The solutions to many vision problems involve integrating measurements from multiple sources. Most existing methods rely on a hidden assumption, i.e., these measurements are consistent. In reality, unfortunately, this may not hold. The fact that naively fusing inconsistent measurements amounts to failing these methods indicates that this is not a trivial problem. This paper presents a novel approach to handling it. A new theorem is proven that gives two algebraic criteria to examine the consistency and inconsistency. In addition, a more general criterion is presented. Based on the theoretical analysis, a new information integration method is proposed and leads to encouraging results when applied to the task of visual tracking.