Covariance‐invariant mapping of data points to nonlinear models

Covariance‐invariant mapping of data points to nonlinear models

A centroid‐ and covariance‐invariant deterministic mapping of sets of discrete data points to nonlinear models is introduced. Conditions for bijectivity of this mapping are developed. Since it can be accomplished by look‐up tables for the special case of equally spaced data, the resulting mapping al...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences Vol. 46; no. 4; pp. 3597 - 3613
Main Author: Grimm, Wolfgang Michael
Format: Journal Article
Language:English
Published: Freiburg Wiley Subscription Services, Inc 15-03-2023
Subjects:
Algorithms
bijective mapping
Centroids
Covariance
cross‐central moments
curve fitting
Data points
fast algorithm
Invariants
Least squares method
Mapping
Mathematical models
nonlinear regression
nonpositive data
Parameter estimation
Parameter identification
real‐time parameter estimation
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Summary:A centroid‐ and covariance‐invariant deterministic mapping of sets of discrete data points to nonlinear models is introduced. Conditions for bijectivity of this mapping are developed. Since it can be accomplished by look‐up tables for the special case of equally spaced data, the resulting mapping algorithm is considered computationally fast. This is attractive for real‐time parameter estimation without the need of iterations and initial guesses of parameter values. Examples show that model parameter identification is easier to apply than by nonlinear least squares regression. Further, the approach is superior to log‐linear regression since it may allow to handle nonpositive observations without any transformations.
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ISSN:0170-4214
1099-1476
DOI:10.1002/mma.8712