Construct a Kalman Filter for a Stochastic System

A Kalman filter gives a useful estimate of the output of a noisy system. The noisy system, in this case the antenna, has white noise going into one of its inputs and has white noise added to its outputs. The Kalman filter takes in both the noisy output from the antenna () and the noise-free input to the antenna () and creates a filtered output signal that is closer to the actual output. The filtered signal is optimal (the error is minimized).

Visualize the response curves: