Orthogonality Principle - Orthogonality Principle For Linear Estimators

Orthogonality Principle For Linear Estimators

The orthogonality principle is most commonly used in the setting of linear estimation. In this context, let x be an unknown random vector which is to be estimated based on the observation vector y. One wishes to construct a linear estimator for some matrix H and vector c. Then, the orthogonality principle states that an estimator achieves minimum mean square error if and only if

• and

If x and y have zero mean, then it suffices to require the first condition.