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

5 Scopus citations

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

ASJC Scopus subject areas

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

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