The state estimation process

State estimation is the process of extracting a best estimate of a variable from a number of measurements that contain noise. 

The classical problem of obtaining a best estimate of a signal by combining two noisy continuous measurements of the same signal was first solved by Weiner (1949). 

His solution required that both the signal and noise be modelled as random proeess with known statistieal properties. 

This work was extended by Kalman and Buey (1961) who designed a state estimation proeess based upon an optimal minimum varianee filter, generally referred to as a Kalman filter. 

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For the regular filter the observation noise covariance if is a constant matrix determined before state estimation. On the other hand, the measurement noise covariance R(t) may be adjusted to compensate for estimation errors. Using finite-duration impulse response (FIR) filter algorithm the observation noise covariance can be adjusted during the state estimation process. 

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