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504,546
State transition matrix of relative motion for the perturbed noncircular reference orbit
 Journal of Guidance, Control, and Dynamics
, 2003
"... The precise analytic solution with the reference orbit eccentricity and perturbation effects is needed for the relative motion of formation flying satellites. Since Hill’s equations have considerable errors and are insufficient for the long term prediction of the relative motion, the new approach, c ..."
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Cited by 23 (4 self)
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, called geometric method, is proposed to obtain the state transition matrix as a precise solution under the effects due to the reference orbit eccentricity and the gravitational perturbations. Based on the transformation and the state transition matrix for the relative orbital elements, the geometric
Explicit model predictive control for systems with parametervarying state transition matrix
 In IFAC World Congress, Seoul
"... Abstract: In this paper we propose a closedloop minmax MPC algorithm based on dynamic programming, to compute explicit control laws for systems with a linear parametervarying state transition matrix. This enables the controller to exploit parameter information to improve performance compared to a ..."
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Cited by 2 (2 self)
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Abstract: In this paper we propose a closedloop minmax MPC algorithm based on dynamic programming, to compute explicit control laws for systems with a linear parametervarying state transition matrix. This enables the controller to exploit parameter information to improve performance compared
1 DEMONSTRATION OF THE DSST STATE TRANSITION MATRIX TIMEUPDATE PROPERTIES USING THE LINUX GTDS PROGRAM
"... The semianalytical theory for the motion of a space object replaces the conventional equations of motion with two formulas: (1) equations of motion for the mean equinoctial elements, and (2) expressions for the short periodic motion in the equinoctial elements. Very complete force models have been ..."
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for the partial derivatives so that (1) the mean element state transition matrix can be integrated backwards in time consistent with the interpolation architecture and (2) the epoch in a mean element orbit determination process can have an arbitrary location in a span of observation data. Both of these new
NASA/TM2002211776 A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix
, 2002
"... Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the l ..."
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Since its founding, NASA has been dedicated to the advancement of aeronautics and space science. The NASA Scientific and Technical Information (STI) Program Office plays a key part in helping NASA maintain this important role. The NASA STI Program Office is operated by Langley Research Center, the lead center for NASA's scientific and technical information. The NASA STI Program Office provides access to the NASA STI Database, the largest collection of aeronautical and space science STI in the world. The Program Office is also NASA's institutional mechanism for disseminating the results of its research and development activities. These results are published by NASA in the NASA STI Report Series, which includes the following report types:
The Infinite Hidden Markov Model
 Machine Learning
, 2002
"... We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. Th ..."
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Cited by 629 (41 self)
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. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying statetransition matrix, and the expected number of distinct hidden states in a finite
Discussion on Solving Systematic Matrix for Linear System of Invariant Time*
"... Abstract. For a given matrix function, determining whether it meets the conditions of the state transition matrix by utilizing the criteria of the state transition matrix. If satisfied, three computing methods of systematic matrix is deduced through both qualities and relationship with the systemati ..."
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Abstract. For a given matrix function, determining whether it meets the conditions of the state transition matrix by utilizing the criteria of the state transition matrix. If satisfied, three computing methods of systematic matrix is deduced through both qualities and relationship
A theory of timed automata
, 1999
"... Model checking is emerging as a practical tool for automated debugging of complex reactive systems such as embedded controllers and network protocols (see [23] for a survey). Traditional techniques for model checking do not admit an explicit modeling of time, and are thus, unsuitable for analysis of ..."
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Cited by 2651 (32 self)
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of realtime systems whose correctness depends on relative magnitudes of different delays. Consequently, timed automata [7] were introduced as a formal notation to model the behavior of realtime systems. Its definition provides a simple way to annotate statetransition graphs with timing constraints
A Fast Quantum Mechanical Algorithm for Database Search
 ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1996
"... Imagine a phone directory containing N names arranged in completely random order. In order to find someone's phone number with a probability of , any classical algorithm (whether deterministic or probabilistic)
will need to look at a minimum of names. Quantum mechanical systems can be in a supe ..."
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Cited by 1126 (10 self)
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superposition of states and simultaneously examine multiple names. By properly adjusting the phases of various operations, successful computations reinforce each other while others interfere randomly. As a result, the desired phone number can be obtained in only steps. The algorithm is within a small constant
Finding community structure in networks using the eigenvectors of matrices
, 2006
"... We consider the problem of detecting communities or modules in networks, groups of vertices with a higherthanaverage density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as “modularity ” over possible div ..."
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Cited by 500 (0 self)
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divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a
Sequential data assimilation with a nonlinear quasigeostrophic model using Monte Carlo methods to forecast error statistics
 J. Geophys. Res
, 1994
"... . A new sequential data assimilation method is discussed. It is based on forecasting the error statistics using Monte Carlo methods, a better alternative than solving the traditional and computationally extremely demanding approximate error covariance equation used in the extended Kalman filter. The ..."
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Cited by 782 (22 self)
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covariance equation are avoided because storage and evolution of the error covariance matrix itself are not needed. The results are also better than what is provided by the extended Kalman filter since there is no closure problem and the quality of the forecast error statistics therefore improves. The method
Results 1  10
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504,546