Thesis
Distributed Linear Least-Squares Scene Reconstruction
Washington State University
Master of Science (MS), Washington State University
2014
Handle:
https://hdl.handle.net/2376/102493
Abstract
This work focuses on distributed reconstruction of a spatial scene from noisy measurements taken by a network of sensors deployed in the space. The scene is modeled in a parametric way, as a linear combination of basis functions. Each sensor is deployed, knows its location, takes a noisy measurement of the scene, completes simple computations, and exchanges data with neighbors according to an undirected graph. The scene reconstruction problem is: given basis functions and sensors measurements, find the coefficients of the basis functions. This is done with a distributed linear least-squares estimate by casting the linear least-squares estimator in the form of averages, and using average consensus techniques to fuse data. Metropolis edge weights are used for average consensus, and asymptotic performance (convergence) analysis is given. The intermediate estimates of this distributed algorithm are characterized and some simulations are included. The error covariance matrix of the linear least-squares estimator is characterized. For the special case where the basis functions are monomials, the error covariance was shown to be related to the inverse of a special Hankel matrix containing sample moments of the sensor distribution in the space. Further, when the distribution of sensor positions is uniform on the one-dimensional interval (0,1), the linear least-squares estimator error covariance matrix is the inverse of the number of sensors times a Hilbert matrix, which can be computed explicitly.
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Details
- Title
- Distributed Linear Least-Squares Scene Reconstruction
- Creators
- Kelvin Bidwell
- Contributors
- Sandip Ray (Degree Supervisor)
- Awarding Institution
- Washington State University
- Academic Unit
- Electrical Engineering and Computer Science, School of
- Theses and Dissertations
- Master of Science (MS), Washington State University
- Publisher
- Washington State University; [Pullman, Washington] :
- Identifiers
- 99900525090301842
- Language
- English
- Resource Type
- Thesis