In this article

we study a chaotic global modeling method based on a set of polynomials defined on the attractor's invariant measure as its kernel.Through analysis of Hénon map data and observed data of ionospheric parameters

it is shown that if the underlying system is simple enough to be represented by low-order polynomials

this method can capture the dynamics of the system.Also

when the noise level is low

we can acquire the equation of the system.When noise level is higher or the system is more complex

we still can use the reconstructed model to perform one-step prediction in a fairly good fashion.