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Online tests of Kalman filter consistency
Author(s) -
Piché Robert
Publication year - 2016
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.2571
Subject(s) - kalman filter , bayesian probability , consistency (knowledge bases) , test (biology) , residual , ensemble kalman filter , extended kalman filter , statistics , mathematics , computer science , test data , filter (signal processing) , algorithm , artificial intelligence , computer vision , paleontology , biology , programming language
Summary 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. Copyright © 2015 John Wiley & Sons, Ltd.