Proceedings ArticleDOI
Efficient Maximum Likelihood Identification of a Positive Semi-Definite Covariance of Initial Population Statistics
David R. Haley,John P. Garner,William S. Levine +2 more
- Iss: 21, pp 1085-1089
TLDR
In this paper, a method for constrained maximum likelihood identification of the initial covariance of an otherwise known linear discrete time dynamical system, with guaranteed positive semi-definite estimate at each step, is presented.Abstract:
A method is presented for constrained maximum likelihood identification of the (positive semi-definite) initial covariance of an otherwise known linear discrete time dynamical system, with guaranteed positive semi-definite estimate at each step. The technique is a modification of Newton-Raphson or Scoring procedures transformed linearly to the space of the Cholesky square root matrix. The required algorithm is specified completely, and numerical and analytic difficulties and their solutions are discussed. It is shown that in cases of interest this procedure can result in order of magnitude reduction in computational costs compared to other iterative ML schemes which guarantee a semi-definite covariance estimate at each step. Formal extension to the maximum likelihood identification of time constants and power spectral densities is presented.read more
Citations
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Proceedings ArticleDOI
A Stochastic Approximation Technique for Generating Maximum Likelihood Parameter Estimates
TL;DR: In this paper, the authors used stochastic approximation (SA) to construct maximum likelihood estimates of system parameters, and showed that this SA procedure is, relative to a Kiefer-Wolfowitz procedure, most efficient for large-scale systems.
Journal ArticleDOI
Maximum likelihood mean and covariance matrix estimation constrained to general positive semi-definiteness
TL;DR: In this article, the optimality conditions for the mean and covariance matrix estimates are given, and a general numerical technique which integrates scoring and Newton's iterations is presented, and convergence performance is examined.
Journal ArticleDOI
Simultaneous perturbation method for processing magnetospheric images
TL;DR: The SPSA method is applied to a problem of estimat-ing the distribution of energetic ion populations in the magnetosphere from global images of the Magnetosphere using multiple objective functions: single image errors and the summation of square image errors.
Proceedings ArticleDOI
The simultaneous perturbation method for processing magnetospheric images
TL;DR: A method based on the simultaneous perturbation stochastic approximation (SPSA) algorithm is applied to a problem of estimating the distribution of energetic ion populations in the magnetosphere from global images of the Magnetosphere.
Journal ArticleDOI
First-order data sensitivity measures with applications to a multivariate signal-plus-noise problem
James C. Spall,D. C. Chin +1 more
TL;DR: In this article, the authors consider the use of first-order measures of the sensitivity of statistical parameter estimates to certain elements within the data and evaluate the accuracy of the measures and give an example of how they will be used in data analysis for a physical system.
References
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Journal ArticleDOI
Maximum likelihood from incomplete data via the EM algorithm
Book ChapterDOI
Some Applications of the EM Algorithm to Analyzing Incomplete Time Series Data
TL;DR: The EM algorithm is reviewed here within the time series context and applied to the parameter estimation and smoothing problem for missing data state-space models and linear estimation (deconvolution) in a frequency domain regression model.
Proceedings ArticleDOI
A partitioned recursive algorithm for the estimation of dynamical and initial-condition parameters from cross-sectional data
TL;DR: A recursive algorithm which asymptotically obtains the maximum likelihood estimate of both sets of unknown parameters is presented and is illustrated by an application to a simplified robotic system.
Proceedings ArticleDOI
Constrained Maximum Likelihood Estimation of Initial Population Statistics from an Ensemble of Kalman Smoother Estimates
TL;DR: In this article, a method for constrained maximum likelihood estimation of the initial mean and covariance of an otherwise known linear discrete-time dynamical system is presented via a hybrid EM/Scoring algorithm which combines the best features of both approaches.