GNSS Pseudorange Fault Detection and Exclusion with Multiple Outliers
Jan Wendel, Airbus Defence and Space GmbH
Date/Time: Thursday, Sep. 22, 9:43 a.m.
Modern GNSS receivers use GNSS signals from multiple constellations like GPS, Galileo, Glonass and Beidou to calculate position, velocity, and time (PVT). Consequently, a large number of pseudorange measurements are available at each epoch. Especially for land-based applications like autonomous driving or train localization, severe multipath and/or non-line-of-sight (NLOS) tracking can occur, leading to faulty pseudorange measurements, i.e. outliers. In order to prevent that these outliers corrupt the position and time solution, these outliers need to be detected and excluded. A common approach is to form subsets of pseudorange measurements, for each subset a position and time solution is calculated. A metric like the weighted sum of squared errors (WSSE) can be used to check the consistency of the measurements contained in a subset, which allows identifying a subset containing only fault-free pseudoranges. Each subset of pseudorange measurements essentially represents a hypothesis which pseudoranges are faulty, namely the pseudoranges not contained in the respective subset. With the large number of available pseudorange measurements due to the use of multiple constellations and the large number of possible simultaneous faults due to the difficult reception conditions land-based applications are faced with, the number of resulting subsets can grow extremely huge. The analysis of all these subsets/hypotheses can lead to a computational complexity that is prohibitive.
Instead of selecting pseudorange subsets, the method proposed in this paper selects candidate position and receiver clock error solutions solutions by defining a suitable grid, which is four dimensional in case three position coordinates and one receiver clock error shall be estimated. In case a candidate position and time solution is close to the true position and time, the pseudorange residuals of the non-faulty pseudoranges will be small, while the pseudorange residuals of the faulty pseudoranges will be large, reflecting the magnitudes of the pseudorange faults. For each candidate position and time solution, the squared sum of pseudorange residuals is calculated, considering only the n-k smallest residuals, where n denotes the number of pseudoranges available at the current epoch, and k denotes the number of simultaneous faults that shall be considered. The candidate solution with the smallest squared sum of n-k smallest residuals is selected. The magnitudes of all residuals of the selected candidate solution are then assessed to identify the faulty pseudoranges. Hereby, over-estimating the number of simultaneous faults is not critical, as long as enough redundancy for fault detection and exclusion is available. Furthermore, the candidate solution is validated by comparing the selected solution with the second best solution sufficiently far away.
The grid of position and receiver clock error candidates can be centered around an all-in-view solution, given that pseudoranges with excessive errors have been excluded by other means, e.g. NLOS tracking is often detectable from a low C/N0. This ensures that the true solution is within the space spanned by the grid. Another constraint that needs to be considered is that the granularity of the grid is sufficiently small compared to the magnitudes of the pseudorange biases that shall be detected.
In the paper, the proposed method will be described in detail. Then, numerical simulations are performed, whereby artificial faults are introduced to the pseudorange measurements. The fault detection capabilities of the proposed method are then compared to state-of-the art fault detection and exclusion techniques, namely
- An fault detection and exclusion approach based on the weighted sum of squared error
- Fault detection and exclusion using robust M-Estimators, whereby Huber and Tuckey cost functions are considered
- Iteratively Re-weighted Least Squares (IRLS), which minimizes the L1-norm and is therefore more robust against outliers than a conventional Least Squares minimizing the L2 norm
- Least Trimmed Squares (LTS)
For each of these techniques used for comparison, the basic idea is described as well, and the fundamental equations are discussed. The numerical simulations show the advantages of the proposed method when the number of outliers is considerable compared to the number of available measurements.
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