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Real-time estimation of parameter sin dynamic systems, which becomes increasingly important in the field of high-precision navigation, requires real-time testing of the models underlying the navigation system. A real-time recursive testing procedure than can be used in conjunction with the Kalman filter algorithm is presented, along with diagnostic tools for inferring the detectability of particular model errors. The testing procedure consists of detection, identification, and adaptation. It can accommodate model errors in the measurement model and dynamic model of the integrated navigation system and is optimal in the uniformly-most-powerful-invariant sense.<>