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370
Unscented Filtering and Nonlinear Estimation
 Proceedings of the IEEE
, 2004
"... The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the ..."
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Cited by 271 (2 self)
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The extended Kalman filter (EKF) is probably the most widely used estimation algorithm for nonlinear systems. However, more than 35 years of experience in the estimation community has shown that is difficult to implement, difficult to tune, and only reliable for systems that are almost linear on the time scale of the updates. Many of these difficulties arise from its use of linearization. To overcome this limitation, the unscented transformation (UT) was developed as a method to propagate mean and covariance information through nonlinear transformations. It is more accurate, easier to implement, and uses the same order of calculations as linearization. This paper reviews the motivation, development, use, and implications of the UT. Keywords—Estimation, Kalman filtering, nonlinear systems, target tracking. I.
Cooperative control of mobile sensor networks: Adaptive gradient climbing in a distributed environment
 IEEE Transactions on Automatic Control
, 2004
"... Abstract—We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy d ..."
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Cited by 164 (18 self)
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Abstract—We present a stable control strategy for groups of vehicles to move and reconfigure cooperatively in response to a sensed, distributed environment. Each vehicle in the group serves as a mobile sensor and the vehicle network as a mobile and reconfigurable sensor array. Our control strategy decouples, in part, the cooperative management of the network formation from the network maneuvers. The underlying coordination framework uses virtual bodies and artificial potentials. We focus on gradient climbing missions in which the mobile sensor network seeks out local maxima or minima in the environmental field. The network can adapt its configuration in response to the sensed environment in order to optimize its gradient climb. Index Terms—Adaptive systems, cooperative control, gradient methods, mobile robots, multiagent systems, sensor networks. I.
Orthogonal Polynomials of Several Variables
 Encyclopedia of Mathematics and its Applications
, 2001
"... Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1 ..."
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Cited by 133 (28 self)
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Abstract. We report on the recent development on the general theory of orthogonal polynomials in several variables, in which results parallel to the theory of orthogonal polynomials in one variable are established using a vectormatrix notation. 1
Parallel Computation of Multivariate Normal Probabilities
"... We present methods for the computation of multivariate normal probabilities on parallel/ distributed systems. After a transformation of the initial integral, an approximation can be obtained using MonteCarlo or quasirandom methods. We propose a metaalgorithm for asynchronous sampling methods and d ..."
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Cited by 107 (7 self)
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We present methods for the computation of multivariate normal probabilities on parallel/ distributed systems. After a transformation of the initial integral, an approximation can be obtained using MonteCarlo or quasirandom methods. We propose a metaalgorithm for asynchronous sampling methods and derive efficient parallel algorithms for the computation of MVN distribution functions, including a method based on randomized Korobov and Richtmyer sequences. Timing results of the implementations using the MPI parallel environment are given. 1 Introduction The computation of the multivariate normal distribution function F (a; b) = j\Sigmaj \Gamma 1 2 (2) \Gamma n 2 Z b a e \Gamma 1 2 x \Sigma \Gamma1 x dx: (1) often leads to computationalintensive integration problems. Here \Sigma is an n \Theta n symmetric positive definite covariance matrix; furthermore one of the limits in each integration variable may be infinite. Genz [5] performs a sequence of transformations resu...
A generalized discrepancy and quadrature error bound
 Math. Comp
, 1998
"... Abstract. An error bound for multidimensional quadrature is derived that includes the KoksmaHlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which dep ..."
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Cited by 94 (11 self)
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Abstract. An error bound for multidimensional quadrature is derived that includes the KoksmaHlawka inequality as a special case. This error bound takes the form of a product of two terms. One term, which depends only on the integrand, is defined as a generalized variation. The other term, which depends only on the quadrature rule, is defined as a generalized discrepancy. The generalized discrepancy is a figure of merit for quadrature rules and includes as special cases the L pstar discrepancy and Pα that arises in the study of lattice rules.
Recent Advances In Randomized QuasiMonte Carlo Methods
"... We survey some of the recent developments on quasiMonte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a highdimensional inte ..."
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Cited by 60 (12 self)
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We survey some of the recent developments on quasiMonte Carlo (QMC) methods, which, in their basic form, are a deterministic counterpart to the Monte Carlo (MC) method. Our main focus is the applicability of these methods to practical problems that involve the estimation of a highdimensional integral. We review several QMC constructions and dierent randomizations that have been proposed to provide unbiased estimators and for error estimation. Randomizing QMC methods allows us to view them as variance reduction techniques. New and old results on this topic are used to explain how these methods can improve over the MC method in practice. We also discuss how this methodology can be coupled with clever transformations of the integrand in order to reduce the variance further. Additional topics included in this survey are the description of gures of merit used to measure the quality of the constructions underlying these methods, and other related techniques for multidimensional integration. 1 2 1.
Models3 Community Multiscale Air Quality (CMAQ) model aerosol component. 1. Model description
 Journal of Geophysical Research
, 2003
"... [1] The aerosol component of the Community Multiscale Air Quality (CMAQ) model is designed to be an efficient and economical depiction of aerosol dynamics in the atmosphere. The approach taken represents the particle size distribution as the superposition of three lognormal subdistributions, called ..."
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Cited by 49 (3 self)
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[1] The aerosol component of the Community Multiscale Air Quality (CMAQ) model is designed to be an efficient and economical depiction of aerosol dynamics in the atmosphere. The approach taken represents the particle size distribution as the superposition of three lognormal subdistributions, called modes. The processes of coagulation, particle growth by the addition of mass, and new particle formation, are included. Time stepping is done with analytical solutions to the differential equations for the conservation of number, surface area, and species mass. The component considers both PM2.5 and PM10 and includes estimates of the primary emissions of elemental and organic carbon, dust, and other species not further specified. Secondary species considered are sulfate, nitrate, ammonium, water, and secondary organics from precursors of anthropogenic and biogenic origin. Extinction of visible light by aerosols is represented by two methods: a parametric approximation to Mie extinction and an empirical approach based upon field data. The algorithms that simulate cloud interactions with aerosols are also described. Results from box model and threedimensional simulations are
Hybrid Bayesian Networks for Reasoning about Complex Systems
, 2002
"... Many realworld systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inferen ..."
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Cited by 48 (0 self)
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Many realworld systems are naturally modeled as hybrid stochastic processes, i.e., stochastic processes that contain both discrete and continuous variables. Examples include speech recognition, target tracking, and monitoring of physical systems. The task is usually to perform probabilistic inference, i.e., infer the hidden state of the system given some noisy observations. For example, we can ask what is the probability that a certain word was pronounced given the readings of our microphone, what is the probability that a submarine is trying to surface given our sonar data, and what is the probability of a valve being open given our pressure and flow readings. Bayesian networks are
Numerical Integration using Sparse Grids
 NUMER. ALGORITHMS
, 1998
"... We present and review algorithms for the numerical integration of multivariate functions defined over ddimensional cubes using several variants of the sparse grid method first introduced by Smolyak [51]. In this approach, multivariate quadrature formulas are constructed using combinations of tensor ..."
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Cited by 41 (16 self)
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We present and review algorithms for the numerical integration of multivariate functions defined over ddimensional cubes using several variants of the sparse grid method first introduced by Smolyak [51]. In this approach, multivariate quadrature formulas are constructed using combinations of tensor products of suited onedimensional formulas. The computing cost is almost independent of the dimension of the problem if the function under consideration has bounded mixed derivatives. We suggest the usage of extended Gauss (Patterson) quadrature formulas as the onedimensional basis of the construction and show their superiority in comparison to previously used sparse grid approaches based on the trapezoidal, ClenshawCurtis and Gauss rules in several numerical experiments and applications.
Is Gauss Quadrature Better Than Clenshaw–Curtis?
, 2008
"... We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to exp ..."
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Cited by 41 (3 self)
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We compare the convergence behavior of Gauss quadrature with that of its younger brother, Clenshaw–Curtis. Sevenline MATLAB codes are presented that implement both methods, and experiments show that the supposed factorof2 advantage of Gauss quadrature is rarely realized. Theorems are given to explain this effect. First, following O’Hara and Smith in the 1960s, the phenomenon is explained as a consequence of aliasing of coefficients in Chebyshev expansions. Then another explanation is offered based on the interpretation of a quadrature formula as a rational approximation of log((z +1)/(z − 1)) in the complex plane. Gauss quadrature corresponds to Padé approximation at z = ∞. Clenshaw–Curtis quadrature corresponds to an approximation whose order of accuracy at z = ∞ is only half as high, but which is nevertheless equally accurate near [−1, 1].