Mathieu Joerger

Kalman Filter-Based Integrity Monitoring Against Sensor Faults

This paper introduces a new Kalman filter-based method for detecting sensor faults in linear dynamic systems. In contrast with existing sequential fault-detection algorithms, the proposed method enables direct evaluation of the integrity risk, which is the probability that an undetected fault causes state estimate errors to exceed predefined bounds of acceptability. The new method is also computationally efficient and straightforward to implement. The algorithm’s detection test statistic is established in three steps. First, the weighted norms of current and past-time Kalman filter residuals are defined as generalized noncentrally chi-square distributed random variables. Second, these residuals are proven to be stochastically independent from the state estimate error. Third, current-time and past-time residuals are shown to be mutually independent, so that the Kalman filter-based test statistic can be recursively updated in real time by simply adding the current-time residual contribution to a previously ...

GPS spoofing detection using RAIM with INS coupling

In this work, we develop, implement, and test a monitor to detect GPS spoofing attacks using residual-based Receiver Autonomous Integrity Monitoring (RAIM) with inertial navigation sensors. Signal spoofing is a critical threat to all navigation applications that utilize GNSS, and is especially hazardous in aviation applications. This work develops a new method to directly detect spoofing using a GPS/INS integrated navigation system that incorporates fault detection concepts based on RAIM. The method is also capable of providing an upper bound on the proposed monitors integrity risk.

Measurement-Level Integration of Carrier-Phase GPS and Laser-Scanner for Outdoor Ground Vehicle Navigation

This paper introduces a navigation system based on combined global positioning system (GPS) and laser-scanner measurements for outdoor ground vehicles. Using carrier-phase differential GPS, centimeter-level positioning is achievable when cycle ambiguities are resolved. However, GPS signals are easily attenuated or blocked, so their use is generally restricted to open-sky areas. In response, in this work we augment GPS with two-dimensional laser-scanner measurements. The latter is available when GPS is not and further enables obstacle detection. The two sensors are integrated in the range domain for optimal navigation performance. Nonlinear laser observations and time-correlated code and carrier-phase GPS signals are processed in a unified and compact measurement-differencing extended Kalman filter. The resulting algorithm performs real-time carrier-phase cycle ambiguity estimation and provides absolute vehicle positioning throughout GPS outages, without a priori knowledge of the surrounding landmark locations. Covariance analysis, Monte Carlo simulations, and experimental testing in the streets of Chicago demonstrate that the performance of the range-domain integrated system far exceeds that of a simpler position-domain implementation, in that it not only achieves meter-level precision over extended GPS-obstructed areas, but also improves the robustness of laser-based simultaneous localization and mapping.

High integrity stochastic modeling of GPS receiver clock for improved positioning and fault detection performance

In this paper, a validated stochastic clock random error model is used to derive a correct time correlation matrix for a sequence of clock random errors. A batch estimator incorporating the complete time correlation matrix is developed to account for clock random errors. Performance improvement for the proposed receiver clock-aided navigation system is fully investigated. A benchmark application of an aircraft precision approach is used to evaluate the system availability performance with a single satellite failure assumption.

Solution separation and Chi-Squared ARAIM for fault detection and exclusion

Future multi-constellation Global navigation satellite system (GNSS) will provide a large number of redundant ranging signals, which will improve the performance of receiver autonomous integrity monitoring (RAIM), but it will also increase the probability of satellite faults, thereby increasing the continuity risk. In response, in this paper, a new Chi-Squared (Chi2) RAIM approach to fault detection and exclusion (FDE) is developed, and compared to Solution Separation (SS) RAIM. The paper first introduces complete integrity and continuity risk equations for Chi2 RAIM FDE, which are currently missing in the literature. Probability bounds are developed, which express the fact that the reduction in continuity risk obtained using exclusion comes at the cost of a higher integrity risk. It is then shown that the Chi2 approach can provide a tighter integrity risk bound as compared to SS, but the SS bound enables risk evaluation in practical implementations where computation resources are limited. Finally, the SS and Chi2 FDE integrity and continuity risk bounds are implemented to establish worldwide availability maps for Advanced RAIM (ARAIM) in an example aircraft approach application using GPS, Galileo, GLONASS and Beidou satellite constellations.

Fault detection and exclusion using solution separation and chi-squared ARAIM

This paper provides new integrity and continuity risk evaluation methods for fault detection and exclusion (FDE) using receiver autonomous integrity monitoring (RAIM). These methods are developed for both solution separation (SS) and Chi-squared RAIM: they capture the fact that exclusion enables continuity risk reduction in exchange for a higher integrity risk. The two approaches are implemented in an example advanced RAIM (ARAIM) application for worldwide vertical guidance of aircraft using multiconstellation Global Navigation Satellite Systems (GNSS).

Measurement error models and fault-detection algorithms for multi-constellation navigation systems

The integration of ranging signals from multiple satellite constellations opens the possibility for rapid, robust and accurate positioning over wide areas. Algorithms for the simultaneous estimation of carrier phase cycle ambiguities and user position and for the detection of faults over a fixed smoothing time-interval were derived in previous work. For high-integrity precision applications, ensuring the robustness of measurement error and fault-models is an exacting task, especially when considering sequences of observations. In this research, a new RAIM-based approach is established, which aims at directly determining the worst-case single-satellite fault profile. Also, the robustness of newly derived ionospheric error models is experimentally evaluated using dual-frequency GPS data collected over several months at multiple locations. An integrity analysis is devised to quantify the impact of traveling ionospheric disturbances (TIDs) on the final user position solution. Finally, overall navigation system performance is assessed for various combinations of GPS, Galileo and low earth orbiting Iridium satellite signals.

Carrier Phase Relative RAIM Algorithms and Protection Level Derivation

The concept of Relative Receiver Autonomous Integrity Monitoring (RRAIM) using time differential carrier phase measurements is investigated in this paper. The precision of carrier phase measurements allows for mitigation of integrity hazards by implementing RRAIM monitors with tight thresholds without significantly affecting continuity. In order to avoid the need for cycle ambiguity resolution, time differences in carrier phase measurements are used as the basis for detection. In this work, we examine RRAIM within the context of the GNSS Evolutionary Architecture Study (GEAS), which explores potential architectures for aircraft navigation utilizing the satellite signals available in the mid-term future with GPS III. The objectives of the GEAS are focused on system implementations providing worldwide coverage to satisfy LPV-200 operations, and potentially beyond. In this work, we study two different GEAS implementations of RRAIM. General formulas are derived for positioning, fault detection, and protection level generation to meet a given set of integrity and continuity requirements.

Stochastic modeling of atomic receiver clock for high integrity gps navigation

The Global Positioning System (GPS) was designed as a passive radio navigation system to provide positioning capability without the need for receiver clock synchronization to GPS time. In theory, a GPS receiver equipped with a high-quality receiver clock can provide better system performance. More importantly for integrity-driven navigation applications, the additional redundancy provided by a clock dynamic model can increase fault detection performance and availability for receiver autonomous integrity monitoring (RAIM). In the work presented here, a stochastic model is used to rigorously account for the time correlation of random errors in high-quality GPS receiver clocks. A batch estimator (BE) is then developed to use GPS measurements collected over time to estimate current user position. The BE incorporates the stochastic clock model to ensure that position errors are properly quantified and, therefore, that navigation integrity is ensured. The resulting improvement in positioning performance is demonstrated using covariance analysis.

Determination of fault probabilities for ARAIM

Two critical parameters for Advanced Receiver Autonomous Integrity Monitoring (ARAIM) are the probability of satellite fault, Psat, and the probability of constellation fault, Pconst. A satellite fault is one whose root cause is only capable of affecting a single satellite; while a constellation fault has a root cause that is capable of affecting more than one satellite at the same time. This paper provides more specific definitions for each of these fault types. We describe how performance commitments supplied by Constellation Service Providers (CSPs) are used to complete the fault definitions and to estimate their probability of occurrence. Providing a precise definition of what constitutes a fault is essential so that all observers are able to agree on whether or not one has occurred. This paper is intended to lead to a framework for an open and transparent system for determining these parameters. This framework is intended to be the basis for an internationally agreed upon process for determining the fault rates that may be safely used for ARAIM.