For multisensor systems with uncertain covariance linearly correlated white noises, an unified approach to design the covariance intersection(CI) fusion minimax robust Kalman estimators(predictor, filter and smoother) is proposed by using the Lyapunov equation approach. A modified CI fusion robust steady-state Kalman estimator and a minimal upper bound of its actual estimation error variances are presented by using the conservative cross-covariances, which overcomes the disadvantage that the upper bound given by the original CI fuser has larger conservativeness, so that the robust accuracy of the original CI fuser is improved. A simulation example of tracking system is given to illustrate the correctness and effectiveness of the proposed method.