A system for testing the covariance fidelity of an optimal reduced state estimator comprises data storage devices for storing testing data, computer processors in communication with the data storage devices, and a memory storing program instructions for execution by the computer processors. Execution of the program instructions may cause the computer processors to provide an optimal reduced state estimator having state variables and unknown, multidimensional, arbitrarily time-varying parameters, subject to known bounded values. A random component and a bias component of the optimal reduced state estimator may be identified, and then separate evaluations of the components may be performed to determine a fidelity of the optimal reduced state estimator. The random component may be evaluated at a selected epoch and a Mahalanobis Distance Value determined for the random component. The bias component may be evaluated at the selected epoch and a probability of containment determined at a selected MDV.