When artificial parameter evolution gets real: particle filtering for time-varying parameter estimation in deterministic dynamical systems
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).
- Publication:
-
Inverse Problems
- Pub Date:
- January 2023
- DOI:
- 10.1088/1361-6420/aca55b
- arXiv:
- arXiv:2204.00074
- Bibcode:
- 2023InvPr..39a4002A
- Keywords:
-
- sequential Monte Carlo;
- parameter estimation;
- time-varying parameters;
- state-space models;
- dynamical systems;
- Bayesian inference;
- online estimation.;
- Statistics - Methodology;
- Mathematics - Dynamical Systems;
- Statistics - Computation
- E-Print:
- 32 pages, 10 figures