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A nonlinear operator approach to estimation in discrete-time systems is described. It involves inferential estimation of a signal which enters a communications channel involving both nonlinearities and transport delays. The measurements are assumed to be corrupted by a colored noise signal which is correlated with the signal to be estimated. The system model may also include a communications channel involving either static or dynamic nonlinearities. The signal channel is represented in a very general nonlinear operator form. The algorithm is relatively simple to derive and to implement.

The non-linear minimum variance (NMV) filtering problem for a non-linear multi-input and multi-output (MIMO) discrete-time system is considered. The NMV filter is designed to minimise a minimum variance criterion. The system model includes channel non-linearities that may be treated as a black box. The NMV filter can avoid the need for a linearisation stage that is required in the extended Kalman filter (EKF). The MIMO NMV filter algorithm is easy to implement, in comparison to the EKF. The main contribution of this paper lies in the design and evaluation of the NMV algorithm for the non-linear MIMO filtering problem. A case study is used to demonstrate performance that is based upon a problem in the medical signal processing area. The design and the real time implementation of the NMV estimator is also considered, for a laboratory based ball and beam experiment. The performance is compared with that of an EKF and real time implementation of both estimators is discussed

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