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