2026-09-18T20:50:52Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/422222022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Emery N. Brown and John L. Wyatt.
Amayo, Esosa O
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2008-09-03T14:59:30Z
2008-09-03T14:59:30Z
2006
2006
http://hdl.handle.net/1721.1/42222
230953882
Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.
Includes bibliographical references (leaves 75-76).
In this thesis we propose the use of the saddlepoint method to construct nonlinear filtering algorithms. To our knowledge, while the saddlepoint approximation has been used very successfully in the statistics literature (as an example the saddlepoint method provides a simple, highly accurate approximation to the density of the maximum likelihood estimator of a non-random parameter given a set of measurements), its potential for use in the dynamic setting of the nonlinear filtering problem has yet to be realized. This is probably because the assumptions on the form of the integrand that is typical in the asymptotic analysis literature do not necessarily hold in the filtering context. We show that the assumptions typical in asymptotic analysis (and which are directly applicable in statistical inference since the statistics applications usually involve estimating the density of a function of a sequence of random variables) can be modified in a way that is still relevant in the nonlinear filtering context while still preserving a property of the saddlepoint approximation that has made it very useful in statistical inference, namely, that the shape of the desired density is accurately approximated. As a result, the approximation can be used to calculate estimates of the mean and confidence intervals and also serves as an excellent choice of proposal density for particle filtering. We will show how to construct filtering algorithms based on the saddle point approximation.
by Esosa O. Amayo.
M.Eng.
76 leaves
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Construction of nonlinear filter algorithms using the saddlepoint approximation
Thesis
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<Abstract>In this thesis we propose the use of the saddlepoint method to construct nonlinear filtering algorithms. To our knowledge, while the saddlepoint approximation has been used very successfully in the statistics literature (as an example the saddlepoint method provides a simple, highly accurate approximation to the density of the maximum likelihood estimator of a non-random parameter given a set of measurements), its potential for use in the dynamic setting of the nonlinear filtering problem has yet to be realized. This is probably because the assumptions on the form of the integrand that is typical in the asymptotic analysis literature do not necessarily hold in the filtering context. We show that the assumptions typical in asymptotic analysis (and which are directly applicable in statistical inference since the statistics applications usually involve estimating the density of a function of a sequence of random variables) can be modified in a way that is still relevant in the nonlinear filtering context while still preserving a property of the saddlepoint approximation that has made it very useful in statistical inference, namely, that the shape of the desired density is accurately approximated. As a result, the approximation can be used to calculate estimates of the mean and confidence intervals and also serves as an excellent choice of proposal density for particle filtering. We will show how to construct filtering algorithms based on the saddle point approximation.</Abstract>
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