SI&DA - Lecture 6 'Maximum Likelihood Method'

Definition of ‘Maximum Likelihood (ML) Estimators’

The maximum likelihood estimator searches for the max value of the pdf function $f_Y^{\theta }(y)$ where $\theta$ is our parameter to be estimated, we have said that $\theta$ is also equal to the mean of this pdf which is also equal to its max value, here’s way the ML Estimator.

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Definition of ‘Logarithmic Likelihood Function’

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$Y_i$ should be $Y$ we consider only 1 Gaussian pdf. $n$ : number of observation. $y_i$ : $i$-esim observation.

Joint PDF of $i$ Gaussians:

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SIandDAHomework

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A common family of problems: Additive Disturbance

${\Sigma }_e$ is the covariance matrix of $e$ ${\Sigma }_e=E[e{e}^T]$