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In the Internet of Things (IoT) paradigm, distributed sensors and actuatorscan observe and act on their environment, communicating wirelessly. In thiscontext, filtering the observations and tracking the network and environmentstate over time is extremely important, and the Kalman Filter (KF) is one ofthe most common tools for this. Several of these applications deal withcensored data, either because of sensor saturation or limited detectionregions: when censoring happens, all measurements below a certain threshold areclipped to the threshold value. The recently proposed Tobit Kalman Filter (TKF)is an adjusted version of the KF that can deal with censored measurements.However, like the traditional KF, it needs full knowledge of the process andmeasurement noise covariances to work, which are not always available inpractice. In this work, we relax this assumption and propose the Adaptive TobitKalman Filter (ATKF), which can dynamically estimate the process andmeasurement noise along with the hidden state of the system from the censoredmeasurements. We apply our solution to navigation and positioning IoTscenarios, obtaining a negligible performance loss with regard to the TKF, evenwith no a priori knowledge of the noise statistics.

The Adaptive Tobit Kalman Filter: Tracking Position with Censored Measurements in the IoT