Notes From Reading Adaptive Signal Theory (5th Ed) by Simon Haykin

Three Basic Kinds Of Estimation

• Filtering - Extraction of Current and previous information. RealTime operation.
• Smoothing - Data after the time of interest is used. Posteriori operation.
• Prediction - forcasting for some time in the future. RealTime operation.

Filter optimization is useful to think of minimising the mean-square-error.

For stationary inputs the Wiener filter is considered optimal in mean-square-error sense.

Plots of the mean-square value of the error signal versus the adjustable parameters of the linear filter is known as the error-performance-surface. The min point on this is the Wiener solution.

Wiener Filter is no good with moving signals, or precense of noise. Kalman Filters are useful in this sitation.