Assume that you have access to a noisy observation (static vector) y, which can be expressed as $y=x+b$ where the static vector $x$ is unknown. The noise $b$ is an independent and identically distributed (i.i.d.) zero-mean noise distributed according to a Gaussian distribution with covariance $C$. The mean of the noise b (0) and its covariance $C$ are known, as well as the noisy measurement $y$. What is the best technique to estimate $x$ from $y$ please?
2026-03-25 19:00:51.1774465251
Estimation from noisy observation
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Since the noise term is iid Gaussian with zero mean and equal variances, the most likely value for each $x_i$ is just $y_i$. If you have some reason to believe the $x_i$ have some prior distribution then you can apply Bayesian inference and then choose the posterior mean vector as a point estimate.