Sensor Calibration and Hysteresis Compensation With Heteroscedastic Gaussian Processes

We deal with the problem of estimating the true measured scalar quantity from the output signal of a sensor that is afflicted with hysteresis and noise. We use a probabilistic, nonparametric sensor model based on heteroscedastic Gaussian processes (GPs), which is trained using a data set of sensor output and ground truth pairs. The inference problem is formulated as state estimation in a dynamical system. We exploit the low dimensionality of the latent state space of the sensor to perform exact probabilistic inference of the measured quantity from a time series of the sensor's output. Compared with the state-of-the-art assumed density filtering algorithm for GPs, which analytically approximates the posterior by a normal distribution during inference, our method reduces the prediction error by 33% on a data set obtained from a novel flexible tactile sensor based on carbon-black filled elastomers. The proposed model can be applied, but is not limited, to any sensor for which the Preisach model of hysteresis holds. The use of probabilistic modeling and inference not only provides a most likely estimate of the measured quantity but also the corresponding confidence interval.