Bayesian strategies for calibrating heteroskedastic static sensors with unknown model structures

Abstract

This paper investigates the problem of calibrating sensors affected by (i) heteroskedastic measurement noise and (ii) a polynomial bias, describing a systematic distortion of the measured quantity. First, a set of increasingly complex statistical models for the measurement process was proposed. Then, for each model the authors design a Bayesian parameters estimation method handling heteroskedasticity and capable to exploit prior information about the model parameters. The Bayesian problem is solved using MCMC methods and reconstructing the unknown parameters posterior in sampled form. The authors then test the proposed techniques on a practically relevant case study, the calibration of Light Detection and Ranging (Lidar) sensor, and evaluate the different proposed procedures using both artificial and field data.