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A state-dependent model and nonlinear operator-based approach to estimation and filtering is introduced for discrete-time multi-channel systems including time delays. The problem involves a signal entering a communications channel involving nonlinearities and transport delay elements. The measurements are assumed to be corrupted by a coloured noise signal which is correlated with the signal to be estimated. The communications channel may include either static or dynamic nonlinearities represented by a general nonlinear operator and/or a state-dependent model form. The theoretical solution does not involve empirical assumptions or linearisation approximations. The resulting algorithm is relatively simple to derive and to implement and the solution has an estimator block structure that can be justified intuitively.