Integrity Monitoring Algorithm Research Articles

Carrier phase error overbounding using Gaussian mixture model for high-precision air navigation integrity monitoring

Carrier phase measurements play a pivotal role in enabling high-precision positioning within future air traffic systems and autonomous vehicles. Current aviation navigation integrity monitoring, primarily using pseudorange measurements, cannot meet system positioning accuracy and integrity requirements, leading to limitations and false alarm risks, especially in complex urban canyons with signal reflections. This work presents a carrier phase-based positioning integrity monitoring algorithm, utilizing the expectation–maximization algorithm to compute parameters for the Gaussian mixture model (GMM) and nonparametric bootstrapping to construct an overbounding model of carrier phase residuals. It establishes a precise protection level (PL) calculation method, which is validated with static and flight data, demonstrating accurate overbounding of carrier phase residuals using GMM. Protection levels during testing remain below the alarm limit and exceed system positioning error, ensuring normal system operation without false or missed alarms, confirming the effectiveness of the established carrier phase error overbounding model.

Time–Frequency Signal Integrity Monitoring Algorithm Based on Temperature Compensation Frequency Bias Combination Model

To ensure the long-term stable and uninterrupted service of satellite navigation systems, the robustness and reliability of time–frequency systems are crucial. Integrity monitoring is an effective method to enhance the robustness and reliability of time–frequency systems. Time–frequency signals are fundamental for integrity monitoring, with their time differences and frequency biases serving as essential indicators. These indicators are influenced by the inherent characteristics of the time–frequency signals, as well as the links and equipment they traverse. Meanwhile, existing research primarily focuses on only monitoring the integrity of the time–frequency signals’ output by the atomic clock group, neglecting the integrity monitoring of the time–frequency signals generated and distributed by the time–frequency signal generation and distribution subsystem. This paper introduces a time–frequency signal integrity monitoring algorithm based on the temperature compensation frequency bias combination model. By analyzing the characteristics of time difference measurements, constructing the temperature compensation frequency bias combination model, and extracting and monitoring noise and frequency bias features from the time difference measurements, the algorithm achieves comprehensive time–frequency signal integrity monitoring. Experimental results demonstrate that the algorithm can effectively detect, identify, and alert users to time–frequency signal faults. Additionally, the model and the integrity monitoring parameters developed in this paper exhibit high adaptability, making them directly applicable to the integrity monitoring of time–frequency signals across various links. Compared with traditional monitoring algorithms, the algorithm proposed in this paper greatly improves the effectiveness, adaptability, and real-time performance of time–frequency signal integrity monitoring.

A computationally efficient Kalman filter-based RAIM algorithm for aircraft navigation with GPS and NavIC

Integrity monitoring with a Kalman filter (KF) has recently attracted significant attention. In this paper, a computationally efficient architecture of a KF-based receiver autonomous integrity monitoring (RAIM) algorithm is discussed for aviation applications to ensure reliable operations of Global Navigation Satellite Systems (GNSS). It is built on the Schmidt KF navigation processor to model time-correlated measurement errors. Reasons for important design choices of the algorithm are clarified. Different strategies are adopted to efficiently include the contributions of past KF measurements in fault detection as well as protection level (PL) calculations. Module-wise most significant numerical complexity is also analyzed in detail. The algorithm performance is studied with simulated Global Positioning System (GPS) and Navigation with Indian Constellation (NavIC) signals for a number of scenarios. They comprise different configurations related to the number of satellites, geometry, total duration, and aircraft dynamics. Fault detection performance of presented KF RAIM is shown to be superior to another innovation-based test with a moving time window. It is demonstrated that KF RAIM running on a single-core virtual machine can complete processing within a small fraction of each time interval. The performance is also analyzed by restricting CPU usage. The processing time of GPS-NavIC KF RAIM at every interval is shown to be consistently less than that of standalone GPS in all scenarios. Therefore, dual constellations not only result in lower PLs, but also require shorter execution times. An explanation for faster execution times with dual GNSS is provided using the numerical complexity of different modules.

Integrity monitoring of NavIC by parsing broadcast ephemeris

Abstract Global navigation satellite systems (GNSS) are used to provide position estimation to the users. These navigation systems must meet the required navigation parameters (RNP) parameters. Among them integrity being the important parameter, defined as a navigation system’s honesty of the information provided to the user by satellites. The extremity of error due to clocks, ephemeris etc., broadcasted in navigation message of NavIC will result in inaccurate information provided by the satellites that tamper the Navigation with Indian constellation (NavIC) system integrity. The information provided by the satellites may be faulty due to various error sources and cannot be used for applications which require very high accuracy. Integrity of the information provided by satellites plays a vital role and the system needs to be notified accordingly. The traditional methods receiver autonomous integrity monitoring (RAIM) algorithms require both navigation and observation data for implementation and involves several computations, hence in this paper an efficient approach considering only navigation message is proposed to monitor the integrity of NavIC. The NavIC Navigation data of 28 days data corresponding to 4 months is collected from IGS website. The integrity check is performed considering the satellite‘s User Range Accuracy Upper Bound (URA UB), fit interval and health parameters from navigation message. It is observed from the results that there are specific instances of integrity failure of NavIC system. However, it is also noticed that 99.5 % of times the integrity provided by NavIC is within specified limits that guarantee the NavIC utility for critical applications.

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.

T-RAIM Approaches: Testing with Galileo Measurements.

Several applications rely on time retrieved from Global Navigation Satellite System (GNSS), and this pushes for integrity tailored to timing. Integrity information could be broadcast by GNSS itself, but currently, there are no GNSSs providing such integrity information for a timing application. The integrity provided by GNSS itself could not be timely enough for real time users and does not include local effects due to multipath or other local interferences. In order to fill the gap, integrity can be locally/autonomously computed by the receiver using Timing Receiver Autonomous Integrity Monitoring (T-RAIM) algorithms. Three T-RAIM algorithms have been designed, implemented, and tested; specifically, the algorithms are Forward-Backward (FB), Danish, and Subset. The algorithms are applied to the classical Position Velocity and Timing (PVT) solution and to the time-only case assuming the receiver coordinates are known. Tests using two identical receivers located in different scenarios, open-sky and obstructed, have been carried out to validate the algorithms proposed. The increased redundancy obtained from the knowledge of the receiver coordinates play a fundamental role for the integrity algorithms performance. The benefits of the T-RAIM algorithms activation, in signal degraded conditions, clearly emerged in terms of frequency error and Allan Deviation (ADEV). A small increase of the execution time has been observed when the T-RAIM algorithms are used.

A Positioning System in an Urban Vertical Heterogeneous Network (VHetNet)

Global navigation satellite systems (GNSSs) are essential in providing localization and navigation services to most of the world due to their superior coverage. However, due to high pathloss and inevitable atmospheric effect, the positioning performance of any standalone GNSS is still poor in urban areas. To enhance the positioning performance of legacy GNSSs in urban areas, a positioning system, which utilizes high altitude platform station (HAPS) and 5G gNodeBs (gNBs), in a futuristic urban vertical heterogeneous network (VHetNet) is proposed. In this paper, we demonstrate the effectiveness of gNBs in improving the vertical positioning performance for both the GPS-only system and the HAPS-aided GPS system by analyzing the impact of the density of gNBs and the pseudorange error of gNB on the positioning performance of the gNB augmented positioning systems. We also demonstrate the effectiveness of receiver autonomous integrity monitoring (RAIM) algorithms on the HAPS and/or gNB aided GPS systems in urban areas.

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.

Recent Advances in Sensor Integrity Monitoring Methods—A Review

In face of the high complexity of modern systems and the increasing reliance on technology, the strategies and methods to evaluate the integrity of systems and the information they provide are of great importance. The use of sensors to provide important information in various applications has become ubiquitous, which puts more pressure on the accuracy of sensor measurements. In the navigation field, in particular, the integrity of positioning information provided by sensors can be critical, as failures can lead to fatalities and catastrophic damages. Extensive research has been done into methods to assess and improve the integrity of positioning information provided by GNSS receivers, led by the high safety requirements in the aviation field. More recently, a shift into the research of integrity solutions suitable for the challenging positioning requirements of autonomous vehicles in urban environment has been a trend. There have been extensive advancements in developing integrity monitoring algorithms for GNSS and navigation in general. However, these methods have not been sufficiently extended into other types of sensors, and the development of integrity methods outside the navigation field have been scarce and scattered. This work aims to provide an overview of recent advances in the integrity monitoring field, including research outside the navigation domain. The goal is to give an introduction to the integrity monitoring concept to a broader audience, as these techniques have been highly specialized by GNSS experts and navigation related research, fostering multi-disciplinary approaches and creative use of existing methods in different areas and applications.

Enhancing navigation integrity for Urban Air Mobility with redundant inertial sensors

Urban Air Mobility (UAM) uses highly automated air vehicles to offer safe and efficient low-altitude urban air transportation services, for which ensuring navigation safety (measured by integrity) is an essential precondition. UAM vehicles can navigate themselves using Global Navigation Satellite Systems (GNSS)/Inertial Measurement Unit (IMU) tightly coupled systems. However, these systems are vulnerable to IMU failures aside from GNSS faults, given that UAM vehicles will use low-cost IMUs. IMU faults can severely degrade navigation integrity, thereby threatening UAM operational safety and increasing the difficulty of urban air traffic management. This issue can be mitigated by employing redundant IMUs. Civil aircraft use consistency checks among multiple high-performance Inertial Navigation Systems (INSs) to enhance navigation integrity. But this approach is not suitable for low-cost IMUs because of fast error accumulation. In response, this work proposes a new approach to enhance navigation integrity for UAM by integrating multiple IMUs with GNSS. In this approach, multiple IMUs and GNSS are tightly coupled by a centralized Kalman filter, and the corresponding integrity monitoring algorithm is developed to (a) detect the faults in GNSS and/or IMUs and (b) evaluate the probabilistic upper bounds on navigation errors, namely protection levels. Simulations are conducted to demonstrate the proposed method and to present sensitivity analyses, and the results suggest the effectiveness of the new approach. This method is beneficial to improving UAM operational safety and can potentially be applied to civil aircraft in the future.

An Effective Integrity Monitoring Scheme for GNSS/INS/Vision Integration Based on Error State EKF Model

It is well-known that the Global Navigation Satellite System/Inertial Navigation System (GNSS/INS) /Vision integration has been increasingly used for safety-critical applications like self-driving cars. However, the performance of the GNSS/INS/Vision integration degrades due to unknown faults. Therefore, it is essential to develop integrity monitoring algorithms for the integrated navigation system. A new protection level (PL) formula to ensure the integrity of the state estimation of the GNSS/INS/Vision integration is proposed, which can be calculated by the relation between the filter estimation error and faults. An integrity risk allocation tree is developed for each sensor fault hypothesis including the nominal hypothesis, and the specific PL is given in the case of GNSS, INS and visual measurement faults. In addition, the performance of the proposed PL is comprehensively evaluated. A field vehicular test was conducted to evaluate the performance of the integrity monitoring algorithm for the GNSS/INS/Vision integration. The results demonstrate that the proposed PL for the GNSS/INS/Vision integration can fit the position error against six different fault modes.

Integrity monitoring for undifferenced and uncombined PPP under local environmental conditions

Integrity monitoring of precise point positioning (PPP) can provide tightly guaranteed absolute position error bounds for safety-critical applications. However, a complex local environment makes PPP integrity monitoring much more challenging, such as urban canyons. Significant prone multipaths and low observation redundancy are the main difficulties in the accuracy and reliability of PPP. Therefore, we proposed a solution separation-based integrity monitoring algorithm, which is based on a single and dual frequency undifferenced and uncombined PPP model considering compensation for the multipath error distortion by Gaussian overbounding. Both the static and the kinematic data are utilized to test the proposed algorithm. The results show that the proposed algorithm can produce an adequate protection level (PL) in horizontal and vertical directions. Furthermore, the proposed algorithm can obtain a smoother PL and positioning error in a dynamic local environment, and effectively suppress misleading information.

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.

Kalman Filter-Based Integrity Monitoring for GNSS and 5G Signals of Opportunity Integrated Navigation

A Kalman filter-based receiver autonomous integrity monitoring algorithm (RAIM) is proposed to exploit sequential measurements from global navigation satellite systems (GNSS) and cellular 5G signals of opportunity (SOPs), to ensure safe vehicular navigation in urban environments. To deal with frequent threats caused by multipath and non-line-of-sight conditions, an innovation-based outlier rejection method is introduced. Next, a fault detection technique based on solution separation test is developed, and the quantification of protection levels is derived. Experimental results of a ground vehicle traveling in an urban environment, while making pseudorange measurements to GPS satellites and cellular 5G towers, are presented to demonstrate the efficacy of the proposed method. Incorporating 5G signals from only 2 towers is shown to reduce the horizontal protection level (HPL) by 0.22 m compared to using only GPS. Moreover, the proposed method is shown to reduce the HPL and vertical protection level (VPL) by 84.42% and 69.63%, respectively, over the snapshot advanced RAIM (ARAIM).

A new method for evaluation of the positional error of low-cost devices based on GNSS integrity for transportation applications

GNSS integrity assessment has always been linked to the need for reliable positional information. Initially used in aviation, positional information gained even more relevance in terrestrial applications with the popularity of GNSS. However, the terrestrial environment has many influences over GNSS signals, which reduces the positional quality of tracking objects. Advances have been achieved in the use of integrity monitoring algorithms, but there are limitations to their use, especially those concerning positional accuracy in urban environments with low-cost devices. This paper aims to discuss a comparative method using two low-cost GNSS receivers designed for transportation applications and to verify whether this method can evaluate positional quality in pre-established locations, as well as the possibilities of using these devices for transportation applications, considering the positional error. Results show that, in the static experiment, the receiver assembled with a GPS antenna active embedded was more accurate than the receiver assembled with an external antenna, presenting better values in 5 out of 10 evaluated sites, while the external antenna performed better in only 2 sites. However, in a kinematic evaluation, the receiver assembled with an external antenna provided better results when considering positional error as assessment criterion, resulting in values less than or equal to 8 meters in 99.7% of the route evaluated, while the embedded antenna had 95.3%.

Measurement Error Detection for Stereo Visual Odometry Integrity

<h3>Abstract</h3> Integrity, a safety-of-life framework from civil aviation for satellite navigation, is greatly under-explored in visual navigation. A new two-factor approach to rejecting measurement outliers is proposed for navigation integrity in stereo visual odometry (VO). In contrast to other treatments using reprojection error as measurement residuals, our choice of landmark matching error inherently connects navigation solutions and integrity monitoring. We propose two methods to detect large measurement residuals that cannot otherwise be identified by existing outlier rejection methods in state-of-the-art VO pipelines. By rejecting these outliers, measurement residuals can be bounded by the distribution overbounding method that provides fundamental inputs for integrity computations. We evaluate our methods using an open-source data set. Overbounding performance is improved in terms of tightness, computational efficiency, and most important of all, scenario tolerance. This could be a good starting point for developing future integrity monitoring algorithms for visual navigation and in particular, stereo VO.

Performance Analyses of a RAIM Algorithm for Kalman Filter with GPS and NavIC Constellations.

This paper evaluates the performance of an integrity monitoring algorithm of global navigation satellite systems (GNSS) for the Kalman filter (KF), termed KF receiver autonomous integrity monitoring (RAIM). The algorithm checks measurement inconsistencies in the range domain and requires Schmidt KF (SKF) as the navigation processor. First, realistic carrier-smoothed pseudorange measurement error models of GNSS are integrated into KF RAIM, overcoming an important limitation of prior work. More precisely, the error covariance matrix for fault detection is modified to capture the temporal variations of individual errors with different time constants. Uncertainties of the model parameters are also taken into account. Performance of the modified KF RAIM is then analyzed with the simulated signals of the global positioning system and navigation with Indian constellation for different phases of aircraft flight. Weighted least squares (WLS) RAIM used for comparison purposes is shown to have lower protection levels. This work, however, is important because KF-based integrity monitors are required to ensure the reliability of advanced navigation methods, such as multi-sensor integration and vector receivers. A key finding of the performance analyses is as follows. Innovation-based tests with an extended KF navigation processor confuse slow ramp faults with residual measurement errors that the filter estimates, leading to missed detection. RAIM with SKF, on the other hand, can successfully detect such faults. Thus, it offers a promising solution to developing KF integrity monitoring algorithms in the range domain. The modified KF RAIM completes processing in time on a low-end computer. Some salient features are also studied to gain insights into its working principles.

Case study of Bayesian RAIM algorithm integrated with Spatial Feature Constraint and Fault Detection and Exclusion algorithms for multi‐sensor positioning

<h3>Abstract</h3> This study proposes three novel integrity monitoring algorithms based on Bayesian Receiver Autonomous Integrity Monitoring (BRAIM). Two problems of integrity monitoring for land-based applications for GNSS challenging environments are explored: requirements for sufficient measurement redundancy and the presence of large biases. The need for measurement redundancy was mitigated by using BRAIM. This enabled the employment of a Fault Detection and Exclusion (FDE) algorithm without the required minimum availability of six measurements. To increase the estimated integrity, a Spatial Feature Constraint (SFC) algorithm was implemented to constrain solutions to feasible locations within a road feature. The performance of the proposed FDE+BRAIM, SFC+BRAIM and FDE+SFC+BRAIM algorithms was evaluated for GPS and multi-sensor data. For the non-Gaussian measurement error distribution and under the test conditions, the best achieved probability of misleading information was of the order of magnitude 10⁻⁸ for road-level requirements. The results provide an initial proof-of-concept for non-Gaussian non-linear multi-sensor integrity monitoring algorithms.

GPS Vector Tracking Receivers with Rate Detector for Integrity Monitoring

In this paper, the integrity monitoring algorithm based on a Kalman filter (KF) based rate detector is employed in the vector tracking loop (VTL) of the Global Positioning System (GPS) receiver. In the VTL approach, the extended Kalman filter (EKF) simultaneously tracks the received signals and estimates the receiver’s position, velocity, etc. In contrast to the scalar tracking loop (STL) that uses the independent parallel tracking loop approach, the VTL technique uses the correlation of each satellite signal and user dynamics and thus reduces the risk of loss lock of signals. Although the VTL scheme provides several important advantages, the failure of tracking in one channel may affect the entire system and lead to loss of lock on all satellites. The integrity monitoring algorithm can be adopted for robustness enhancement. In general, the standard integrity monitoring algorithm can timely detect the step type erroneous signals. However, in the presence of ramp type slowly growing erroneous signals, detection of such type of error takes much more time since the error cannot be detected until the cumulative exceeds the specified threshold. The integrity monitoring based on the rate detector possesses good potential for resolving such problem. The test statistic based on the pseudorange residual in association with the EKF is applied for determination of whether the test statistic exceeds the allowable threshold values. The fault detection and exclusion (FDE) mechanism can then be employed to exclude the hazardous erroneous signals for the abnormal satellites to assure normal operation of GPS receivers. Feasibility of the integrity monitoring algorithm based on the EKF based rate detector will be demonstrated. Performance assessment and evaluation will be presented.