Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system
- 1 August 1981
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 26 (4) , 970-974
- https://doi.org/10.1109/tac.1981.1102753
Abstract
This paper investigates the identification of unknown noise covariance matrices Q and R of an LTI discrete-time dynamic system. Two algorithms based on maximum a posteriori (MAP) and maximum likelihood (ML) cost functions are evaluated. It is demonstrated that the cost functions exhibit local minima versus those elements of Q and R which dominate the steady-state output covariance matrix. The following three special cases are considered: 1) single-input single-output (SISO) system; 2) multiinput single-output (MISO) systems; and 3) single-input multioutput (SIMO) systems with a diagonal R . For these special cases, specific identifiability criteria are presented and verified by examples. The improvement of the MAP algorithm over the ML algorithm is also demonstrated.Keywords
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