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On Analysis and Design of Algorithms for Robust Estimation from Relative Measurements

Chan, N. P.K. (2016) On Analysis and Design of Algorithms for Robust Estimation from Relative Measurements.

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Abstract:The problem of estimating the states of a group of agents from noisy pairwise difference measurements between agents’ states has been studied extensively in the past. Often, the noise is modeled as a Gaussian distribution with constant variance; in other words, the measurements all have the same quality. However, in reality this is not the case and measurements can be of different quality which, for a sensible estimation, needs to be taken into account. In the current work, we assume the noise to be a mixture of Gaussian distributions. Our contribution is two fold. First, we look at the problem of estimation. Several Maximum-likelihood type estimators are considered, based on the availability of information regarding the noise distributions We show that for networks represented by a tree, the quality of the measurements is not of importance for the estimation. Also, the WLSP yields the best performance among the approaches considered. Furthermore, the benefit of the approaches as presented in this report as opposed to the least squares approach is apparent when a graph is more connected. Second, we consider also the problem of adding new edges with possibly unknown quality to the network with the aim to decrease the uncertainty in the estimation. It is observed that the first few edges will more likely add edges which are not close to each other for the cycle graph, or edges which have initially a low value for the degree, that is they have a few neighbors. Keywords: Weighted Graph, Expectation Maximization, State Estimation, Link Addition.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Systems and Control MSc (60359)
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