On the extended RLS adaptive bilinear filters

Recursive least squares (RLS) adaptive nonlinear filtering using bilinear system models is considered. It is proved that the extended RLS adaptive bilinear filter and the equation-error RLS adaptive bilinear filter are both guaranteed to be stable in the sense that the time average of the squared estimation error is bounded whenever the underlying process that generates the input signals is stable in the same sense. Results of several simulation experiments that compare the usefulness of adaptive bilinear system models with that of truncated second-order Volterra system models in a communication system problem are presented. The adaptive bilinear filter is shown to exhibit good parsimony in the use of coefficients compared with the truncated adaptive Volterra filter. The modeling efficiency and the guaranteed stability of the extended RLS adaptive bilinear filters should make them very attractive choices in nonlinear filtering applications.