Biased Cramér-Rao lower bound calculations for inequality-constrained estimators.

Unbiased Cramér-Rao lower bound (CRB) theory can be used to calculate lower bounds to the variances of unbiased estimates of a set of parameters given only the probability density function of a random vector conditioned on the true parameter values. However, when the estimated parameter values are required to satisfy inequality constraints such as positivity, the resulting estimator is typically biased. To calculate CRBs for biased estimates of the parameter values, an expression for the bias gradient matrix must also be known.