A new look at bounding integrity risk in the presence of time-correlated errors

Steven E. Langel, Mathieu Joerger, Samer M. Khanafseh, Boris S. Pervan

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

A new approach is developed to upper bound integrity risk for safety-critical GNSS applications when the autocorrelation functions of measurement and process noise are uncertain. The algorithm is recursive and significantly expands the applicable range of existing methods. In Kalman filtering, models must be specified for autocorrelated measurement and process noise. This paper assumes that the noise processes are the output of known linear systems driven by white noise. However, the system parameters are only known to lie in specified intervals. Following the approach in [6], an augmented state model is first developed to propagate the estimate error covariance matrix when there is parameter uncertainty. It is shown that the error variance for a specified state is a polynomial in the unknown parameters whose order grows linearly with time. An exact upper bound on integrity risk is determined by maximizing the variance. Next, a recursive algorithm is derived to update the variance's Taylor series expansion. This enables an approximate bound to be established by maximizing a polynomial whose order is low and remains fixed over time. The Taylor remainder theorem is used to introduce conservatism and provide justification that the approximate bound is at least as large as the exact bound. For a one-dimensional navigation problem, we show that the number of series terms needed to obtain a tight upper bound on integrity risk is less than 10.

Original languageEnglish (US)
Title of host publication30th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2017
PublisherInstitute of Navigation
Pages2436-2451
Number of pages16
ISBN (Electronic)9781510853317
StatePublished - Jan 1 2017
Event30th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2017 - Portland, United States
Duration: Sep 25 2017Sep 29 2017

Publication series

Name30th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2017
Volume4

Conference

Conference30th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2017
CountryUnited States
CityPortland
Period9/25/179/29/17

ASJC Scopus subject areas

  • Software
  • Computer Science Applications
  • Electrical and Electronic Engineering

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    Langel, S. E., Joerger, M., Khanafseh, S. M., & Pervan, B. S. (2017). A new look at bounding integrity risk in the presence of time-correlated errors. In 30th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2017 (pp. 2436-2451). (30th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS 2017; Vol. 4). Institute of Navigation.