Online tests of Kalman filter consistency

Robert Piché

    Research output: Contribution to journalArticleScientificpeer-review

    29 Citations (Scopus)
    3616 Downloads (Pure)


    The normalised innovation squared (NIS) test, which is used to assess whether a Kalman filter's noise assumptions are consistent with realised measurements, can be applied online with real data, and does not require future data, repeated experiments or knowledge of the true state. In this work, it is shown that the NIS test is equivalent to three other model criticism procedures, which are as follows: (i) it can be derived as a Bayesian p-test for the prior predictive distribution; (ii) as a nested-model parameter significance test; and (iii) from a recently-proposed filter residual test. A new NIS-like test corresponding to a posterior predictive Bayesian p-test is presented.

    Original languageEnglish
    Pages (from-to)115–124
    JournalInternational Journal of Adaptive Control and Signal Processing
    Issue number1
    Publication statusPublished - 2016
    Publication typeA1 Journal article-refereed


    • Kalman filter
    • Model consistency
    • Normalised innovations squared
    • Predictive distribution

    Publication forum classification

    • Publication forum level 1

    ASJC Scopus subject areas

    • Control and Systems Engineering
    • Electrical and Electronic Engineering
    • Signal Processing


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