In this paper, we consider the nonparametric distributed parameter estimation problem using one-bit quantized data from peripheral sensors. Assuming that the sensor observations are bounded, nonparametric distributed ...
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In this paper, we consider the nonparametric distributed parameter estimation problem using one-bit quantized data from peripheral sensors. Assuming that the sensor observations are bounded, nonparametric distributed estimators are proposed based on the knowledge of the first N moments of sensor noises. These estimators are shown to be either unbiased or asymptotically unbiased with bounded and known estimation variance. Further, the uniformly optimal quantizer based only on the first moment information and the optimal minimax quantizer with the knowledge of the first two moments are determined. The proposed estimators are shown to be consistent even when local sensor noises are not independent but m-dependent. The relationship between the proposed approaches and dithering in quantization is also investigated. The superiority of the proposed quantization/estimation schemes is illustrated via illustrative examples.
The solution of an elliptic boundary value problem is an infinitely differentiable function of the coefficient in the partial differential equation. When the (coefficient-dependent) energy norm is used, the result is ...
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The solution of an elliptic boundary value problem is an infinitely differentiable function of the coefficient in the partial differential equation. When the (coefficient-dependent) energy norm is used, the result is a smooth, convex output least-squares functional. Using total variation regularization, it is possible to estimate discontinuous coefficients from interior measurements. The minimization problem is guaranteed to have a solution, which can be obtained in the limit from finite-dimensional discretizations of the problem. These properties hold in an abstract framework that encompasses several interesting problems: the standard (scalar) elliptic BVP in divergence form, the system of isotropic elasticity, and others.
Recursive Maximum Likelihood (RML) is a popular methodology for estimating unknown static parameters in state-space models. We describe how a completely decentralized version of RML can be implemented in dynamic graph...
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ISBN:
(纸本)9781424409532
Recursive Maximum Likelihood (RML) is a popular methodology for estimating unknown static parameters in state-space models. We describe how a completely decentralized version of RML can be implemented in dynamic graphical models through the propagation of suitable messages that are exchanged between neighbouring nodes of the graph. The resulting algorithm can be interpreted as a generalization of the celebrated belief propagation algorithm to compute likelihood gradients. This algorithm is applied to solve the sensor registration and localisation problem for sensor networks. An exact implementation is given for dynamic linear Gaussian models without loop. If loops are present, a loopy version of the algorithm is described. For non-linear non Gaussian scenarios, a Sequential Monte Carlo (SMC) or particle filter implementation is sketched.
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