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

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