Cramer-Rao inequality

The parameters A,k and b must be estimated from sr The general problem of parameter estimation is to estimate a parameter, 0, given a number of samples, x,-, drawn from a population that has a probability distribution P(x, 0). It can be shown that there is a minimum variance bound (MVB), known as the Cramer-Rao inequality, that limits the accuracy of any method of estimating 0 [55]. There are a number of methods that approach the MVB and give unbiased estimates of 0 for large sample sizes [55]. Among the more popular of these methods are maximum likelihood estimators (MLE) and least-squares estimation (LS). The MLE... 

It should be noted that the multi-term estimates [Eqs. (32), (34), (47)] retain the optimality of LSM estimates, i.e. they have smallest errors as determined by the Cramer-Rao inequality, Eq. (16). However, the Cramer-Rao inequality is valid only if all assumptions about noise in both the measurements and the a priori terms are correct. Therefore, the validation of the assumptions is important, while problematic in reality. A useful consistency check can be performed using the achieved value of the minimized quadratic form (a) [Eq. (30)]. For example, in case of zero biases, the minimum value of the three-term (a) [Eq (48)] has a distribution with mean... 

To optimize or compare measurement protocols, an index of quality must be quantified for each estimated parameter. For a parameter taken separately, the performance of estimation is a function of both the variance (or precision) and the bias (or accuracy) of the estimate. The covariance matrix of each unbiased estimator 0 checks the inequality of Frechet-Cramer-Rao 24... 

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