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An Introduction to the Kalman Filter
 UNIVERSITY OF NORTH CAROLINA AT CHAPEL HILL
, 1995
"... In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discretedata linear filtering problem. Since that time, due in large part to advances in digital computing, the Kalman filter has been the subject of extensive research and application, particularly in the area o ..."
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Cited by 1132 (13 self)
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of autonomous or assisted navigation.
The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports
Gradient projection for sparse reconstruction: Application to compressed sensing and other inverse problems
 IEEE JOURNAL OF SELECTED TOPICS IN SIGNAL PROCESSING
, 2007
"... Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined with a spa ..."
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Cited by 522 (16 self)
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Many problems in signal processing and statistical inference involve finding sparse solutions to underdetermined, or illconditioned, linear systems of equations. A standard approach consists in minimizing an objective function which includes a quadratic (squared ℓ2) error term combined with a
Shape modeling with front propagation: A level set approach
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1995
"... Shape modeling is an important constituent of computer vision as well as computer graphics research. Shape models aid the tasks of object representation and recognition. This paper presents a new approach to shape modeling which retains some of the attractive features of existing methods and over ..."
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Cited by 799 (20 self)
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of object boundaries. The resulting equation of motion is solved by employing entropysatisfying upwind finite difference schemes. We present a variety of ways of computing evolving front, including narrow bands, reinitializations, and different stopping criteria. The efficacy of the scheme is demonstrated
Nineteen Dubious Ways to Compute the Exponential of a Matrix, TwentyFive Years Later
, 2003
"... In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency indica ..."
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Cited by 427 (0 self)
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In principle, the exponential of a matrix could be computed in many ways. Methods involving approximation theory, differential equations, the matrix eigenvalues, and the matrix characteristic polynomial have been proposed. In practice, consideration of computational stability and efficiency
Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems
, 1992
"... We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many of the examp ..."
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Cited by 456 (20 self)
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We introduce the framework of hybrid automata as a model and specification language for hybrid systems. Hybrid automata can be viewed as a generalization of timed automata, in which the behavior of variables is governed in each state by a set of differential equations. We show that many
Efficient exact stochastic simulation of chemical systems with many species and many channels
 J. Phys. Chem. A
, 2000
"... There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more comm ..."
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Cited by 417 (5 self)
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There are two fundamental ways to view coupled systems of chemical equations: as continuous, represented by differential equations whose variables are concentrations, or as discrete, represented by stochastic processes whose variables are numbers of molecules. Although the former is by far more
How to improve Bayesian reasoning without instruction: Frequency formats
 Psychological Review
, 1995
"... Is the mind, by design, predisposed against performing Bayesian inference? Previous research on base rate neglect suggests that the mind lacks the appropriate cognitive algorithms. However, any claim against the existence of an algorithm, Bayesian or otherwise, is impossible to evaluate unless one s ..."
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Cited by 384 (28 self)
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specifies the information format in which it is designed to operate. The authors show that Bayesian algorithms are computationally simpler in frequency formats than in the probability formats used in previous research. Frequency formats correspond to the sequential way information is acquired in natural
Learning from demonstration
 Advances in Neural Information Processing Systems 9
, 1997
"... By now it is widely accepted that learning a task from scratch, i.e., without any prior knowledge, is a daunting undertaking. Humans, however, rarely attempt to learn from scratch. They extract initial biases as well as strategies how to approach a learning problem from instructions and/or demonstra ..."
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Cited by 392 (32 self)
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By now it is widely accepted that learning a task from scratch, i.e., without any prior knowledge, is a daunting undertaking. Humans, however, rarely attempt to learn from scratch. They extract initial biases as well as strategies how to approach a learning problem from instructions and/or demonstrations of other humans. For learning control, this paper investigates how learning from demonstration can be applied in the context of reinforcement learning. We consider priming the Qfunction, the value function, the policy, and the model of the task dynamics as possible areas where demonstrations can speed up learning. In general nonlinear learning problems, only modelbased reinforcement learning shows significant speedup after a demonstration, while in the special case of linear quadratic regulator (LQR) problems, all methods profit from the demonstration. In an implementation of pole balancing on a complex anthropomorphic robot arm, we demonstrate that, when facing the complexities of real signal processing, modelbased reinforcement learning offers the most robustness for LQR problems. Using the suggested methods, the robot learns pole balancing in just a single trial after a 30 second long demonstration of the human instructor. 1.
Approximate accelerated stochastic simulation of chemically reacting systems
 J. Chem. Phys
, 2001
"... The stochastic simulation algorithm ͑SSA͒ is an essentially exact procedure for numerically simulating the time evolution of a wellstirred chemically reacting system. Despite recent major improvements in the efficiency of the SSA, its drawback remains the great amount of computer time that is ofte ..."
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Cited by 336 (6 self)
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parameter selection and error mitigation for the leap method are described, and simulation results for two simple model systems are exhibited. With further refinement, the leap method should provide a viable way of segueing from the exact SSA to the approximate chemical Langevin equation, and thence
Analytic Analysis of Algorithms
, 1992
"... . The average case analysis of algorithms can avail itself of the development of synthetic methods in combinatorial enumerations and in asymptotic analysis. Symbolic methods in combinatorial analysis permit to express directly the counting generating functions of wide classes of combinatorial struct ..."
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Cited by 326 (13 self)
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structures. Asymptotic methods based on complex analysis permit to extract directly coefficients of structurally complicated generating functions without a need for explicit coefficient expansions. Three major groups of problems relative to algebraic equations, differential equations, and iteration
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