Covariance Estimation and Gaussianity Assessment for State and Measurement Noise

Abstract

Článek je věnován odhadu vlastností poruch stochastického dynamického systému popsaného stavovým modelem. V článku je pozornost věnována nestrannému odhadu kovariančních matic poruch a statistickému rozhodnutí, zda poruchy jsou Gaussovské či ne. Navržené přístupy a metody jsou implementovány v prostředí MATLAB a důkladně validovány v numerických simulacích.

This paper deals with estimation and assessment of the characteristics of the noises of a system described by the linear state-space model. In particular, the emphasis on the recently introduced Noise Covariance Matrices Estimation with Gaussianity Assessment (NEGA) method demonstrates the ability to provide unbiased and consistent estimates of the state and measurement noise covariance matrices and a statistical hypothesis-test-based decision regarding the noises Gaussianity for a time-varying model. The NEGA method is briefly reviewed and theoretically extended in three directions; (i) design parameter specification, (ii) thorough analysis on selection of a statistical test for Gaussianity assessment, and (iii) design of efficient algorithm for the time-invariant models. The theoretical results are illustrated in a Monte-Carlo based numerical study using exemplary MATLAB implementations of the method.