State Estimation with Differential Privacy under Scale Enlargement of the Sensor Network

In this paper, we consider networked control systems consisting of a data aggregator and multiple sensors, where the data aggregator collects the data from the sensors and runs a Kalman filter to estimate the plant's states. To preserve the privacy of the plant's states, the sensors send differentially private measurements of the states to the aggregator. We consider the scenario that an extra sensor is available and discuss the estimation performance of the Kalman filter after adding the extra sensor while still preserving differential privacy. We consider two schemes of sensor addition: integral scheme and separate scheme. In the integral scheme, we design the privacy noises for all sensors in the new sensor group, which means that the privacy noises of the original sensors will be updated. In the separate scheme, the privacy noises of the original sensor group are keep unchanged and we only design the privacy noise of the additional sensor. For both schemes, we analyze the effect of adding an extra sensor on estimation accuracy while ensuring differential privacy. We propose a differential privacy mechanism for sensor addition and show that using this mechanism, the estimation accuracy can always be improved after adding an extra sensor.