The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-121

“Time and Lag Recursive Computation of Cumulants from a State Space Models”

by Ananthram Swami and Jerry M. Mendel

July 1988

Time and lag recursive algorithms for the computation of the cumulants of the state vector and the output process of a multiple-input multiple-output (MIMO) time-varying state-space model (SSM) are derived by using a Kronecker product representation for the cumulants of vector processes. The noise processes are not assumed to be stationary. Elegant expressions are obtained when the SSM is time-invariant and in observable form. For MIMO linear processes, closed-form expressions relating the output cumulants to the SSM parameters and to the impulse response matrices are established. Symmetry relations for the cumulants of vector processes are also discussed. Computational aspects are discussed in detail; and some system identification issues are addressed.

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