Journal ArticleDOI
Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations
N. K. Gupta,Raman K. Mehra +1 more
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TLDR
Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined and new results on the calculation of state sensitivity functions via reduced order models are given.Abstract:
This paper discusses numerical aspects of computing maximum likelihood estimates for linear dynamical systems in state-vector form. Different gradient-based nonlinear programming methods are discussed in a unified framework and their applicability to maximum likelihood estimation is examined. The problems due to singular Hessian or singular information matrix that are common in practice are discussed in detail and methods for their solution are proposed. New results on the calculation of state sensitivity functions via reduced order models are given. Several methods for speeding convergence and reducing computation time are also discussed.read more
Citations
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An approach to time series smoothing and forecasting using the em algorithm
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Bayesian Filtering and Smoothing
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TL;DR: This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework and learns what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.
Book
Bayesian Filtering and Smoothing
TL;DR: This compact, informal introduction for graduate students and advanced undergraduates presents the current state-of-the-art filtering and smoothing methods in a unified Bayesian framework, learning what non-linear Kalman filters and particle filters are, how they are related, and their relative advantages and disadvantages.
References
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Journal ArticleDOI
A method for the solution of certain non – linear problems in least squares
TL;DR: In this article, the problem of least square problems with non-linear normal equations is solved by an extension of the standard method which insures improvement of the initial solution, which can also be considered an extension to Newton's method.
Journal ArticleDOI
A Rapidly Convergent Descent Method for Minimization
Roger Fletcher,M. J. D. Powell +1 more
TL;DR: A number of theorems are proved to show that it always converges and that it converges rapidly, and this method has been used to solve a system of one hundred non-linear simultaneous equations.
Journal ArticleDOI
The differentiation of pseudoinverses and nonlinear least squares problems whose variables separate.
Gene H. Golub,Victor Pereyra +1 more
TL;DR: Algorithms are presented which make extensive use of well-known reliable linear least squares techniques, and numerical results and comparisons are given.
Journal ArticleDOI
Maximum likelihood identification of Gaussian autoregressive moving average models
TL;DR: It is shown that the procedure described by Hannan (1969) for the estimation of the parameters of one-dimensional autoregressive moving average processes is equivalent to a three-stage realization of one step of the NewtonRaphson procedure for the numerical maximization of the likelihood function, using the gradient and the approximate Hessian.