The sixth paper, by Christopher. Kreucher, Alfred Hero, Keith .... Switzerland, and the Henry Booker Gold Medal from URSI, as well as other prizes and awards.
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Large-Scale Dynamic Systems Large-scale dynamic systems are highly pervasive in their occurrence and applications, which range from modeling the brain to power systems, sensors and the environment. BY SIMON HAYKIN, Fellow IEEE
Guest Editor ERIC MOULINES
Guest Editor
I. INTRODUCTION 1 All dynamic systems share a basic feature: the state of the system, be it scalar or vector, varies with time. Typically, the state is not measurable directly. Rather, in an indirect manner, it makes its effect measurable through a set of observables. As such, the characterization of dynamic systems is described by a state-space model, which, in general, embodies two equations. 1) State-evolution equation, which, as a Markov chain, describes the evolution of the state as a function of time xtþ1 ¼ f t ðxt ; wt Þ
2)
(1)
where t denotes discrete time, xt denotes the state vector at time t, the vector wt denotes dynamic noise, and f t (.,.) is a vector-valued function of its arguments. Measurement equation, which takes one of two forms, depending on whether the system is passive or active. a) Passive dynamic system, described by yt ¼ gt ðxt Þ; vt Þ
b)
(2a)
where the vector yt denotes the set of observables, the vector vt denotes measurement noise, and gt (.,.) denotes another vectorvalued function. Active dynamic system, described by yt ¼ gt ðxt ; at Þ; vt Þ
(2b)
1 This introduction is adapted from: S. Haykin, A. Hero, and E. Moulines, BModeling, identification, and control of large-scale dynamic systems,[ presented at the 2005 IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA.
Digital Object Identifier: 10.1109/JPROC.2007.893241
0018-9219/$25.00 Ó 2007 IEEE
where the additional vector at denotes action taken by the system at time t. The subscript t in both f t and gt is included to cover situations where these functions are time-varying. According to (2a) and (2b), it is the action at that distinguishes an active dynamic system from a passive one. Most important, an active dynamic system explores its environment by taking action at whenever the environment resides in state xt ; we may therefore think of ðxt ; at Þ as a state-action pair. Just as the environment state xt spans a state space, the action at spans a space of its own called the action space. The constituents of the action space may be different modalities, waveforms, functions, etc., over which the system is able to operate. On this basis, we say an active dynamic system is of a largescale kind due to a combination of three factors: 1) high dimensionality of the environment state space; 2) high computational complexity of the nonlinear predictive model used in tracking the state of the environment; and 3) high search complexity of the action space. In contrast, a passive dynamic system merely listens to its environment;
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and through observables produced by the environment, it infers the state of the environment. Accordingly, a passive dynamic system is said to be of a large-scale kind solely on the basis of factors 1) and 2). The availability of an action space or its absence has serious implications for the specific functions which a dynamic system can perform. Specifically, an active dynamic system is capable of interacting with its environment; hence, through searching over the action space for an optimal policy, it has a natural capability to perform optimal control. On the other hand, a passive dynamic system is well positioned to model its environment and use the model for the purposes of classifying the environment and tracking its state. This brief introduction sets the stage for describing the organization of this special issue devoted to largescale dynamic systems.
II. ORGANIZATION OF THE S PECIAL I SS UE The issue is made up of ten invited papers, which span a wide range of topics, all the way from ion channels to the environment. Specifically, the first two papers deal with the human brain. The first paper, authored by Vikram Krishnamurthy and Shin-Ho Chung, deals with modeling and estimating biological membrane ion channels. Ion channels are water-filled angstromsized pores formed by protein macromolecules in the cell membrane. They regulate the flow of ions into and out of a cell and hence they control all electrical activities in a cell. The paper deals with ion permeation, that is, how individual ions interact with the protein atoms in an ion channel and travel through the channel. The paper presents a large-scale multiparticle stochastic dynamical simulation model called Brownian dynamics for ion permeation. This model capture the dynamics of the ions at a femtosecond time scale and angstrom-unit spatial scale. Then, the 850
paper presents a novel extension called adaptive controlled Brownian dynamics, for estimating the force experienced by a permeating ion at each discrete position along the ionconducting pathway. The profile of this force, commonly known as the potential of mean force, results from the electrostatic interactions between the ions in the conduit and all the charges carried by atoms forming the channel the protein, as well as the induced charges on the protein wall. The authors illustrate the use of adaptive controlled Brownian dynamics in gramicidin channels and sodium channels. The second paper, by Anthony Brockwell, Robert Kass and Andrew Schwartz, deals with recent advances in understanding brain function and its relation to behavior, exemplified by neural activity recorded from the motor cortex. Research findings have important implications in medicine and other fields. For example, it is now possible to build devices that provide direct interfaces between the brain and the external world. The authors describe some of the current understanding of motor cortical function. They then discuss a typical statespace model and filtering based approach to control a robotic prosthetic arm directly from motor cortical activity; and they demonstrate results of the approach on experimental data gathered from a monkey. The next three papers deal with nonlinear filtering. In the third paper, Oliver Cappe´, Simon Godsill, and Eric Moulines build on the pioneering contribution of Gordon et al. (1993), which is commonly regarded as the first instance of modern sequential Monte Carlo (SMC) approaches (sometimes also referred to as Bparticle filtering[ methods). Initially focused on applications to tracking and vision, these techniques are now very widespread and have had a significant impact in virtually all areas of signal processing concerned with Bayesian dynamical models. This paper is intended to serve both as an introduction to SMC
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algorithms for nonspecialists and as a reference to recent contributions in domains where the techniques are still under significant development, including smoothing, estimation of fixed parameters and use of SMC methods beyond the standard filtering contexts. The fourth paper, by Simon Godsill, Jaco Vermaak, Willian Ng, and Jack Li, develops new tracking procedures using particle filters. Standard algorithms in tracking and other state-space models typically assume identical and synchronous sampling rates for the state and measurement processes. However, real trajectories of objects are typically characterized by prolonged smooth sections, with sharp, but infrequent, changes. Thus, a more parsimonious representation of a target trajectory may be obtained by direct modeling of manoeuvre times in the state process, independently from the observation times. This is achieved by assuming the state arrival times to follow a random process themselves, so that state points may be allocated along the trajectory according to the degree of variation, which is consistent with the data. The resulting variable dimension state-inference problem is solved by developing an efficient variable-rate particle filtering algorithm to recursively update the posterior distribution of the state sequence as new data become available. The methodology is quite general and can be applied across many models where dynamic model uncertainty occurs on-line. Specific models are proposed for the dynamics of a moving object under internal forcing, expressed in terms of the intrinsic dynamics of the object. The performance of the algorithms with these dynamic models is demonstrated on several challenging manoeuvring target tracking problems in clutter. The fifth paper, by Ienkaran (Haran) Arasaratnam, Simon Haykin, and Robert Elliott, discusses a new version of the quadrature Kalman filter (QKF), developed theoretically and tested experimentally. The authors first derive the new QKF for
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nonlinear systems with additive Gaussian noise by linearizing the process and measurement functions using statistical linear regression, (SLR), through a set of GaussHermite quadrature points that parameterize the Gaussian density. Moreover, they discuss how the new QKF can be extended and modified to take into account specific details of a given application. Then, they go on to extend the use of the new QKF to discrete-time, nonlinear systems with additive, possibly non-Gaussian noise. A bank of parallel QKFs, called the Gaussian sum-quadrature Kalman filter, (GS-QKF), approximates the predicted and posterior densities as a finite number of weighted sums of Gaussian densities. The weights are obtained from the residuals of the QKFs. Three different Gaussian mixture reduction techniques are presented to alleviate the growing number of the Gaussian sum terms inherent to the GS-QKFs. Simulation results exhibit a significant improvement of the GS-QKFs over the currently used approaches, namely, particle filters and Gaussian-sum extended Kalman filters, to solve nonlinear non-Gaussian filtering problems. The sixth and seventh papers deal with sensor networks. The sixth paper, by Christopher Kreucher, Alfred Hero, Keith Kastella, and Mark Morelande, addresses the problem of sensor management for a large network of agile sensors. Sensor management, as defined therein, refers to the process of dynamically retasking agile sensors based on measurements received, models of the environment, and models of the sensor. Sensors may be agile in a variety of ways; for example, sensors may have the ability to reposition, point an antenna, choose sensing mode, or waveform. The goal of sensor management in a large network is to choose actions for the individual sensors dynamically, so that the utility of the overall network is maximized. The approach presented in the paper is a novel combination of particle filtering for nonparametric density estimation,
information theory for comparing possible action sequences, and a physicomimetic approximation for computational tractability. The seventh paper, by Nikita Visnevski, Vikram Krishnamurthy, Alex Wang, and Simon Haykin, discusses multifunction radars (MFRs). MFRs are sophisticated sensors with complex dynamic modes that are widely used in surveillance and tracking. This paper demonstrates that stochastic context-free grammars (SCFGs) are adequate models for capturing the essential features of the MFR dynamics. Specifically, MFRs are modeled as systems that Bspeak[ a language that is characterized by a stochastic context-free grammar. The paper shows that such a grammar is modulated by a Markov chain representing radar’s policy of operation. The paper also demonstrates how some well-known statistical signal processing techniques can be applied to MFR signal processing using these stochastic syntactic models. The eighth paper, by Saeid Habibi, discusses a new method for state estimation referred to as the smooth variable structure filter (SVSF). The SVSF is mode-based and applies to systems that may be represented by a linear or a smooth nonlinear function. It allows for the explicit definition of the source of uncertainty and can guarantee stability, given an upper bound for uncertainties and noise levels. The performance of the SVSF improves with more refined definition of upper bounds on parameter variations or uncertainties. Furthermore, most filtering methods provide only one measure of performance: the filter innovation vector or (output) estimation error. However, in addition to the innovation vector, the SVSF has a secondary set of performance indicators that quantify the degree of modeling error specific to each state or parameter that is being estimated. The combined robustness and multiple indicators of performance allow for dynamic refinement of internal models in the SVSF. Dynamic refinement and robustness are features that are
particularly advantageous in fault diagnosis and prediction. In this paper, the application of SVSF pertaining to fault detection is provided; the characteristics of this filter in terms of its accuracy and rate of convergence are discussed. In the ninth paper, Marija Ilic discusses the modeling, monitoring and control of electric power systems, presented from the point of view of large-scale dynamic systems. The author highlights that currently used models rely on strong assumptions which help simplify the complexity related to the sheer size of the problem. This has been quite successful and forms the basis of today’s Supervisory Control and Data Acquisition (SCADA) systems and hierarchical control for normal operations. In order to review the models used and to assess the assumptions and their contextual use, the paper formalizes more complex models first. In the latter parts of this paper the author considers the second class of complexities related to emerging behaviors in electric power systems when they are operated outside of the normal operating regions; this can occur either during abnormal technical conditions caused by large equipment failures, or as a result of changing the decision making from hierarchical to open-access paradigms in the evolving electric power systems. A vision of a novel informationbased multilayered Dynamic Energy Control Protocols (DECPs) framework for facilitating evolution into open access just-in-time (JIT) and just-in-place (JIP) electricity services of the future is presented. The author conjectures that these protocols will play an essential role in enhanced energy utilization and its long-term impacts on the environment. The last paper of the issue is coauthored by David Thomson, Louis Lanzerotti, Frank Vernon, Marc Lessard, and Lindsay Smith. This paper describes some unanticipated effects of solar modes on engineering and scientific systems. They begin with historical, scientific, and statistical
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background, then present evidence for the effects of solar modes on various systems. Engineering evidence for these modes was first noticed in an investigation of communications satellite failures and second in a study of excessive dropped calls in cellular phone systems. The paper also includes several sections on multitaper estimates of spectra, canonical coherences, and related statistical techniques used to separate the various
components of this complex system. In an attempt to understand this unexpected source of problems, the authors have found that solar modes are detectable in the interplanetary magnetic fields and energetic particles at the Ulysses spacecraft, five astronomical units from the earth. These modes couple into the magnetosphere, the ionosphere, the geomagnetic field, and atmospheric pressure, which are easily detected in induced voltages on
ocean cables and finally in seismic data where they literally shake the earth. h
Acknowledgment The constructive comments and specific inputs provided by the many reviewers of all ten papers are gratefully acknowledged. The special issue is all the more improved and polished because of those highly valuable comments and inputs.
ABOUT THE GUEST EDITORS Simon Haykin (Fellow, IEEE) received the B.Sc. (First-class Honours), Ph.D., and D.Sc. degrees in electrical engineering from the University of Birmingham, Birmingham, U.K. Currently, he holds the title of Distinguished University Professor in the ECE Department at McMaster University, Hamilton, ON, Canada. He is the author of numerous books, including widely used books: Communication Systems (4th ed., Wiley), Adaptive Filter Theory (4th ed., PrenticeHall), Neural Networks: A Comprehensive Foundation (2nd ed., PrenticeHall), and the newly published Adaptive Radar Signal Processing (Wiley), as well as numerous refereed journal papers. Dr. Haykin is a Fellow of the Royal Society of Canada, recipient of the Honourary Degree of Doctor of Technical Sciences from ETH, Zurich, Switzerland, and the Henry Booker Gold Medal from URSI, as well as other prizes and awards.
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Eric Moulines was born in Bordeaux, France, in 1963. He graduated from Ecole Polytechnique, Paris, France, in 1984 and from Ecole Nationale ´rieure des Te ´le ´communications (ENST), Paris, Supe in 1986. He received the Ph.D. degree in signal processing from ENST in 1990 and the Habilitation ` Diriger des recherches in applied mathematics a ´ Rene ´ (probability and statistics) from Universite Descartes Paris V in 1996. From 1986 to 1990, he was a member of the technical staff at CNET, working on signal processing applied to low-bit rate speech coding and text-to-speech synthesis. From 1990 to 1996, he ´le ´was an Associate Professor at Ecole Nationale Superieure des Te communications, where he is currently a Full Professor (1996Ypresent). He has authored more than 80 journal papers and the book Inference in Hidden Markov Models (Springer Series in Statistics, 2005). His teaching and research interests include applied probability, mathematical and computational statistics and statistical signal processing. Currently, he is working on hidden Markov models, Markov chain Monte Carlo methods, sequential Monte Carlo methods, and time series modeling with main applications to digital communications, inverse problems, tracking in complex environment, and Internet traffic analysis. Prof. Moulines is a member of the IEEE committee Signal Processing: Theory and Methods.
