Identification des param\`etres d'un mod\`ele logistique en dynamique des populations avec sortie affine

TL;DR

This paper presents a two-level parameter estimation method for a logistic population model, combining offline and online algorithms, with convergence analysis for the adaptive recursive level.

Contribution

It introduces a novel two-level estimation approach for logistic population models, including an adaptive recursive algorithm with proven convergence.

Findings

The offline AIG algorithm estimates parameters globally from data blocks.

The online ARE algorithm refines parameter estimates adaptively.

Convergence of the ARE algorithm is demonstrated through a new model and probability law.

Abstract

We study the parameters identification of a dynamic model of a population living in a given host environment governed by a logistic law. We use a statistic Kullback-Leibler type method to derive the algorithm for estimating the parameters of the model in two levels. The first level AIG is an offline algorithm and global it is obtained using the critical points of the reestimation transformation between two parameters. It estimates the parameters in a global iterative manner starting from a block of data. The second level ARE is adaptive recursive and is used online. It constitutes a refinement of the AIG algorithm. The convergence of the AIG algorithm is an open problem. The convergence of the ARE algorithm is demonstrated by constructing a new model, a new space and a new probability law.