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Target tracking with Kalman filters is hampered by target maneuvering and unknown process and measurement noises. We show that moving data windows may be used to analyze state and measurement error sequences, determining robust estimates of bias and covariance. For steps in the system forcing functions and non-Gaussian measurement errors, the robust estimators yield improvements over linear bias and covariance estimators. Extensive simulations compare conventional, linear adaptive, and robust adaptive average step responses of a first-order system filter. Quantities examined are state estimate, state error, process and measurement covariance estimates, Kalman gain, and input step estimate.