Tutorial 3: Recent Advances in Robust Statistics for Signal Processing
Sunday, May 26, 2-5pm
Abdelhak M. Zoubir, Visa Koivunen
Many areas of engineering today show that the distribution of the measurements is far from Gaussian as it contains outliers, which cause the distribution to be heavy tailed. Impulsive (heavy tailed) noise can cause optimal signal processing techniques, especially the ones derived using the nominal Gaussian probability model, to be biased or to even break down. The occurrence of impulsive noise has been reported, for example, in outdoor mobile communication channels, due to switching transients in power lines or automobile ignition, in radar and sonar systems as a result of natural or man-made electromagnetic and acoustic interference. In geolocation position estimation and tracking, non-line-of-sight (NLOS) signal propagation, caused by obstacles such as buildings or trees, results in outliers in the measurements, to which conventional position estimation methods are very sensitive. In classical short-term load forecasting, the prediction accuracy is adversely influenced by outliers, which are caused by nonworking days or exceptional events such as strikes, soccer's World Cup, or natural disasters.
Robustness aims at analysing the impact on statistical methods caused by a discrepancy between the modeling assumptions and reality. It provides methods which sacrifice some efficiency at the exact model to gain resistance against the effects of deviations. It is a theoretical framework that studies, analyses and develops, for example, estimators by relaxing the strict statistical assumptions of the classical parametric estimation. Thus, the techniques of robust statistics are resistant to deviations from the assumptions.
In our tutorial, we address robustness for multichannel estimation and detection problems as well as regression for independently and identically distributed (i.i.d.) data. The important case of complex valued data, as frequently encountered in array processing, radar, and wireless applications is given special attention. A rather extensive treatment of the important and challenging case of dependent data for the signal processing practitioner is also included. For all these problems, a comparative analysis of the most important robust methods is carried out by evaluating their performance theoretically, using simulations as well as real-world data.
Our tutorial gives not only an overview and an introduction to robust statistics for signal processing practitioners, but also a comparative discussion of the very recent developments. Indeed, it is not always clear which robust estimator a practitioner should choose. This limits the popularity and applicability of robust statistical methods since the engineers are confronted with a large number of methods where the right choice for each application is neither straightforward nor clear. We will therefore discuss the pros and cons of each approach for the practical case. Many real-life applications will be included, which will allow assessment of the performance and the computational complexity of the different robust estimation methods, not only from a theoretical viewpoint, but from a practical engineering perspective. Showing the performance gain when using sophisticated robust methods will emphasize their practical importance and usefulness.
The tutorial will be based on our recent manuscript and will have the following structure. Note that we will introduce and compare different estimators using both the theory and real-life applications.
- Basic Concepts of Robustness
- Robustifying the Regression Model
- Introduction and Recent Advances in Robust Estimation of the Linear Regression Model (Application: Localization of a Mobile User Equipment)
- Robust Methods for Complex Valued Multichannel Data
- Introduction and Recent Advances in Robust Statistics for Complex Valued Data (Applications: Robust M Estimation for Complex Valued Data, Robust Detection of Circularity)
- Introduction and Recent Advances in Robust Estimation of the Covariance Matrix (Applications: Robust Direction of Arrival Estimation, Robust High Resolution Frequency Estimation)
- Robust Methods for Dependent Data
- Outlier Propagation and the Breakdown of Robust Methods for Independent Data
- Introduction and Recent Advances in Robust Estimation for ARMA Models (Application: Electric Load Forecasting)
- Robust Filters and Robust Spectrum Estimation (Application: ECG Analysis in Presence of Motion Artifacts)
Abdelhak M. Zoubir
Abdelhak M. Zoubir received his Dr.-Ing. degree from Ruhr-Universität Bochum, Germany. He was with Queensland University of Technology, Australia, from 1992 to 1998. He then joined Curtin University of Technology, Australia, as a professor of telecommunications and was interim head of the School of Electrical and Computer Engineering from 2001 to 2003. Since 2003, he has been a professor of signal processing at Technische Universität Darmstadt, Germany. He is an IEEE Distinguished Lecturer (Class 2010-2011), past chair of the Signal Processing Theory and Methods Technical Committee of the IEEE Signal Processing Society, and he is the editor-in-chief of the IEEE Signal Processing Magazine. His research interest lies in statistical methods for signal processing, applied to telecommunications, radar, sonar, car engine monitoring, and biomedicine. He has published over 300 journal and conference papers in these areas. He is a Fellow of the IEEE.
Visa Koivunen received the D.Sc. degree from the University of Oulu, Finland. He was a visiting researcher at the University of Pennsylvania from 1992 to 1995. Since 1999, he has been a professor at Aalto University (Helsinki University of Technology, Finland), where he is currently an academy professor. He is vice chair and one of the principal investigators in the Smart Radios and Wireless Systems Centre of Excellence in Research nominated by the Academy of Finland. He has been an adjunct faculty member at the University of Pennsylvania and a visiting fellow at Nokia Research Center and Princeton University. His research interests include statistical, communications and array signal processing. He has published over 350 journal and conference papers in these areas. He received the 2007 IEEE Signal Processing Society Best Paper Award. He is an Editorial Board Member of the IEEE Signal Processing Magazine and a Fellow of the IEEE.