Adaptive spectrum estimation by including prior information into the window method

A block adaptive autocorrelation, and spec trum, estimation scheme is studied. Its relation to a recently proposed variational formulation of the classical window method is shown. Under this interpretation, the gain of the adaptive scheme turns out to take the value of the window at the corresponding autocorrelation lag. An extension of the functional being minimized in the variational formulation gives the error which is minimized at each step of the adaptive scheme, and leads also to an extended window method including prior information into the estimate. Stability and statiscal assymtotic behavior is studied under simplifying assumtions.