State and parameters estimation of nonlinear dynamical systems: Kalman, Unscented Kalman, and Particle Filters

The study of nonlinear dynamic systems presents complex challenges across various scientific domains, notably in engineering and physics. This research addresses the critical need for state and parameter estimation through the development of innovative Bayesian inference techniques, with a specific focus on Kalman filters, Unscented Kalman filters, and Particle filters. The primary objective is to bridge existing gaps in parameter estimation methods, creating techniques that not only fit data but also unveil the fundamental relationships governing system behaviors. This research establishes a robust foundation in the realm of nonlinear dynamic systems, introducing the theoretical underpinnings of Bayesian inference techniques. It provides a clear framework for numerical implementation and demonstrates practical utility in real-world scenarios. To this end, numerical examples of nonlinear mechanical systems are considered first, considering both process and measurements uncertainties. Then, experimental data of a geometrically nonlinear vibrating system is collected and used to validate the proposed approaches. The developed Bayesian inference techniques display promising results in estimating parameters, offering insights into complex system behaviors. This work contributes to the field of nonlinear dynamics, enhancing our ability to understand and manipulate complex behaviors while addressing the critical demand for model parameter estimation.