This article considers the robust estimation problem of linear multisensor systems subject to constraints and additive and multiplicative uncertainties where the decaying of measurements is regarded as the multiplicative uncertainty when taking into account the fading channels between the estimator and sensors. Based on the H performance criterion, a moving horizon H estimation algorithm is proposed from an approximation of the H full information estimation, which describes the estimation problem as a minimax optimization problem. Sufficient conditions for the feasibility and stability of the proposed algorithm are discussed, under which the estimation errors are ultimately bounded. To reduce the difficulty of solving minimax problem, an approximate solution is provided. The simulation comparison results show the effectiveness of the proposed algorithm.