We address the problem of GPS navigation in the presence of spoofing, and propose a dynamical model in which an estimate-dependent term is integrated into the state dynamics. This term represents a control input used ...
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We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode transitions in the presence of spurious, or cluttered measurements. The system is assumed to follow, at e...
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ISBN:
(纸本)9781618399144
We consider the problem of tracking the state of a hybrid system capable of performing a bounded number of mode transitions in the presence of spurious, or cluttered measurements. The system is assumed to follow, at each time, one of a predefined dynamical models. Two types of uncertainties make the problem challenging. The first is the data uncertainty that follows from the fact that the true measurement of the state is indistinguishable from the clutter measurements that do not carry useful information. The second problem is the intrinsic model uncertainty. Both reasons prevent the computation of the optimal estimator. On the other hand, the mode transitions are not Markov thus ruling out the direct use of standard approaches for state estimation in cluttered environment. We derive an efficient estimation scheme for systems in cluttered environments capable of performing a bounded number of mode transitions. At the heart of this scheme is a transformation of the non-Markov model set to an equivalent Markovian one and a subsequent utilization of standard approaches matched to the new mode set. The algorithm's performance is evaluated via a simulation study, and shown to outperform the standard popular approaches in a typical example.
Given a parametrized family of finite frames, we consider the optimization problem of finding the member of this family whose coefficient space most closely contains a given data vector. This nonlinear least squares p...
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We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, ...
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ISBN:
(纸本)9780262232531
We investigate the problem of automatically constructing efficient representations or basis functions for approximating value functions based on analyzing the structure and topology of the state space. In particular, two novel approaches to value function approximation are explored based on automatically constructing basis functions on state spaces that can be represented as graphs or manifolds: one approach uses the eigenfunctions of the Laplacian, in effect performing a global Fourier analysis on the graph;the second approach is based on diffusion wavelets, which generalize classical wavelets to graphs using multiscale dilations induced by powers of a diffusion operator or random walk on the graph. Together, these approaches form the foundation of a new generation of methods for solving large Markov decision processes, in which the underlying representation and policies are simultaneously learned.
We propose a unified framework that extends the inference methods for classical hidden Markov models to continuous settings, where both the hidden states and observations occur in continuous time. Two different settin...
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The simplifications arising in elasticity theory from consideration of resultant boundary conditions instead of mathematically exact pointwise conditions have been the key to widespread application of the subject. Thu...
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The simplifications arising in elasticity theory from consideration of resultant boundary conditions instead of mathematically exact pointwise conditions have been the key to widespread application of the subject. Thus, for example, theories for strength of materials, plates, and shells rely on such relaxed boundary conditions for their development. The justification of this approximation is usually based on some form of the celebrated Saint-Venant's principle. A comprehensive survey of contemporary research concerning Saint-Venant's principle (covering primarily the period 1965–1981) was given by Horgan and Knowles (1983). Since that time, several developments have taken place demonstrating continued interest in understanding the ramifications of Saint-Venant's principle from both a physical and mathematical point of view. In this article we review these developments, thus providing an update on contributions to this fundamental engineering principle.
?1989 American Society of Mechanical Engineers
In this paper, we propose a numerical method based on Bernstein polynomials and their operational matrices for solving both linear and non-linear delay differential equations (DDEs). The Bernstein operational matrices...
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This paper deals with the scattering theory for the one‐dimensional discrete Schr?dinger equation with a random potential having large support. The main result is that a fluctuation deep within the scattering region ...
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This paper deals with the scattering theory for the one‐dimensional discrete Schr?dinger equation with a random potential having large support. The main result is that a fluctuation deep within the scattering region has a very small effect on the scattering of wave packets; the region of random potential is effectively opaque.
Spontaneous oscillator synchrony is a form of self-organization in which populations of interacting oscillators ultimately cycle together. This phenomenon occurs in a wide range of physical and biological systems. In ...
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