Extended Kalman frequency domain adaptive filtering with data-aided state initialization

Extended Kalman Estimators are applied to the adaptation of the coefficients of a frequency domain filter to remove quasi-stationary colored noise from a received angle-modulated signal. In this application, the estimator´s states are near-minimum variance coefficient estimates and the estimator´s inputs are a nonlinear function of observations of spectral components of the colored noise environment. The First Order Extended Kalman Estimator Formulation is sufficiently general to accommodate the nonlinearity of the observations, but it lacks the robust starting characteristics of a linear estimator in this application. Divergence of the coefficients can occur if the initial estimates are far from their true values. A technique using linear estimators, with initial states corresponding to the a priori initial coefficients was developed to smooth the observations providing good initial estimates prior to turn-on of the Extended Kalman Estimator. This technique can be applied to a wide range of noisy environments when little or no information is available for making initial coefficient estimates.