Cramér-Rao Bound

The Cramér-Rao bound (CRB) is a fundamental bound in estimation theory. "Estimation" refers here to finding the parameters of a random process.

The CRB shows that for estimators (algorithms) that on average estimate a the correct value (unbiased estimators), there is a lower bound on the accuracy. Accuracy refers here to the variance (or equivalently to the mean squared error).

So, whatever fancy unbiased algorithm you will come up with, its average variance cannot be lower than the CRB.

So, the CRB tells you something about your measurement setup at hand. It can even show possibilities to improve estimation of certain parameters without being specific about the used algorithm.

The multi-parameter CRB gives a kind of "minimal" covariance matrix whose uncertainty ellipsoid is always inside the uncertainty ellipsoid of any unbiased multi-parameter estimator.