Generality of Maximum Likelihood Least Squares

Note that the maximum likelihood estimate coincides with the least squares estimate whenever the signal model is of the form

$\displaystyle x(n) = {\hat x}(n) + v(n)$ (6.53)

where $ v(n)$ is zero-mean Gaussian noise, and $ {\hat x}(n)$ is any deterministic model for the mean of $ x(n)$ . This is an extremely general formulation that can be applied in many situations beyond sinusoids in white noise.

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Likelihood Function