  In the Internet of Things (IoT) paradigm, distributed sensors and actuators
can observe and act on their environment, communicating wirelessly. In this
context, filtering the observations and tracking the network and environment
state over time is extremely important, and the Kalman Filter (KF) is one of
the most common tools for this. Several of these applications deal with
censored data, either because of sensor saturation or limited detection
regions: when censoring happens, all measurements below a certain threshold are
clipped 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 and
measurement noise covariances to work, which are not always available in
practice. In this work, we relax this assumption and propose the Adaptive Tobit
Kalman Filter (ATKF), which can dynamically estimate the process and
measurement noise along with the hidden state of the system from the censored
measurements. We apply our solution to navigation and positioning IoT
scenarios, obtaining a negligible performance loss with regard to the TKF, even
with no a priori knowledge of the noise statistics.
