In this book, Andrew Harvey sets out to provide a unified and comprehensive theory of structural time series models. Unlike the traditional ARIMA models, structural time series models consist explicitly of unobserved components, such as trends and seasonals, which have a direct interpretation. As a result the model selection methodology associated with structural models is much closer to econometric methodology. The link with econometrics is made even closer by the natural way in which the models can be extended to include explanatory variables and to cope with multivariate time series. From the technical point of view, state space models and the Kalman filter play a key role in the statistical treatment of structural time series models. The book includes a detailed treatment of the Kalman filter. This technique was originally developed in control engineering, but is becoming increasingly important in fields such as economics and operations research. This book is concerned primarily with modelling economic and social time series, and with addressing the special problems which the treatment of such series poses. The properties of the models and the methodological techniques used to select them are illustrated with various applications. These range from the modellling of trends and cycles in US macroeconomic time series to to an evaluation of the effects of seat belt legislation in the UK.

Forecasting, Structural Time Series Models and the Kalman Filter

We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Stochastic Differential Equations

System Identification I

This paper addresses to some of the latest contributions on the application of Finite Control Set Model Predictive Control (FCS-MPC) in Power Electronics. In FCS-MPC , the switching states are directly applied to the power converter, without the need of an additional modulation stage. The paper shows how the use of FCS-MPC provides a simple and efficient computational realization for different control objectives in Power Electronics. Some applications of this technology in drives, active filters, power conditioning, distributed generation and renewable energy are covered. Finally, attention is paid to the discussion of new trends in this technology and to the identification of open questions and future research topics.

State of the Art of Finite Control Set Model Predictive Control in Power Electronics

Model predictive control (MPC) is a very attractive solution for controlling power electronic converters. The aim of this paper is to present and discuss the latest developments in MPC for power converters and drives, describing the current state of this control strategy and analyzing the new trends and challenges it presents when applied to power electronic systems. The paper revisits the operating principle of MPC and identifies three key elements in the MPC strategies, namely the prediction model, the cost function, and the optimization algorithm. This paper summarizes the most recent research concerning these elements, providing details about the different solutions proposed by the academic and industrial communities.

/pdf/model-predictive-control-for-power-converters-and-drives-1x9taym0xu.pdf

Model Predictive Control for Power Converters and Drives: Advances and Trends

In this chapter, background on sampling and Fourier analysis of signals is provided. The chapter provides a brief review of the key concepts to establish notation. In particular, the continuous and discrete-time Fourier transform are defined. Sampling of signals and the aliasing effect are then presented. Finally, the use of antialiasing filters and reconstruction of signals from samples are also discussed.

Background on Sampling of Signals

In this paper we address the joint estimation of the channel impulse response in orthogonal frequency division multiplexing systems with phase distortion, namely phase noise and carrier frequency offset, phase noise bandwidth and the additive noise variance. The estimation algorithm is based on an implementation of the Extended Kalman Filter within the general framework of the Expectation-Maximization algorithm. We focus on the partial training case, where the transmitted signal is not fully known. To tackle this problem, we utilize a Rao-Blackwellized Extended Kalman Filter. We also compare our results with another nonlinear filtering technique, namely Rao-Blackwellized Particle Filtering, applied to this joint estimation problem. The performance of the two filtering techniques considered in this paper is evaluated in terms of the mean square error of the channel estimates and the numerical complexity introduced by each of these techniques.

EM-based ML channel estimation in OFDM systems with phase distortion using RB-EKF

Sampled-data models depend on knowledge or assumptions about the intersample behavior of the signals. In this sense, it is possible to use B-splines in the hold device as an interpolating function to represent an assumption about the smoothness of the system input signal or prior knowledge about it. In this paper, we obtain a sampled-data model for a continuous-time nonlinear system when the input is generated by a B-spline generalized hold. Moreover, an explicit characterization of the sampling zero dynamics is given, showing that these zero dynamics are asymptotically equal to the asymptotic sampling zeros of the linear case when the sampling period goes to zero.

B-spline Generalized Hold for Nonlinear Sampled-Data Systems

In this paper, we propose an iterative algorithm to perform model selection. This algorithm is a sequential technique that utilizes ideas from filtering theory. We found that the value of initial parameters in our method plays a key role in selecting models. We study the effect of those parameters, and propose guidelines on how to choose them. Finally, we explore and discuss extensions of the algorithm.

A filtering approach for model selection

In this paper we obtain the maximum likelihood estimate of the parameters of discrete-time state-space models by using a dual time-frequency domain approach. We propose an Expectation Maximization formulation that considers a (non-bijective) linear transformation of the available data. Such a transformation may correspond to different options: selection of time-domain data, transformation to the frequency domain, or selection of frequency-domain data obtained from time-domain samples. We also explore the application of these ideas to Errors-In-Variables systems.

Juan I. Yuz

Papers

Background on Sampling of Signals

EM-based ML channel estimation in OFDM systems with phase distortion using RB-EKF

B-spline Generalized Hold for Nonlinear Sampled-Data Systems

A filtering approach for model selection

Identification of state-space systems using a dual time-frequency domain approach