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Adaptive Kalman filtering with unknown constant or varying process noise covariance matrix is studied. A resolution is proposed to directly estimate or tune the process noise covariance matrix in Kalman filtering using variational Bayesian technique. By state augmentation, conjugacy of the process noise covariance matrix's inverse-Wishart distribution is realized in the estimation at each time instant. The methodological development is given. Illustration examples are presented to demonstrate the improved state filtering performance and the process noise covariance tracking performance of the new method. [ABSTRACT FROM AUTHOR]