This paper is concerned with the distributed state estimation problem over wireless sensor networks. The communication links are unreliable that are subject to random link failures modeled as a set of independent Bernoulli processes. To estimate the plant state collaboratively, a Kalman-consensus filtering approach is developed where the sensors spread the local information obtained from the Kalman filtering algorithm by performing a consensus of the inverse covariance matrices at each time instant. Sufficient conditions for the stochastic boundedness of the Kalman-consensus filter are established. It is shown that the filtering performance is directly influenced by the network connectivity and the collective observability. A numerical example is illustrated to verify the proposed results.