A finite-difference method for linearization in nonlinear estimation algorithms
type: Item
instance of: scholarly article
title: A finite-difference method for linearization in nonlinear estimation algorithms
zbMATH Open document ID: 0916.93021
DOI: 10.1016/S0005-1098(97)00127-1
author: Tor Steinar Schei
published in: Automatica
publication date: 1998-10-27T00:00:00Z
review text: Consider a random vector \(x\) with expected value \(\overline x\) and covariance matrix \(X\). The problem is to estimate a covariance matrix \(Y\) of the vector \(y= f(x)\), where \(f\) is a given nonlinear function. A new linearization method is proposed. In the case of a unit matrix \(X\) the method is defined by \[ Y\approx FXF^T,\quad F= \{F(i,j)\}= \Biggl\{{f_i(\overline x+ e_j)- f_i(\overline x- e_j)\over 2}\Biggr\},\tag{1} \] where \(F(i,j)\) is a matrix element of \(F\), \(f_i\) is a component of \(f\), and \(e_j\) is the unit vector along coordinate axis \(j\) in the space spanned by \(x\). The procedure (1) is extended to general matrices \(X\) by a square root factorization of \(X\). This method is more accurate than the ordinary Jacobian linearization. It also has the advantage that it can be used for the models where the first derivative of \(f(x)\) is discontinuous for certain values of \(x\). A numerical example of such a model is shown in Section 4. The method is numerically efficient for large dimensions. The linearization method is applied to the extended Kalman filter algorithm, which is an optimal minimum variance estimator for nonlinear systems.
Mathematics Subject Classification ID: 93B18
Mathematics Subject Classification ID: 93E10
Mathematics Subject Classification ID: 93E11
zbMATH DE Number: 1192940
zbMATH Keywords: covariance matrix
zbMATH Keywords: nonlinear
zbMATH Keywords: linearization method
zbMATH Keywords: extended Kalman filter
reviewed by: A. Kukush
describes a project that uses: cheney-kincaid
MaRDI profile type: Publication
cites work: Q3993534
cites work: Factorization methods for discrete sequential estimation
cites work: Q3798123
cites work: Q3359644
cites work: Stochastic processes and filtering theory
cites work: Q3342413
cites work: Q5585825
cites work: Filtering and error analysis via the&lt;tex&gt;UDU^{T}&lt;/tex&gt;covariance factorization
Wikidata QID: Q127109852
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description: scientific article; zbMATH DE number 1192940