Statistical analysis and experimental validation of data-driven dynamic measurement methods

Student thesis: Doctoral Thesis

Abstract

Measurements are dynamical processes where the unknown input’s
value is estimated using the sensor’s natural response. The classic
approach is to pass the sensor’s natural response through another
system. This additional system is designed based on a sensor model
and requires redesign every time we use another sensor.
A model-independent algorithm can estimate the input directly using only the sensor response. In this way, the data-driven estimation
method can work with different sensor technologies. In some cases,
the data-driven methods can reduce even more the estimation time
compared with the classical approach.
This thesis deals with a data-driven method that estimates in realtime the value of constant input from its corresponding sensor response. The data-driven method finds the input value by solving
a system of linear equations, in which the regression matrix has a
specific structure, and there is a correlation between the regression
matrix and the regressor because the measurement noise enters both.
To validate the method for metrology applications, we study the
statistical properties of the estimated input. The result of this study
is the quantification of the estimation bias and variance. Using these
two features, we describe the input estimation quality in simulations
and real-life experiments.
Date of Award21 Sep 2020
Original languageEnglish
Awarding Institution
  • Vrije Universiteit Brussel
  • Faculty of Engineering
  • Electricity
SupervisorIvan Markovsky (Promotor), Rik Pintelon (Promotor), Patrick Guillaume (Jury), Roger Vounckx (Jury), Philippe Dreesen (Jury), Nikolaos Deligiannis (Jury), Lyudmila Mihaylova (Jury) & Guillaume Mercère (Jury)

Keywords

  • Cramér-Rao Lower Bound
  • Errors in Variables
  • Frequency Response Function
  • Least Squares
  • Linear Time Invariant
  • Linear Time Varying
  • Monte Carlo
  • Maximum Likelihood
  • Mean Squared Error
  • Recursive Least Squares
  • Root Mean Square
  • Single-Input Single-Output
  • Signal-to-Noise Ratio
  • Time-Varying

Cite this

'