Explicit Reduced-Order Integral Formulations of State and Parameter Estimation Problems for a Class of Nonlinear Systems

TL;DR

This paper introduces a novel integral reformulation technique for state and parameter estimation in nonlinear systems, leveraging parallel computation and periodic data to reduce problem dimensionality.

Contribution

It presents a new integral-based approach for nonlinear system estimation that exploits parallel processing and periodic data to simplify inference.

Findings

Method successfully applied to a benchmark voltage dynamics model.

Reduces inference dimensionality for periodic data.

Enhances computational speed through parallelization.

Abstract

We propose a technique for reformulation of state and parameter estimation problems as that of matching explicitly computable definite integrals with known kernels to data. The technique applies for a class of systems of nonlinear ordinary differential equations and is aimed to exploit parallel computational streams in order to increase speed of calculations. The idea is based on the classical adaptive observers design. It has been shown that in case the data is periodic it may be possible to reduce dimensionality of the inference problem to that of the dimension of the vector of parameters entering the right-hand side of the model nonlinearly. Performance and practical implications of the method are illustrated on a benchmark model governing dynamics of voltage in generated in barnacle giant muscle.