Abstract
Theoretical results related to properties of a regularized recursive algorithm for estimation of a high dimensional vector of parameters are presented and proved. The recursive character of the procedure is proposed to overcome the difficulties with high dimension of the observation vector in computation of a statistical regularized estimator. As to deal with high dimension of the vector of unknown parameters, the regularization is introduced by specifying a priori non-negative covariance structure for the vector of estimated parameters. Numerical example with Monte-Carlo simulation for a low-dimensional system as well as the state/parameter estimation in a very high dimensional oceanic model is presented to demonstrate the efficiency of the proposed approach.
Highlights
IntroductionIn [1] a statistical regularized estimator is proposed for an optimal linear estimator of unknown vector in a linear model with arbitrary non-negative covariance structure =z Hx + v (1)
In [1] a statistical regularized estimator is proposed for an optimal linear estimator of unknown vector in a linear model with arbitrary non-negative covariance structure =z Hx + v (1)where z is the p-vector observation, H is the ( p × n) observation matrix, x is the n-vector of unknown parameters to be estimated, v is the p-vector representing the observation error
It is seen that initialized by the same initial state, if the innovation variances in EnOI, CHF have a tendency to increase, this error remains stable for the PEF during all assimilation period
Summary
In [1] a statistical regularized estimator is proposed for an optimal linear estimator of unknown vector in a linear model with arbitrary non-negative covariance structure =z Hx + v (1). Where z is the p-vector observation, H is the ( p × n) observation matrix, x is the n-vector of unknown parameters to be estimated, v is the p-vector representing the observation error. How to cite this paper: Hoang, H.S. and Baraille, R. (2014) Some Properties of a Recursive Procedure for High Dimensional Parameter Estimation in Linear Model with Regularization.
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