity is the measure of trust used in GNSS positioning especially in safety-critical applications. Advanced receiver autonomous integrity monitoring (ARAIM), taking full advantage of multi-constellation GNSS, shows huge potential to provide vertical navigation in civil aviation en route navigation and terminal approaches. However, the multi-constellation ARAIM also greatly exposes computational complexity and potential performance hazards in fault modes determination and fault-tolerant positioning. From the perspective of integrity risk control, rather than the pursuit of better positioning accuracy blindly for safety-critical applications, the concept of constellation dynamic selection is proposed and implemented in ARAIM and the performance analysis is discussed in this paper. Only the best two constellations which have the best vertical geometry performance are involved in ARAIM calculation anytime anywhere. The proposed method shows superiority in both integrity availability and computational complexity in both simulations and actual GNSS signal experiments. While the computational complexity is less than 10% of that using four constellations, 100% availability under LPV-200 criteria can be achieved in worldwide coverage experiment. The proposed method also overcomes the shortcomings of ARAIM with two fixed constellations and shows good robustness under depleted scenarios. Furthermore, the statistics results from observation stations proved the applicability and generality of the proposed method under current developing GNSS constellations.

Vertical Protection Level Optimization and Availability Analysis for Advanced RAIM

With the introduction of global navigation satellite systems (GNSSs) in aviation, there has been increased dependency on GNSS position. Multi-constellation GNSS services and equipment will remain a solution for many aircraft positions in safety. Multi-constellation GNSS can improve robustness and navigation performance. Therefore, advanced receiver autonomous integrity monitoring (advanced RAIM or ARAIM) technology is being developed as an augmentation method for GNSS users under multi-constellation. ARAIM can allow increased service level globally and provide vertical guidance during the approach phase for aircrafts. Since the traditional ARAIM algorithm uses the average allocation strategy to allocate integrity and continuity risk, an allocation approach based on the particle swarm optimization (PSO) algorithm is presented in this article. Different allocation strategies for integrity and continuity risk are chosen as different particles, and the weighted sum of vertical protection level corresponding to different fault subsets is selected as the fitness function to optimize the allocation strategy and the corresponding VPL. Based on real GNSS data, the ARAIM algorithm under multi-constellation is analyzed. The experimental results demonstrate that the integrity and continuity risk allocation method based on the proposed algorithm optimizes the VPL and improves the global availability of ARAIM under multi-constellation.

Progress of global ARAIM availability of BDS-2/BDS-3 with TGD and ISB

Advanced RAIM (ARAIM) is an extension of Receiver Autonomous Integrity Monitoring (RAIM) by enhancing the vertical navigation capabilities, so it can be applied to higher-level precision applications. But when the observation data of the second-generation BDS (BDS-2) and the third-generation BDS (BDS-3) are combined to evaluate the ARAIM availability, the evaluation be affected by the Timing Group Delay (TGD) of different satellite signals and the Inter-system Bias (ISB) between BDS-2 and BDS-3, which is ignored by the existing literature. Therefore, in this article, we deduced the mathematical model of ARAIM and the calculation formula of Vertical Protection Level (VPL) by considering the combined influence of TGD and ISB. We used the BDS observation data and ephemeris files of 374 International GNSS Service (IGS) stations around world on July 29, 2021 to calculate the VPL of these stations and evaluate the global ARAIM availability. The results show that the number of visible BDS satellites is 8.033 and the Geometric Dilution of Precision (GDOP) is 1.721, which can meet the basic needs of global ARAIM calculations. Furthermore, when considering the combined influence of TGD and ISB, the evaluation of ARAIM availability by Multiple Hypothesis Solution Separation (MHSS) is significantly better than that without considering the combined TGD and ISB influence or their individual influence. The average VPL values at these IGS stations in four cases are 124.925 m, 13.882 m, 32.610 m and 9.962 m, and the corresponding ARAIM availability percentages are 90.839%, 95.241%, 96.751% and 99.660%, respectively. Finally, the minimum coverage of ARAIM availability based on BDS can reach 90.839%, which can meet the aviation demand for ARAIM availability in most regions and times.

Code phase tracking error based autonomous integrity monitoring for GNSS/INS ultra-tightly integrated system

The ultra-tight integration of GNSS (Global Navigation Satellite System) and INS (Inertial Navigation System) may suffer from faults in GNSS, INS and integration filter. Both the faults occurred at the current epoch and at previous epochs affect the position solution deviation of ultra-tight integration at the current epoch, and the effect is reflected in GNSS code phase tracking errors. In this paper, a new autonomous integrity monitoring algorithm is proposed for the federated GNSS/INS ultra-tight integrations in which the code phases of local GNSS signal replicas for GNSS signal tracking are completely derived from the integrated navigation solution. In the proposed algorithm, GNSS code phase tracking errors are employed to construct the test statistics for fault detection through a MHSS (Multiple Hypothesis Solution Separation) method improved from the classical MHSS used in ARAIM (Advanced Receiver Autonomous Integrity Monitoring). With the improved MHSS, the proposed algorithm can account for GNSS nominal biases, multiple GNSS faults and the faults in INS and integration filter. The protection levels under multiple hypothesis are also derived. A semi-physical simulation of the federated ultra-tight integration of GPS (Global Positioning System) and INS in airplane approaching case and a vehicle-based field test of the federated ultra-tight integration of GPS, Galileo and INS are conducted to validate the proposed algorithm. The experiments show that the designed fault detection can effectively detect the occurred faults and the derived protection levels can correctly bound the caused position solution error.

Robust Modeling of GNSS Orbit and Clock Error Dynamics

<h3>Abstract</h3> In this paper, we develop new stochastic orbit and clock error models for positioning, fault detection, and integrity monitoring over time. GPS and Galileo orbit and clock data are evaluated and ranging errors are analyzed and modeled over time. This work is intended for time-sequential safety-critical navigation systems including global navigation satellite systems (GNSSs) integrated with inertial navigation systems (INSs) and Kalman filter implementations of Advanced Receiver Autonomous Integrity Monitoring (ARAIM).

Integrity Risk Under Temporal Correlation for Horizontal ARAIM

Integrity requirements for safety-critical global navigation satellite system applications, such as in civil aviation for the nonprecision approach through precision approach, are defined in a per hour or per approach (i.e., 150s) basis by the International Civil Aviation Organization. This article presents a novel methodology for mapping such operational requirements to the specific risk at an algorithmic level for advanced receiver autonomous integrity monitoring (ARAIM), in particular horizontal ARAIM (H-ARAIM). We thoroughly evaluated the actual risk over time by performing extensive first-order Gauss Markov Process Monte Carlo runs for the propagation of time-correlated position errors and test statistics over one hour exposure time and accounting for multiple events of loss of integrity over the time interval. A comparison of the risk over time and the risk for a single epoch leads to the number of effectively independent samples. The current integrity equation was modified using the number such that a specific risk requirement is allocated to a single sample for the determination of the protection level. This study also examined the impact of the modified risk allocation on the existing fault detection and exclusion algorithm by conducting H-ARAIM availability simulations and by comparing the results based on the newly proposed method with that obtained using the existing single sample-based risk allocation. In our preliminary assessment, little impact on the global availability (availability loss of approximately up to 1%) of the inflated terms of the integrity equation due to the number of valid samples was found.