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Let $M \in \mathbb{R}^{m \times n}$. Let $S \in \mathbb{R}^{m \times N_t}, U \in \mathbb{R}^{n \times N_t}$, with $ N_t \gg m,n$. Moreover, $\epsilon = S - M U$, with $\epsilon$ zero mean white noise with covariance $C_e$.

How to estimate $M$ using a least squares and using the knowledge of $S,M, Ce$ ? Is there a closed-form expression ?

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  • $\begingroup$ I changed $N_t>>m,n$ to $N_t\gg m,n.$ This is coded as N_t\gg m,n. $\endgroup$ Commented Oct 13, 2023 at 19:33
  • $\begingroup$ @baptiste You probably don't want to estimate $M$ using the knowledge of $M$ itself. I think there is a typo somewhere. $\endgroup$ Commented Mar 19 at 9:39

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