Time and lag recursive computation of cumulants from a state-space model

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 time-varying state-space model are derived, using a Kronecker product representation for the cumulants of vector processes. The noise processes are not assumed to be stationary. Symmetry relations for the cumulants of vector processes are discussed. Computational aspects are examined in detail. It is conjectured that the recursive equations derived will be useful in developing state estimators and even optimal controllers based on higher order statistics