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Identifiability of unknown noise covariance matrices for some special cases of a linear, time-invariant, discrete-time dynamic system

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3 Author(s)
Tsang, W. ; Northeastern University, Boston, MA, USA ; Glover, J. ; Bach, R.

This paper investigates the identification of unknown noise covariance matricesQandRof 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 ofQandRwhich 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 diagonalR. 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.

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Automatic Control, IEEE Transactions on  (Volume:26 ,  Issue: 4 )