Definition
Let be an unknown random vector variable, and let be a known random vector variable (the measurement or observation). An estimator of is any function of the measurement . The estimation error vector is given by and its mean squared error (MSE) is given by the trace of error covariance matrix
- ,
where the expectation is taken over both and . When is a scalar variable, then MSE expression simplifies to . Note that MSE could equivalently be defined in other ways, since
The MMSE estimator is then defined as the estimator achieving minimal MSE.
Read more about this topic: Minimum Mean Square Error
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