Multiscale distributed estimation with applications to GPS augmentation and network spectra
- Distributed estimation uses a network of sensors to measure a set of variables. The computation tasks required for finding the optimal estimate can be divided among the sensor nodes in a way that can be implemented as an iterative process using nodes with little computational power. Most algorithms for distributed estimation work for small networks, but convergence rates decrease with network size, making them impractical for use in large networks. We present a consensus algorithm with a convergence rate that scales logarithmically with network size by arranging nodes in a multigrid network structure. The algorithm can adapt to changes in the network structure and allows for selection of several parameters, representing a trade-off between performance and robustness of the network. We also describe how the algorithm is adapted to account for time-varying measurements and measurement weights. We present two applications of these methods. Our first application is an algorithm that allows us to determine the spectral properties of a state transition matrix on the network. Since the convergence rate of a consensus algorithm is related to the spectral properties of the state transition matrix, we can use this information to evaluate the effects of changes to the network structure. Our second application is a distributed GPS augmentation system. Traditional GPS augmentation systems use reference receivers to find a set of error correction values, which is broadcast to surrounding mobile receivers. Our distributed augmentation system uses only mobile receivers with unknown locations, which are able to obtain a set of correction values by sharing and processing data in a distributed network. The resulting method can be used to improve GPS point positioning accuracy in areas where fixed augmentation systems are not available.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Stanford University, Department of Aeronautics and Astronautics
|West, Matthew, 1975-
|West, Matthew, 1975-
|Statement of responsibility
|Submitted to the Department of Aeronautics and Astronautics.
|Thesis (Ph. D.)--Stanford University, 2010.
- © 2010 by Christina Selle
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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