In this paper, the augment Kalman filter (AKF) approach is discussed under the infinity condition. It is proved that the AKF in infinity condition is equivalent to the minimum-variance unbiased (MVU) estimation proposed in Gillijns & De Moor [(2007). Unbiased minimum-variance input and state estimation for linear discrete-time systems. Automatica, 43(1), 111-116]. This result can be regarded as a new contribution in the field of joint input and state estimation. Meanwhile, this result gives another way to estimate the state and unknown input simultaneously. Finally, the theoretical result is validated by simulations.