Properties
- Under some weak regularity assumptions, the MMSE estimator is uniquely defined, and is given by
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- In other words, the MMSE estimator is the conditional expectation of given the known observed value of the measurements.
- If and are jointly Gaussian, then the MMSE estimator is linear, i.e., it has the form for matrix and constant . As a consequence, to find the MMSE estimator, it is sufficient to find the linear MMSE estimator. Such a situation occurs in the example presented in the next section.
- The orthogonality principle: An estimator is MMSE if and only if
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- and
- for every affine function of the measurements.
Read more about this topic: Minimum Mean Square Error
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