Bounding sequential estimation errors due to Gauss-markov noise with uncertain parameters

Steven Langel, Omar García Crespillo, Mathieu Joerger

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

1 Citation (Scopus)

Abstract

This paper describes the derivation and implementation of a new method to overbound Kalman filter (KF) based estimate error distributions in the presence of time-correlated measurement and process noise. The method is specific to problems where each input noise component is first-order Gauss-Markov with a distinct variance σ2 ∈ [σmin2 , σmax2 ] and time constant τ ∈ [τmin, τmax]. The bounds on σ2 and τ are known. Reference [1] derives an overbound for the continuous-time KF, and we extend the result to the more common case of sampled-data systems with discrete-time measurements. We prove that the KF covariance matrix overbounds the estimate error distribution when Gauss-Markov processes are defined using a time constant τmax and a process noise variance inflated by (τmax/τmin). We also show that the overbound is tightest by initializing the variance of the Gauss-Markov process with σ02 = 2σmax2 /[1 + (τmin/τmax)]. The new method is evaluated using covariance analysis for an example application in advanced receiver autonomous integrity monitoring (ARAIM) [2].

Original languageEnglish (US)
Title of host publicationProceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019
PublisherInstitute of Navigation
Pages3079-3098
Number of pages20
ISBN (Electronic)0936406232, 9780936406237
DOIs
StatePublished - Jan 1 2019
Externally publishedYes
Event32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019 - Miami, United States
Duration: Sep 16 2019Sep 20 2019

Publication series

NameProceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019

Conference

Conference32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019
CountryUnited States
CityMiami
Period9/16/199/20/19

Fingerprint

Kalman filters
Error analysis
Time measurement
Markov processes
Covariance matrix
Monitoring
integrity
recipient
time
monitoring

ASJC Scopus subject areas

  • Communication
  • Computer Science Applications
  • Information Systems
  • Software
  • Electrical and Electronic Engineering
  • Computer Networks and Communications

Cite this

Langel, S., Crespillo, O. G., & Joerger, M. (2019). Bounding sequential estimation errors due to Gauss-markov noise with uncertain parameters. In Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019 (pp. 3079-3098). (Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019). Institute of Navigation. https://doi.org/10.33012/2019.17014

Bounding sequential estimation errors due to Gauss-markov noise with uncertain parameters. / Langel, Steven; Crespillo, Omar García; Joerger, Mathieu.

Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019. Institute of Navigation, 2019. p. 3079-3098 (Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019).

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

Langel, S, Crespillo, OG & Joerger, M 2019, Bounding sequential estimation errors due to Gauss-markov noise with uncertain parameters. in Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019. Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019, Institute of Navigation, pp. 3079-3098, 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019, Miami, United States, 9/16/19. https://doi.org/10.33012/2019.17014
Langel S, Crespillo OG, Joerger M. Bounding sequential estimation errors due to Gauss-markov noise with uncertain parameters. In Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019. Institute of Navigation. 2019. p. 3079-3098. (Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019). https://doi.org/10.33012/2019.17014
Langel, Steven ; Crespillo, Omar García ; Joerger, Mathieu. / Bounding sequential estimation errors due to Gauss-markov noise with uncertain parameters. Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019. Institute of Navigation, 2019. pp. 3079-3098 (Proceedings of the 32nd International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GNSS+ 2019).
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