A reduced complexity sub-optimal nonlinear predictor

In this paper radial basis function (RBF) and Volterra series (VS) nonlinear predictors are examined with a view to reducing their complexity while maintaining prediction performance. A geometrical interpretation is presented which results in a predictor which although suboptimal is of considerably reduced complexity. The geometric interpretation indicates that while a multiplicity of choices of reduced state predictors exists, some choices are better than others in terms of the numerical conditioning of the solution. Two algorithms are developed using this signal subspace approach to find reduced state solutions which are "close to" the minimum norm solution and which share its numerical properties. The performance of these algorithms is assessed using chaotic time series as test signals.