A Globally K-Exponentially Stable Nonlinear Observer for the Wave Encounter Frequency

In this work we have designed a signal based K-exponentially stable frequency estimator for the estimation of the wave encounter frequency at sea. The frequency estimator under consideration is a second-order filter designed for the estimation of the frequency of a sinusoid with unknown amplitude, frequency, and phase. The wave encounter frequency is estimated using measurements of the roll angle of the ship. The frequency estimator is able to estimate the frequency correctly when the ship is experiencing parametric roll resonance and when the resonance has damped out. The frequency estimator is therefore fitted with a switching gain in the frequency adaptation law. A stability proof is provided for the estimator with switching gain. The effectiveness of the designed estimator is demonstrated in a simulation study. In this simulation study we use a roll angle measurement generated by a second-order model of ship's roll dynamics. The frequency estimator is validated using experimental data.