Abstract: An adaptive Kalman filtering algorithm based on variational Bayesian learning is suggested to cope with the problem in which colored and time-varying measurement noise is introduced. By use of differencing, the model is converted back to a normal model in which measurement noise is white but correlated with process noise. Kalman filtering is modified owing to the correlation and variational Bayesian learning is combined to jointly estimate the measurement noise and the state in a recursive manner. The simulation results demonstrate that this adaptive algorithm is capable of tracking time-varying noise and provides more accurate state estimation than standard Kalman filtering with colored and time-varying noise.