System Identification I

Cyclostationarity: half a century of research

The paper gives a survey of errors-in-variables methods in system identification. Background and motivation are given, and examples illustrate why the identification problem can be difficult. Under general weak assumptions, the systems are not identifiable, but can be parameterized using one degree-of-freedom. Examples where identifiability is achieved under additional assumptions are also provided. A number of approaches for parameter estimation of errors-in-variables models are presented. The underlying assumptions and principles for each approach are highlighted.

Errors-in-Variables Methods in System Identification

2017 25th European Signal Processing Conference (EUSIPCO)

Precise dynamic models of processes are required for many applications, ranging from control engineering to the natural sciences and economics. Frequently, such precise models cannot be derived using theoretical considerations alone. Therefore, they must be determined experimentally. This book treats the determination of dynamic models based on measurements taken at the process, which is known as system identification or process identification. Both offline and online methods are presented, i.e. methods that post-process the measured data as well as methods that provide models during the measurement. The book is theory-oriented and application-oriented and most methods covered have been used successfully in practical applications for many different processes. Illustrative examples in this book with real measured data range from hydraulic and electric actuators up to combustion engines. Real experimental data is also provided on the Springer webpage, allowing readers to gather their first experience with the methods presented in this book. Among others, the book covers the following subjects: determination of the non-parametric frequency response, (fast) Fourier transform, correlation analysis, parameter estimation with a focus on the method of Least Squares and modifications, identification of time-variant processes, identification in closed-loop, identification of continuous time processes, and subspace methods. Some methods for nonlinear system identification are also considered, such as the Extended Kalman filter and neural networks. The different methods are compared by using a real three-mass oscillator process, a model of a drive train. For many identification methods, hints for the practical implementation and application are provided. The book is intended to meet the needs of students and practicing engineers working in research and development, design and manufacturing.

Identification of Dynamic Systems: An Introduction with Applications

Brief paper: Maximum likelihood identification of noisy input-output models

The Frisch scheme in algebraic and dynamic identification problems

In the framework of speech enhancement, several parametric approaches based on an a priori model for a speech signal have been proposed. When using an autoregressive (AR) model, three issues must be addressed. (1) How to deal with AR parameter estimation? Indeed, due to additive noise, the standard least squares criterion leads to biased estimates of AR parameters. (2) Can an estimation of the variance of the additive noise for each speech frame be obtained? A voice activity detector is often used for its estimation. (3) Which estimation rules and techniques (filtering, smoothing, etc.) can be considered to retrieve the speech signal? Our contribution in this paper is threefold. First, we propose to view the identification of the noisy AR process as an errors-in-variables problem. This blind method has the advantage of providing accurate estimations of both the AR parameters and the variance of the additive noise. Second, we propose an alternative algorithm to standard Kalman smoothing, based on a constrained minimum variance estimation procedure with a lower computational cost. Third, the combination of these two steps is investigated. It provides better results than some existing speech enhancement approaches in terms of signal-to-noise-ratio (SNR), segmental SNR, and informal subjective tests.

Roberto Diversi

Papers

Brief paper: Maximum likelihood identification of noisy input-output models

The Frisch scheme in algebraic and dynamic identification problems

Speech Enhancement Combining Optimal Smoothing and Errors-In-Variables Identification of Noisy AR Processes

Identification of ARX and ARARX Models in the Presence of Input and Output Noises

A New Criterion in EIV Identification and Filtering Applications