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A New Extension of the Kalman Filter to Nonlinear Systems
, 1997
"... The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which ..."
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Cited by 448 (4 self)
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The Kalman filter(KF) is one of the most widely used methods for tracking and estimation due to its simplicity, optimality, tractability and robustness. However, the application of the KF to nonlinear systems can be difficult. The most common approach is to use the Extended Kalman Filter (EKF) which simply linearises all nonlinear models so that the traditional linear Kalman filter can be applied. Although the EKF (in its many forms) is a widely used filtering strategy, over thirty years of experience with it has led to a general consensus within the tracking and control community that it is difficult to implement, difficult to tune, and only reliable for systems which are almost linear on the time scale of the update intervals. In this paper a new linear estimator is developed and demonstrated. Using the principle that a set of discretely sampled points can be used to parameterise mean and covariance, the estimator yields performance equivalent to the KF for linear systems yet general...
An Introduction to Estimation Theory
 OFFICE NOTE SERIES ON GLOBAL MODELING AND DATA ASSIMILATION
, 1997
"... Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connectin ..."
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Cited by 81 (6 self)
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Despite the explosive growth of activity in the field of Earth System data assimilation over the past decade or so, there remains a substantial gap between theory and practice. The present article attempts to bridge this gap by exposing some of the central concepts of estimation theory and connecting them with current and future data assimilation approaches. Estimation theory provides a broad and natural mathematical foundation for data assimilation science. Stochasticdynamic modeling and stochastic observation modeling are described first. Optimality criteria for linear and nonlinear state estimation problems are then explored, leading to conditionalmean estimation procedures such as the Kalman filter and some of its generalizations, and to conditionalmode estimation procedures such as variational methods. A detailed derivation of the Kalman filter is given to illustrate the role of key probabilistic concepts and assumptions. Extensions of the Kalman filter to nonlinear observat...
InformationTheoretic Control of Multiple Sensor Platforms
, 2002
"... Ben Grocholsky Doctor of Philosophy The University of Sydney March 2002 InformationTheoretic Control of This thesis is concerned with the development of a consistent, informationtheoretic basis for understanding of coordination and cooperation decentralised multisensor multiplatform systems. Au ..."
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Cited by 50 (4 self)
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Ben Grocholsky Doctor of Philosophy The University of Sydney March 2002 InformationTheoretic Control of This thesis is concerned with the development of a consistent, informationtheoretic basis for understanding of coordination and cooperation decentralised multisensor multiplatform systems. Autonomous systems composed of multiple sensors and multiple platforms potentially have significant importance in applications such as defence, search and rescue, mining or intelligent manufacturing. However, the e#ective use of multiple autonomous systems requires that an understanding be developed of the mechanisms of coordination and cooperation between component systems in pursuit of a common goal. A fundamental, quantitative, understanding of coordination and cooperation between decentralised autonomous systems is the main goal of this thesis.
Recurrent Multilayer Perceptrons for Identification and Control: The Road to Applications
, 1995
"... : This study investigates the properties of arti#cial recurrent neural networks. Particular attention is paid to the question of how these nets can be applied to the identi#cation and control of nonlinear dynamic processes. Since these kind of processes can only insu#ciently be modelled by conve ..."
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Cited by 21 (3 self)
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: This study investigates the properties of arti#cial recurrent neural networks. Particular attention is paid to the question of how these nets can be applied to the identi#cation and control of nonlinear dynamic processes. Since these kind of processes can only insu#ciently be modelled by conventional methods, di#erent approaches are required. Neural networks are considered to be useful for this purpose due to their ability to approximate a wide class of continuous functions. Among the numerous network structures, especially the recurrentmultilayer perceptron #RMLP# architecture is promising from application point of view. This network architecture has the wellknown properties of multi layer perceptrons and moreover these nets have the ability to incorporate temporal behavior. Departing from the original process description the applicability of RMLPs is investigated and di#erent learning algorithms for this network class are outlined. Furthermore, besides the conventional...
Predictive lineargaussian models of stochastic dynamical systems
 In 21st Conference on Uncertainty in Artificial Intelligence
, 2005
"... Models of dynamical systems based on predictive state representations (PSRs) are defined strictly in terms of observable quantities, in contrast with traditional models (such as Hidden Markov Models) that use latent variables or statespace representations. In addition, PSRs have an effectively infin ..."
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Cited by 17 (9 self)
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Models of dynamical systems based on predictive state representations (PSRs) are defined strictly in terms of observable quantities, in contrast with traditional models (such as Hidden Markov Models) that use latent variables or statespace representations. In addition, PSRs have an effectively infinite memory, allowing them to model some systems that finite memorybased models cannot. Thus far, PSR models have primarily been developed for domains with discrete observations. Here, we develop the Predictive LinearGaussian (PLG) model, a class of PSR models for domains with continuous observations. We show that PLG models subsume Linear Dynamical System models (also called Kalman filter models or statespace models) while using fewer parameters. We also introduce an algorithm to estimate PLG parameters from data, and contrast it with standard Expectation Maximization (EM) algorithms used to estimate Kalman filter parameters. We show that our algorithm is a consistent estimation procedure and present preliminary empirical results suggesting that our algorithm outperforms EM, particularly as the model dimension increases. 1
An Inertial Measurement Unit for User Interfaces
, 2000
"... Inertial measurement components, which sense either acceleration or angular rate, are being embedded into common user interface devices more frequently as their cost continues to drop dramatically. These devices hold a number of advantages over other sensing technologies: they measure relevant param ..."
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Cited by 15 (4 self)
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Inertial measurement components, which sense either acceleration or angular rate, are being embedded into common user interface devices more frequently as their cost continues to drop dramatically. These devices hold a number of advantages over other sensing technologies: they measure relevant parameters for human interfaces and can easily be embedded into wireless, mobile platforms. The work in this dissertation demonstrates that inertial measurement can be used to acquire rich data about human gestures, that we can derive efficient algorithms for using this data in gesture recognition, and that the concept of a parameterized atomic gesture recognition has merit. Further we show that a framework combining these three levels of description can be easily used by designers to create robust applications.
Parameter estimation for partially observed hypoelliptic diffusions
, 2009
"... Summary. Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exa ..."
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Cited by 11 (1 self)
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Summary. Hypoelliptic diffusion processes can be used to model a variety of phenomena in applications ranging from molecular dynamics to audio signal analysis. We study parameter estimation for such processes in situations where we observe some components of the solution at discrete times. Since exact likelihoods for the transition densities are typically not known, approximations are used that are expected to work well in the limit of small intersample times ∆t and large total observation times N∆t. Hypoellipticity together with partial observation leads to illconditioning requiring a judicious combination of approximate likelihoods for the various parameters to be estimated. We combine these in a deterministic scan Gibbs sampler alternating between missing data in the unobserved solution components, and parameters. Numerical experiments illustrate asymptotic consistency of the method when applied to simulated data. The paper concludes with application of the Gibbs sampler to molecular dynamics data. 1.
Predictive linearGaussian models of controlled stochastic dynamical systems
 In ICML
, 2006
"... We introduce the controlled predictive linearGaussian model (cPLG), a model that uses predictive state to model discretetime dynamical systems with realvalued observations and vectorvalued actions. This extends the PLG, an uncontrolled model recently introduced by Rudary et al. (2005). We show t ..."
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Cited by 5 (1 self)
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We introduce the controlled predictive linearGaussian model (cPLG), a model that uses predictive state to model discretetime dynamical systems with realvalued observations and vectorvalued actions. This extends the PLG, an uncontrolled model recently introduced by Rudary et al. (2005). We show that the cPLG subsumes controlled linear dynamical systems (LDS, also called Kalman filter models) of equal dimension, but requires fewer parameters. We also introduce the predictive linearquadratic Gaussian problem, a costminimization problem based on the cPLG that we show is equivalent to linearquadratic Gaussian problems (LQG, sometimes called LQR). We present an algorithm to estimate cPLG parameters from data, and show that our algorithm is a consistent estimation procedure. Finally, we present empirical results suggesting that our algorithm performs favorably compared to expectation maximization on controlled LDS models. 1.
Extended Kalman Filtering for the Modeling and Analysis of ICG Pharmacokinetics using NIR Optical Methods
"... A number of studies indicate that compartmental modeling of indocyanine green (ICG) pharmacokinetics, as measured by near infrared (NIR) techniques, may provide diagnostic information for tumor differentiation. However, compartmental parameter estimation is a highly nonlinear problem with limited d ..."
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A number of studies indicate that compartmental modeling of indocyanine green (ICG) pharmacokinetics, as measured by near infrared (NIR) techniques, may provide diagnostic information for tumor differentiation. However, compartmental parameter estimation is a highly nonlinear problem with limited data available in a clinical setting. Furthermore, pharmacokinetic parameter estimates show statistical variation from one data set to another. Thus, a systematic and robust approach is needed to model, estimate and quantify ICG pharmacokinetic parameters. In this paper, we propose to model ICG pharmacokinetics in extended Kalman filtering (EKF) framework. EKF effectively models multiplecompartment and multiplemeasurement systems in the presence of measurement noise and uncertainties in model dynamics. It provides simultaneous estimation of pharmacokinetic parameters and ICG concentrations in each compartment. Moreover, recursive nature of the Kalman filter estimator potentially allows real time monitoring of time varying pharmacokinetic rates and concentration changes in different compartments. We tested our approach using the ICG concentration data acquired from four Fischer rats carrying adenocarcinoma tumor cells. Our study indicates that EKF model may provide additional parameters that may be useful for tumor differentiation.
Preface
"... This book is the result of an unsuccessful joke. During the summer of 1990, we were both participating in the Complex Systems Summer School of the Santa Fe Institute. Like many such programs dealing with “complexity, ” this one was full of exciting examples of how it can be possible to recognize whe ..."
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This book is the result of an unsuccessful joke. During the summer of 1990, we were both participating in the Complex Systems Summer School of the Santa Fe Institute. Like many such programs dealing with “complexity, ” this one was full of exciting examples of how it can be possible to recognize when apparently complex behavior has a simple understandable origin. However, as is often the case in young disciplines, little effort was spent trying to understand how such techniques are interrelated, how they relate to traditional practices, and what the bounds on their reliability are. These issues must be addressed if suggestive results are to grow into a mature discipline. Problems were particularly apparent in time series analysis, an area that we both arrived at in our respective physics theses. Out of frustration with the fragmented and anecdotal literature, we made what we thought was a humorous suggestion: run a competition. Much to our surprise, no one laughed and, to our further surprise, the Santa Fe Institute promptly agreed to support it. The rest is history (630 pages worth). Reasons why a competition might be a bad idea abound: science is a thoughtful activity, not a simple race; the relevant disciplines are too dissimilar and the questions too difficult to permit meaningful comparisons; and the required effort might be prohibitively large in return for potentially misleading results. On the other hand, regardless of the very different techniques and language games of the different disciplines that study time series (physics, biology, economics,...), very