This paper gives an optimal solution of the two-stage Kalman filter for linear stochastic systems subject to random bias. It is shown that the state estimate can be expressed as X-k/k = (X) over tilde(k/k)+ beta(k/k)b(k/k) where (X) over tilde(k/k) is a modified bias-free state estimate and b(k/k) the optimal estimate of random bias.