Statistical Sensor Calibration Algorithms

Abstract: The use of sensors is ubiquitous in our IT-based society; smartphones, consumer electronics, wearable devices, healthcare systems, industries, and autonomous cars, to name but a few, rely on quantitative measurements for their operations. Measurements require sensors, but sensor readings are corrupted not only by noise but also, in almost all cases, by deviations resulting from the fact that the characteristics of the sensors typically deviate from their ideal characteristics.This thesis presents a set of methodologies to solve the problem of calibrating sensors with statistical estimation algorithms. The methods generally start with an initial statistical sensor modeling phase in which the main objective is to propose meaningful models that are capable of simultaneously explaining recorded evidence and the physical principle for the operation of the sensor. The proposed calibration methods then typically use training datasets to find point estimates of the parameters of these models and to select their structure (particularlyin terms of the model order) using suitable criteria borrowed from the system identification literature. Subsequently, the proposed methods suggest how to process the newly arriving measurements through opportune filtering algorithms that leverage the previously learned models to improve the accuracy and/or precision of the sensor readings.This thesis thus presents a set of statistical sensor models and their corresponding model learning strategies, and it specifically discusses two cases: the first case is when we have a complete training dataset (where “complete” refers to having some ground-truth informationin the training set); the second case is where the training set should be considered incomplete (i.e., not containing information that should be considered ground truth, which implies requiring other sources of information to be used for the calibration process). In doing so, we consider a set of statistical models consisting of both the case where the variance of the measurement error is fixed (i.e., homoskedastic models) and the case where the variance changes with the measured quantity (i.e., heteroskedastic models). We further analyzethe possibility of learning the models using closed-form expressions (for example, when statistically meaningful, Maximum Likelihood (ML) and Weighted Least Squares (WLS) estimation schemes) and the possibility of using numerical techniques such as Expectation Maximization (EM) or Markov chain Monte Carlo (MCMC) methods (when closed-form solutions are not available or problematic from an implementation perspective). We finally discuss the problem formulation using classical (frequentist) and Bayesian frameworks, and we present several field examples where the proposed calibration techniques are applied on sensors typically used in robotics applications (specifically, triangulation Light Detection and Rangings (Lidars) and Time of Flight (ToF) Lidars).