Two critical parameters for advanced receiver autonomous integrity monitoring are the probability of satellite fault and the probability of constellation fault. This paper provides specific definitions for each of these fault types. We describe how these faults are evaluated and how 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.

Localization safety, or integrity risk, is the probability of undetected localization failures and a common aviation performance metric used to verify a minimum accuracy requirement. As autonomous robots become more common, applying integrity risk metrics will be necessary to verify localization performance. This letter introduces a new method, solution separation, to quantify landmark-based mobile robot localization safety for fixed-lag smoothing estimators and compares it's computation time and fault detection capabilities to a chi-squared integrity monitoring method. Results show that solution separation is more computationally efficient and results in a tighter upper-bound on integrity risk when few measurements are included, which makes it the method of choice for lightweight, safety-critical applications such as UAVs. Conversely, chi-squared requires more computing resources but performs better when more measurements are included, making the method more appropriate for high performance computing platforms such as autonomous vehicles.

In this article, we develop new stochastic tropospheric error models for positioning, fault detection, and integrity monitoring over time. We first perform time-domain and frequency-domain analyses of residual tropospheric delays observed over 12 months at multiple globally distributed locations. We then derive bounding error models for time-sequential safety-critical navigation systems including global navigation satellite systems integrated with inertial navigation systems and Kalman filter implementations of advanced receiver autonomous integrity monitoring.

Safety-critical navigation applications require that estimation errors be reliably quantified and bounded. This can be challenging for linear dynamic systems if the process noise or measurement errors have uncertain time correlation. In many systems (e.g., in satellite-based or inertial navigation systems), there are sources of time-correlated sensor errors that can be well modeled using Gauss-Markov processes (GMP). However, uncertainty in the GMP parameters, particularly in the correlation time constant, can cause misleading error bounds. In this paper, we develop time-correlated models that ensure tight upper bounds on the estimation error variance, assuming that the actual error is a stationary first-order GMP with a variance and time constant that are only known to reside within an interval. We first use frequency-domain analysis to derive stationary GMP models in both the continuous and discrete time domains, which outperform models previously described in the literature. Then, we derive an even tighter estimation error bound using a non-stationary GMP model, for which we determine the minimum initial variance that guarantees bounding conditions. Both models can easily be implemented in a linear estimator like the Kalman filter.

In this work, a new time‐sequential positioning and fault detection method is developed for dual‐frequency, multi‐constellation Advanced Receiver Autonomous Integrity Monitoring (ARAIM). Unlike conventional “snapshot” ARAIM, sequential ARAIM exploits changes in satellite geometry at the cost of slightly higher computation and memory loads. From the perspective of users on Earth, the motion of any given GNSS satellite is small over short time intervals. But the accumulated geometry variations of redundant satellites from multiple GNSS can be substantial. This paper quantifies performance benefits brought by satellite motion to ARAIM. It specifically addresses the following challenges: (a) defining raw GNSS code and carrier error models over time, (b) designing estimators and fault detectors exploiting geometric diversity for positioning, cycle ambiguity estimation, and integrity evaluation, and (c) formulating these algorithms in a computationally efficient implementation. Performance improvements provided by sequential ARAIM over snapshot ARAIM are evaluated by worldwide availability analysis for aircraft approach navigation.

In this paper, a new safety risk evaluation method is developed, simulated, and tested for laser-based navigation algorithms using feature extraction (FE) and data association (DA). First, at FE, we establish a probabilistic measure of separation between features to quantify the sensor's ability to distinguish landmarks. Then, an innovation-based DA process is designed to evaluate the impact on integrity risk of incorrect associations, while considering all potential measurement permutations. The algorithm is analyzed and tested in a structured environment.