Safety-Critical Automotive Positioning Based on SEPB without Atmospheric Corrections

Rod Bryant, Olivier Julien, Chris Hide, M. Skorupa, H. Dorahy, Ian Sheret

Abstract: The design of a GNSS-based integrity concept for automotive applications presents many challenges that are related to the complicated propagation channel encountered in a typical road environment. The presence of obstacles and/or reflectors on or beside the road such as large trucks, buildings, trees, walls, overpasses or tunnels can result in a large variation in the number of received signals or in the quality of the GNSS measurements and have a negative impact on the Gaussianity of the error distribution and the independence of these errors both in time and across measurements. u-blox has been working, among other solutions, on a new integrity concept referred to as Single Epoch Position Bound (SEPB) [1, 2]. It is built on: • a Bayesian estimation framework • the use of multi-frequency multi-GNSS pseudorange and carrier phase measurements • a snapshot position computation to avoid modeling time correlation • highly dynamic non-Gaussian error modeling SEPB has been shown to provide particularly tight bounds on the position. Non-Gaussian GNSS measurement error models have some major advantages in the context of high-integrity automotive positioning. For the same integrity risk, non-Gaussian error models can yield tighter position bounds than traditional Gaussian overbounding techniques, and in addition the mathematical analysis is simplified. The only major disadvantage is that the position bound evaluation can be computationally demanding, particularly if there are many unknown nuisance parameters which need to be included in the state. This is because the Bayesian framework provides the posterior distribution of the position as a function of a potentially large number of states, and evaluating bounds thus results in a computationally intensive numerical integration. To some extent, it is possible to mitigate this by computing the SEPB bound at low frequency (e.g. once every few seconds) and propagating the bound in between, but even with this optimization the computational requirements are still high. One major area for concern when using code and phase measurements in SEPB is the ionosphere. Using ionosphere-free measurements is possible but undesirable because SEPB then cannot take advantage of phase measurements. Indeed, SEPB does not fix integer phase ambiguities, but rather it integrates over the integer ambiguities when forming bounds, and hence it benefits greatly from phase measurements. There is thus a need to model the ionospheric delay. Due to spatial variations, it is difficult to safely model the ionosphere with anything other than a per-satellite parameter, which naturally leads to a large number of unknown states in the system when multiple GNSS are used. Previous published work on SEPB has side-stepped this problem by relying on short baseline RTK corrections, which made ionospheric errors negligible. However, for the non-Gaussian approach to be useful in real-world products it is essential that non-negligible ionospheric effects can be accommodated. In this paper we describe and evaluate advances in SEPB which includes per-satellite ionosphere states. We find that adding per-satellite ionosphere states does result in some increase in computational load, but that with careful design of the numerical integration scheme this load is still tractable for real-time applications. The use of bound propagation between SEPB solutions is shown to lead to an increase of the bound that remains acceptable. The bounding performance is finally evaluated based on a significant amount of real road data together with the use of a PPP correction service, to show that useful position bounds can be obtained without any atmospheric corrections. [1] Bryant, R., Julien, O., Hide, C., Moridi, S., Sheret, I., "Novel Snapshot Integrity Algorithm for Automotive Applications: Test Results Based on Real Data," 2020 IEEE/ION Position, Location and Navigation Symposium (PLANS), Portland, Oregon, April 2020, pp. 670-681. [2] Bryant, Rod, Julien, Olivier, Hide, Chris, Skorupa, M., Sheret, Ian, "Road Vehicle Integrity Bound Propagation Using GNSS/IMU/Odometer," Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), September 2020, pp. 585-611.
Published in: Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021)
September 20 - 24, 2021
Union Station Hotel
St. Louis, Missouri
Pages: 1843 - 1858
Cite this article: Bryant, Rod, Julien, Olivier, Hide, Chris, Skorupa, M., Dorahy, H., Sheret, Ian, "Safety-Critical Automotive Positioning Based on SEPB without Atmospheric Corrections," Proceedings of the 34th International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2021), St. Louis, Missouri, September 2021, pp. 1843-1858.
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