This paper proposes a state estimation scheme over lossy bidirectional communication channels by means of a UIO (unknown input observer) and gain switching. Under some conditions on loss patterns and on system matrices, the proposed scheme guarantees that a weighted square norm of the estimation error either decreases monotonically, or stays below the latest-received value, if observation is received or lost, respectively. The switching gains are designed by solving LMIs (linear matrix inequalities) simultaneously.