This paper is devoted to sensor scheduling for a class of sensor networks whose sensors are spatially distributed and measurements are influenced by state dependent noise. Sensor scheduling is required to achieve power saving since each sensor operates with a battery power source. The sensor scheduling problem is formulated as model predictive control which minimizes a quadratic cost function with communication costs, since communications among sensors take much power. A fast and optimal sensor scheduling algorithm is proposed for a class of sensor networks. From a theoretical standpoint, we present that computation time of the proposed algorithm increases exponentially with the number of sensor types, while that of standard algorithms is exponential in the number of the sensors. The proposed algorithm is faster than standard one, since the number of sensor types is always less than or equal to the number of sensors.