A Kalman filter algorithm for estimating sinusoids in colored noise

When the input to the adaptive line enhancer (ALE) contains colored noise, it is shown that implementations of adaptive line enhancers using recursive least squares (RLS) algorithms result in suboptimal estimates of the least squares weight vector. Looking at RLS filtering as a Kalman filtering problem makes it possible to account for the presence of colored observation noise by implementing a model of the colored noise using an augmented state equation. The RLS filter derived from this augmented state equation and the corresponding augmented observation equation is shown to have improved performance over the standard RLS filter for ALE prediction lengths greater than and significantly less than the decorrelation time of the colored observation noise.