A practical sub-space adaptive filter

Abstract

A Sub-Space Adaptive Filter (SSAF) model is developed using, as a basis, the Modified Probabilistic Neural Network (MPNN) and its extension the Tuneable Approximate Piecewise Linear Regression (TAPLR) model. The TAPLR model can be adjusted by a single smoothing parameter continuously from the best piecewise linear model in each sub-space to the best approximately piecewise linear model over the whole data space. A suitable value in between ensures that all neighbouring piecewise linear models merge together smoothly at their boundaries. This model was developed by altering the form of the MPNN, a network used for general nonlinear regression. The MPNNs special structure allows it to be easily used to model a process by appropriately weighting piecewise linear models associated with each of the network's radial basis functions. The model has now been further extended to allow each piecewise linear model section to be adapted separately as new data flows through it. By doing this, the proposed SSAF model represents a learning/filtering method for nonlinear processes that provides one solution to the stability/plasticity dilemma associated with standard adaptive filters.