This paper addresses a sensor scheduling problem for a class of networked sensor systems 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. A networked sensor system usually consists of a large number of sensors, but the sensors can be classified into a few different types. We therefore introduce a concept of sensor types in the sensor model to provide a fast and optimal sensor scheduling algorithm for a class of networked sensor systems, where the sensor scheduling problem is formulated as a model predictive control problem. The computation time of the proposed algorithm increases exponentially with the number of the sensor types, while that of standard algorithms is exponential in the number of the sensors. In addition, we propose a fast sensor scheduling algorithm for a general class of networked sensor systems by using a linear approximation of the sensor model.