Convergence and error bounds of adaptive filtering under model structure and regressor uncertainties

Adaptive filtering algorithms are investigated when system models are subject to model structure errors and regressor signal perturbations. System models for practical applications are often approximations of high-order or nonlinear systems, introducing model structure uncertainties. Measurement and actuation errors cause signal perturbations, which in turn lead to uncertainties in regressors of adaptive filtering algorithms. Employing ordinary differential equation （ODE） methodologies, we show that convergence properties and estimation bias can be characterized by certain differential inclusions. Conditions to ensure algorithm convergence and bounds on estimation bias are derived. These findings yield better understanding of the robustness of adaptive algorithms against structural and signal uncertainties.