Construct a robust high-precision detector with multiple low-precision sensors

This paper consider the problem of combining the binary decisions of multiple sensors to produce a better final decision. It assumes that the detection probability and false alarm probability of individual sensors are unknown, but bounded. We prove that only by increasing the number of sensors, we can achieve any target detection and false alarm probabilities. So we can construct an arbitrarily high-precision detector with low-precision sensors under the condition that the number of such component sensors is above a certain level. These results provide a practical trade-off between the number of sensors and sensor accuracy, which is important in the design of sensor networks.