Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

Gurumoorthy, K. S., Grudzien, C., Apte, A., Carrassi, A. ORCID: https://orcid.org/0000-0003-0722-5600 and Jones, C. K. R. T. (2017) Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution. SIAM Journal on Control and Optimization, 55 (2). pp. 741-759. ISSN 0363-0129 doi: 10.1137/15M1025839

Abstract/Summary

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/90354
Identification Number/DOI	10.1137/15M1025839
Refereed	Yes
Divisions	No Reading authors. Back catalogue items Science > School of Mathematical, Physical and Computational Sciences > National Centre for Earth Observation (NCEO) Science > School of Mathematical, Physical and Computational Sciences > Department of Meteorology
Publisher	Society for Industrial and Applied Mathematics
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