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We can use this information to refine our estimate of .If the residual is small, so is the correction to the estimate. The pertinent equation is (from the block diagram): Equation 6 The only task now is to find the quantity .

Equation 7 Associated with each of these errors is a mean squared error, or variance: Equation 8 where the operator E{ } represents the expected, or average, value.

These definitions will be used in the calculation of the quantity .

Equation 11 This expression is still quite complicated.

To simplify it we will consider the numerator and the denominator separately.

We have assumed that a copy of the original system (i.e., the gains a, b, and h arranged as shown) should be used to form the estimator.