Reduced rank Volterra filter for robust identification of nonlinear systems (Q2702519)

The reduced rank polynomial filter (a vector-valued polynomial operator with dominant kernel) is studied. A Volterra filter is a polynomial operator that minimizes the mean square error between its output for a given reference random variable and the desired random variable to be approximated. It is postulated that a drastic reduction of computational complexity is achieved by the rank reduction. This rank reduction can make polynomial filters more robust to noise by restricting the influence of higher order multiplications of noise. An explicit formula is given to determine recursively all the coefficient matrices of the optimal reduced rank polynomial filter with minimal mean square error. A numerical example indicates that the proposed method realizes well trade-off between the computational complexity and the estimation accuracy. All proofs are omitted, they will be shown in a later paper.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00062].