Aimed at the problems that in distributed state estimation systems, the fusion methods are often employed to systematically combine multiple estimates of the state into a single, more accurate estimate, and if the correlation structure is unknown, conservative strategies are typically pursued with less accurate, an inverse covariance intersection fusion robust steady-state Kalman filter is proposed to gain more accurate estimate. As a major advantage of the novel approach, the fusion results prove to be more accurate than those provided by the well-known covariance intersection method. The geometric interpretation of the accuracy relations is given based on the covariance ellipses. A Monte-Carlo simulation example for a two-sensor system shows that its actual accuracy is close to that of the optimal Kalman fuser with known cross-covariance.