Joint Estimation of Sea State and Vessel Parameters Using a Mass-Spring-Damper Equivalence Model

TL;DR

Real-time estimation of sea state from onboard vessel sensors is challenging when the wave-to-vessel transfer function is unknown or variable. The authors introduce a mass-spring-damper equivalence to represent wave–vessel interactions as a superposition of regular components and employ a square-root cubature Kalman filter to jointly estimate the irregular wave excitations, vessel parameters, and states. They derive process-noise statistics and a Posterior Cramer-Rao lower bound to quantify estimator performance, then validate the approach with extensive Monte Carlo simulations and high-fidelity PanShipL data, showing wave-spectrum estimates comparable to transfer-function–aware methods. The results demonstrate the method’s potential for real-time sea-state estimation in operational settings, even with unknown or varying vessel characteristics.

Abstract

Real-time sea state estimation is vital for applications like shipbuilding and maritime safety. Traditional methods rely on accurate wave-vessel transfer functions to estimate wave spectra from onboard sensors. In contrast, our approach jointly estimates sea state and vessel parameters without needing prior transfer function knowledge, which may be unavailable or variable. We model the wave-vessel system using pseudo mass-spring-dampers and develop a dynamic model for the system. This method allows for recursive modeling of wave excitation as a time-varying input, relaxing prior works' assumption of a constant input. We derive statistically consistent process noise covariance and implement a square root cubature Kalman filter for sensor data fusion. Further, we derive the Posterior Cramer-Rao lower bound to evaluate estimator performance. Extensive Monte Carlo simulations and data from a high-fidelity validated simulator confirm that the estimated wave spectrum matches methods assuming complete transfer function knowledge.

Figures (14)

• Figure 1: (a) Illustration of an irregular wave form and its constituent harmonics in time and frequency domains. (b) Sea wave-induced vessel response captured by the heave and pitch motions of a sea vessel.
• Figure 2: The wave-vessel interaction model using a set of $N$ interconnected mass-spring-damper blocks, each representing a regular wave-vessel interaction, where $\sum_n x_n$ is the vessel's collective response when impacted by an irregular wave excitation, $\sum_n p_n(\omega_n)$.
• Figure 3: An overview of the two-stage approach for joint estimation of vessel parameters and sea states using noisy vessel motion measurements.
• Figure 4: (a). Vessel specifications expressed in meters. (b). The scaled vessel model (1:5)
• Figure 5: Estimation of vessel parameter breadth $B$ with $\pm1\sigma$ using the proposed joint estimation approach.