Square-root adaptive Wave Filtering for marine vessels

In this paper, the problem of designing numerically stable recursive estimators for adaptive Wave Filtering (WF) of marine vessels is addressed. The WF technique consists of a recursive optimization procedure to identify the dominant wave frequency (the uncertain parameter) by minimizing an appropriate defined performance index and the application of the Kalman filter for dynamic positioning purpose. The computational approach yields to a set of the filter sensitivity equations and a set of matrix Riccati-type sensitivity equations. Recently proposed WF methodology [1] is based on the conventional Kalman filter and its derivatives (with respect to unknown system parameters) that is known to be numerically unstable. To improve the numerical stability we are focusing in the techniques developed in the Kalman filtering community to solve ill conditioned problems. More precisely, here the square-root variant of the adaptive WF scheme is designed to improve accuracy and robustness for a finite-precision computer arithmetics. Then, it is examined on the dynamic positioning model of marine vessels.