Does lim (t to infty) E(x-x hat) = 0 imply that there will be less disturbance over time?

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\(E(x)\,\) here denotes the expected value of \(x\,\), where \(x\,\) is a random variable. \(\lim_{t\to\infty} E(x-\hat x)=0\,\) only implies that the mean estimation error will converge to zero over time. Disturbance, however, will affect the variance of the error, which is given by \( E(x-\hat x)^2\,\). In CDS 110b, we will learn how to design observers that minimize this estimation variance if the disturbance can be modeled as Gaussian noise.