When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems. (1st January 2023)

• Record Type: Journal Article
• Authors: Arnold, Andrea
• Is Part Of: Inverse problems. Volume 39:Number 1(2023)
• Publication Date: 2023-01-01
• Subjects: sequential Monte Carlo -- parameter estimation -- time-varying parameters -- state-space models -- dynamical systems -- Bayesian inference -- online estimation.; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/aca55b
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of these problems includes time-varying parameters with unknown evolution models that often cannot be directly observed. This work develops a systematic particle filtering approach that reframes the idea behind artificial parameter evolution to estimate time-varying parameters in nonstationary inverse problems arising from deterministic dynamical systems. Focusing on systems modeled by ordinary differential equations, we present two particle filter algorithms for time-varying parameter estimation: one that relies on a fixed value for the noise variance of a parameter random walk; another that employs online estimation of the parameter evolution noise variance along with the time-varying parameter of interest. Several computed examples demonstrate the capability of the proposed algorithms in estimating time-varying parameters with different underlying functional forms and different relationships with the system states (i.e. additive vs. multiplicative).