In this project, I will investigate Korteweg-De Vries (KdV) wave-modelling equations, and the ensemble Kalman filter (EnKF), a data assimilation method which will be used to make inferences on simulated KdV data. In particular, the EnKF is an inferential sequential algorithm which can be applied to a discretised KdV to estimate the underlying process, as well as the equation parameters when employed in conjunction with likelihood techniques. In the first stages of the project I will seek to gain an understanding of the KdV and the cognate data-generation process. I will then investigate the EnKF, with the goal of implementation on KdV data with known parameters. Finally, I will implement an EnKF with a parameter estimation step to estimate the unknown parameters in the model.
University of Wollongong
Michael Kaminski is a third-year student at the University of Wollongong, studying a Bachelor of Mathematics Advanced with majors in applied mathematics and applied statistics. He has also studied computer science, and is planning to commence an honours year in 2022. At the moment, he is particularly interested in stochastic processes and partial differential equations. These two areas are blended together in his research project, along with Bayesian statistics, since he hopes to gain more exposure to the Bayesian statistical framework. His project also involves collaborative research with the University of Western Australia. In addition to his passion for the theoretical aspects of both mathematics and statistics, he is fascinated by the widespread applications that statistics can find in many industries and fields of research.