Non-linear minimum variance state-space-based estimation for discrete-time multi-channel systems

A new state equation and non-linear operator-based approach to estimation is introduced for discrete-time multi-channel systems. This is a type of deconvolution or inferential estimation problem, where a signal enters a communications channel involving both non-linearities and transport delays. The measurements are corrupted by a coloured noise signal, which is correlated with the signal to be estimated both at the inputs and outputs of the channel. The communications channel may include either static or dynamic non-linearities represented in a general non-linear operator form. The optimal non-linear estimator is derived in terms of the state equations and non-linear operators that describe the system. The algorithm is relatively simple to derive and to implement in the form of a recursive algorithm. The main advantage of the approach is the simplicity of the non-linear estimator theory and the straightforward structure of the resulting solution. The results may be applied to the solution of channel equalisation problems in communications or fault detection problems in control applications.