Covariance‐invariant mapping of data points to nonlinear models

摘要

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.