Adaptive Wave Filtering for Dynamic Positioning of Marine Vessels using Maximum Likelihood Identification: Theory and Experiments

Abstract

This paper addresses a filtering problem that arises in the design of dynamic positioning systems for ships and offshore rigs subjected to the influence of sea waves. The dynamic model of the vessel captures explicitly the sea state as an uncertain parameter. The proposed adaptive wave filter borrows from maximum likelihood identification techniques. The general form of the logarithmic likelihood function is derived and the dominant wave frequency (the uncertain parameter) is identified by maximizing this function. To this effect, a bank of Kalman filters is used to evaluate the log-likelihood function for different values of the uncertain parameter. After each identification step a new set of Kalman filters is designed to estimate the dominant wave frequency with better accuracy. The proposed sea state identification technique enables adaptive Wave Filtering (WF) and Dynamic Positioning (DP) systems to operate in different operational conditions and hence, it is a step forward to the development of a so-called all-year marine estimation and control system. The results are experimentally verified by model testing a DP operated ship, the Cybership III, under different sea conditions in a towing tank equipped with a hydraulic wave maker.

Design of inertial navigation systems for marine craft with adaptive wave filtering aided by triple‐redundant sensor packages

“…The matrices A.t /, B and C are given in (14). The term E i w i in (14) is neglected in the design because the observers are solely driven by the innovation signal Q y i and Figure 4.…”

“…Nguyen et al [10] and Brodtkorb et al [11] dealt with time-varying encounter frequencies using four passive observers, based on [7], parameterized with four different and constant encounter frequencies employed in a hybrid framework.Hassani et al [12] presented an adaptive wave filtering scheme utilizing the KF and a linearized vessel model, yielding a local result, where the encounter frequency candidates had to be chosen in advance. Later, these results were extended by Hassani et al [13,14] to include estimation of the dominating wave frequency with a discrete-time gradient-based algorithm and with a maximum likelihood algorithm together with a bank of KFs, respectively.Bryne et al [15] have developed a six degree of freedom (DOF), time-varying nonlinear inertial navigation system (INS) observer, with USGES stability properties, exploiting the position reference (PosRef) system's quality indicator, customized for marine surface vessels, based on the results of Grip et al [16]. However, Bryne et al did not consider wave filtering.…”

“…Hassani et al [12] presented an adaptive wave filtering scheme utilizing the KF and a linearized vessel model, yielding a local result, where the encounter frequency candidates had to be chosen in advance. Later, these results were extended by Hassani et al [13,14] to include estimation of the dominating wave frequency with a discrete-time gradient-based algorithm and with a maximum likelihood algorithm together with a bank of KFs, respectively.…”

“…Later, these results were extended by Hassani et al [13]- [14] to include estimation of the dominating wave frequency with a discrete-time gradient based algorithm and with a maximum likelihood algorithm together with a bank of Kalman filters, respectively.…”

Evaluation of wave-frequency motions extraction from dynamic positioning measurements using the empirical mode decomposition

“…The velocity vector ν = [u, v, r] T represents the surge, sway velocities (u, v) and the yaw rate (r), M ∈ R 3×3 is the inertia matrix including the rigid-body mass and hydrodynamic added mass matrices, D ∈ R 3×3 is the linear damping matrix, τ c = [τ surge , τ sway , τ yaw ] T is the control vector in the body-frame obtained from a nonlinear PID controller [11], and b ∈ R 3 is a bias vector term that accounts for slowly-varying disturbances and unmodeled dynamics. In the bias model (6), T b ∈ R 3×3 is a diagonal matrix of bias constants, and E b ∈ R 3×3 is a diagonal matrix that weights the amplitudes of the white noise vector w b ∈ R 3 .…”