Multidimensional nonlinear noise-cancelling filters of the Volterra-Wiener class (Q2702537)

The nonlinear optimal noise cancelling problem for higher-order non-Gaussian stochastic sequences is considered, where optimal is to understand in the least squares sense. Multidimensional nonlinear filters of the Volterra-Wiener class are studied.NEWLINENEWLINENEWLINEThe third degree nonlinear noise-cancelling filter problem is considered in some details. A multidimensional nonlinear orthogonal solution is proposed. The third degree nonlinear noise cancelling filter of the Volterra-Wiener class is derived geometrically by using the generalized Gram-Schmidt orthogonalization of the countable Volterra-type functional basis. In the non-Gaussian case the nonlinear approach assures better estimation accuracy than the linear treatment of the problem. The algorithm was tested in three examples.NEWLINENEWLINEFor the entire collection see [Zbl 0952.00062].