Robust adaptive unscented Kalman filter for bearings-only tracking in three dimensional case

This paper proposes an improved version of Unscented Kalman Filter (UKF), namely Robust Adaptive UKF (RAUKF), with a special focus on Bearings-Only Target Tracking for three-dimensional case (3DBOT). The automatic tuning of the noise covariance matrices and the robust estimation of the target states form a critical point for the performance of the Kalman-type filtering algorithms, especially in the variable environmental conditions exposed in underwater. The key idea of the proposed filter is to combine robust aspects of UKF and adaption of the process and measurement noise covariance matrices with low computational complexity. The main contribution of this paper is to adjust these matrices by means of the steepest descent algorithm, and the H_∞ technique is embedded to achieve superior performance in terms of accuracy and robustness against initial conditions and model uncertainties. Different experiments are performed to evaluate the performance of the proposed algorithm in the 3DBOT problem with a single moving observer. Simulations demonstrate that the proposed filter produce more accurate results with satisfactory computational burden in comparison with other methods.     

Evaluation of a regional ocean reanalysis system for the East Asian Marginal Seas based on the ensemble Kalman filter

Ocean Science Journal - This study introduces the East Asian Marginal Seas (EAMS) reanalysis system and evaluates its products from 1982 to 2006. The EAMS reanalysis system consists of an ocean...     

The heave response of a spar buoy

The vertical response of spar buoys to waves is examined. The response is the product of a rather complex wave forcing function and the resonant response of the buoy. With compound spar buoys (that is, consisting of more than one section of different diameters) the forcing function has a zero at a frequency which is usually close to the resonant frequency, but which can be arranged to be somewhat higher with beneficial effects on the response. Only the effects of pressure and inertia are considered, since this paper is mainly concerned to clarify some specific general principles and it is difficult to include the effects of drag, which are complex.     

Parameter sensitivity of three Kalman filter schemes for assimilation of water levels in shelf sea models

In applications of data assimilation algorithms, a number of poorly known assimilation parameters usually need to be specified. Hence, the documented success of data assimilation methodologies must rely on a moderate sensitivity to these parameters. This contribution presents a parameter sensitivity study of three well known Kalman filter approaches for the assimilation of water levels in a three dimensional hydrodynamic modelling system. The filters considered are the ensemble Kalman filter (EnKF), the reduced rank square root Kalman filter (RRSQRT) and the steady Kalman filter. A sensitivity analysis of key parameters in the schemes is undertaken for a setup in an idealised bay. The sensitivity of the resulting root mean square error (RMSE) is shown to be low to moderate. Hence the schemes are robust within an acceptable range and their application even with misspecified parameters is to be encouraged in this perspective. However, the predicted uncertainty of the assimilation results are sensitive to the parameters and hence must be applied with care. The sensitivity study further demonstrates the effectiveness of the steady Kalman filter in the given system as well as the great impact of assimilating even very few measurements.     

The representer method, the ensemble Kalman filter and the ensemble Kalman smoother: A comparison study using a nonlinear reduced gravity ocean model

This paper compares contending advanced data assimilation algorithms using the same dynamical model and measurements. Assimilation experiments use the ensemble Kalman filter (EnKF), the ensemble Kalman smoother (EnKS) and the representer method involving a nonlinear model and synthetic measurements of a mesoscale eddy. Twin model experiments provide the “truth” and assimilated state. The difference between truth and assimilation state is a mispositioning of an eddy in the initial state affected by a temporal shift. The systems are constructed to represent the dynamics, error covariances and data density as similarly as possible, though because of the differing assumptions in the system derivations subtle differences do occur. The results reflect some of these differences in the tangent linear assumption made in the representer adjoint and the temporal covariance of the EnKF, which does not correct initial condition errors. These differences are assessed through the accuracy of each method as a function of measurement density. Results indicate that these methods are comparably accurate for sufficiently dense measurement networks; and each is able to correct the position of a purposefully misplaced mesoscale eddy. As measurement density is decreased, the EnKS and the representer method retain accuracy longer than the EnKF. While the representer method is more accurate than the sequential methods within the time period covered by the observations (particularly during the first part of the assimilation time), the representer method is less accurate during later times and during the forecast time period for sparse networks as the tangent linear assumption becomes less accurate. Furthermore, the representer method proves to be significantly more costly (2–4 times) than the EnKS and EnKF even with only a few outer iterations of the iterated indirect representer method.     

On the heave radiation of a rectangular structure

In this paper, an analytic solution to the heave radiation problem of a rectangular structure is presented. To solve the problem analytically, the nonhomogeneous boundary value problem is linearly decomposed into homogeneous ones, which can be readily solved. To provide further comparisons to the present analytic solution, a boundary element method is also presented to solve the problem. The present analytic solution is compared with the result by Black et al. [(1971)] Radiation and scattering of water waves by rigid bodies. J. Fluid Mech. 46, 151–164], and the boundary element solution, and the comparisons show very good agreements. Upon examination of the present analytic solution, it is shown that the solution satisfies the nonhomogeneous boundary condition in a sense of series convergence. Using the present analytic solution, the generated waves, the added mass and the radiation damping coefficients, as well as the hydrodynamic effects of the submergence and the width of the structure, are investigated.     

Heave motion suppression of a Spar with a heave plate

Vortex shedding flow of an oscillating vertical cylinder with a disk attached at its keel is considered. This configuration is of interest for the offshore oil and gas industry. A finite difference method is employed to solve the incompressible Navier–Stokes equations in the primitive-variables formulation. Test cases were used to guide selection of the size of flow domain, numerical parameters, and to verify that the resultant method was both convergent and accurate. Numerical simulations have shown that the geometry configurations of the cylinder and disk, such as aspect ratio of the disk t_d/D_d and diameter ratio, D_d/D_c have significant influence on the vortex shedding modes and associated hydrodynamic properties, e.g. hydrodynamic damping and added mass coefficients. These in turn affect the performance in heave motion control of the structures.     

An active source electromagnetic sounding system for marine use

Instrumentation has been developed for carrying out active source electromagnetic sounding experiments in the deep oceans. Experiments of this type are directly and uniquely sensitive to the presence of molten or partially molten material, to temperature structure and to the porosity of upper crustal rocks such as those that accommodate hydrothermal circulation systems. Electromagnetic sounding experiments therefore represent an extremely desirable addition to the existing range of geophysical techniques for studying geological processes in thermally, hydrothermally or magmatically active regions—for example, at oceanic spreading centres.The instruments can be operated in regions of rugged, unsedimented sea bottom terrain, and are designed for investigating the distribution of electrical conductivity within the oceanic crust and uppermost mantle. The instrumentation consists of a deep towed, horizontal electric dipole transmitter and a set of free-fall, sea bottom, horizontal electric field recording devices.The transmitter is a deep-towed instrument, which is provided with power from the towing ship through a conducting cable. The transmitter package is fitted with an integral echo sounder, which allows it to be towed safely a short distance above the seabed. Electromagnetic signals are transmitted from a neutrally-buoyant antenna array, which is streamed behind the deep tow.The sea bottom receiving instruments each consist of a recoverable package which contains the instrumentation and digital recording system, an acoustic release unit, four low-noise, porous electrodes arranged in two orthogonal, horizontal dipoles, and a disposable bottom weight.The instruments have been used at sea on three occasions. On their most recent use, active source signals were successfully recorded during an experiment to investigate crustal magmatism and hydrothermal circulation beneath the axis of the East Pacific Rise.     

Application of particle filter combined with extended Kalman filter in model identification of an autonomous underwater vehicle based on experimental data

This study proposes a method for identification of the nonlinear dynamic model of an AUV while some states are unmeasured; hence, it concentrates on a nonlinear “state and parameter estimation” issue. In this method, a local linearization is used for solving the nonlinear dynamics based on the extended Kalman filter (EKF), and a particle filter (PF) is used to minimize errors and variances of the nonlinear system. In other words, the PF is combined with the EKF in the form of the extended Kalman particle filter (EKPF). The EKPF method is independent of the initial values and satisfies the limits of the parameters and also the assumption that the hydrodynamic coefficients are constant. Hence, it is shown when the ranges or signs of some parameters are known, the EKPF is a more accurate estimator than the EKF. Moreover, a new simulation is done using the model estimated by the EKPF and the results are compared and validated with the measured data of a new experimental test. It is shown that the obtained model can predict the trajectory path with the total normalized root-mean-square error (NRMSE) of 14% and the surge mean speed with the NRMSE of 5%; and it describes the 6DOF motion of the AUV more accurate than the EKF model.     

Inversion for Time-Evolving Sound-Speed Field in a Shallow Ocean by Ensemble Kalman Filtering

In the context of the recent Maritime Rapid Environmental Assessment/Blue Planet 2007 sea trial (MREA/BP07), this paper presents a range-resolving tomography method based on ensemble Kalman filtering of full-field acoustic measurements, dedicated to the monitoring of environmental parameters in coastal waters. The inverse problem is formulated in a state–space form wherein the time-varying sound-speed field (SSF) is assumed to follow a random walk with known statistics and the acoustic measurements are a nonlinear function of the SSF and the bottom properties. The state–space form enables a straightforward implementation of a nonlinear Kalman filter, leading to a data assimilation problem. Surface measurements augment the measurement vector to constrain the range-dependent structure of the SSF. Realistic scenarios of vertical slice shallow-water tomography experiments are simulated with an oceanic model, based on the MREA/BP07 experiment. Prior geoacoustic inversion on the same location gives the bottom acoustic properties that are input to the propagation model. Simulation results show that the proposed scheme enables the continuous tracking of the range-dependent SSF parameters and their associated uncertainties assimilating new measurements each hour. It is shown that ensemble methods are required to properly manage the nonlinearity of the model. The problem of the sensitivity to the vertical array (VA) configuration is also addressed.      

水下机器人主动升沉补偿系统研究

介绍一种基于水下机器人常规液压收放绞车的主动升沉补偿系统,利用加速度传感器获得母船的升沉运动信号,控制绞车的运转来降低母船的升沉运动对水下机器人的影响。通过理论计算建立主动升沉补偿系统的数学模型,仿真分析绞车运动对水下机器人升沉运动的补偿效果,并利用主动升沉补偿系统实验台验证基于常规液压收放绞车的主动升沉补偿方案的可行性。     

Limiting heave response of a wave energy device by draft adjustment with upper surface immersion

Many studies have been published concerning the influence of the immersed shape (in still water) of a floating body on its response and power capture from ocean waves. With a few notable exceptions, much of this analysis has assumed small amplitude motion and linear models have been employed to predict response. The form of the upper surface of such a body has received little attention. Here, we show how the shape of the upper (top) surface of a floating body can be designed to ensure that the response amplitude of the body is within a specified value. This is of considerable importance to the survivability of wave energy devices. The approach used is to achieve a large increase of both natural period and hydrodynamic damping for only a small change of float mass. These two factors impose a hydrodynamic limit on the displacement which may be exploited to avoid the ‘end-stop’ problem often encountered in wave device design. To demonstrate the change of response, experimental measurements are presented of the response of an axisymmetric float with rounded base and conical upper surface with rounded perimeter due to a range of regular, irregular and focused wave conditions. Power extraction is not considered since the mechanically undamped response represents the worst case. In contrast to a simple, straight-sided axisymmetric float, a smaller change of mass is required to satisfy a particular response amplitude limit. Although a significant reduction is not expected, hydrodynamic damping may reduce with increasing physical scale, and this remains to be quantified.     

Added mass and damping of a sphere section in heave

The Norwegian wave-power buoy¹ consists of a half-immersed floating sphere which is open to the sea at the bottom end. It is a two degree-of-freedom device involving the independent motion of the outer rigid sphere and the pressure across the internal free surface. A simpler model of the device is to represent the oscillatory flow through the bottom opening as another rigid body motion being that of the curved surface which would complete the sphere.The wave-induced forces on this surface and also the outer spherical surface due to independent oscillations of either are determined semi-analytically using a simple extension of the method of Havelock,² recently simplified and generalised by Hulme,³ for the complete half-immersed sphere. In particular the 2 × 2 added mass and damping matrices are determined as a function of frequency and relative size of bottom opening to sphere radius. These quantities are essential in any theoretical analysis of a multi-degree of freedom wave-energy device.     

新型圆筒型FPSO垂荡抑制结构优化设计

针对传统圆筒型FPSO垂荡运动剧烈的特点,提出一种带有垂荡抑制结构的圆筒型FPSO。采用1∶77.8的缩尺比制作模型,进行垂荡纵摇衰减试验,得到带有不同垂荡抑制结构模型的固有周期和无因次阻尼系数,进而选取最优的垂荡抑制结构型式。之后计算并对比传统圆筒型FPSO和新型圆筒型FPSO垂荡纵摇运动的固有周期和幅频响应函数。在此基础上,结合我国南海海洋环境条件,设计新型圆筒型FPSO的系泊系统,计算分析自存工况下的耦合动力响应,并与传统圆筒型FPSO进行对比。结果表明,文中提出的垂荡抑制结构可以有效增大系统垂荡纵摇运动的固有周期,改善运动性能,提高系泊的安全性。     

Experimental studies of a damaged ship section in forced heave motion

This work documents a detailed series of experiments performed in a wave flume on a thin walled prismatic hull form. The model consists of a rectangular opening located on the side. The length of the model is slightly smaller than the flume breadth to achieve two-dimensional (2D) behavior in the experiments. Forced oscillatory heave tests in calm water have been carried out by varying the model-motion parameters and examining both intact and damaged conditions. Video recordings, measurements of the wave elevation inside the damaged compartment and of the force on the model were performed in all the experiments. The effect of damage opening in the model on hydrodynamic loads is examined by comparing with an intact section. A theoretical analysis is used to explain the behavior of added mass and damping coefficients in heave for a 2D damaged section. The presented results demonstrate occurrence of sloshing and piston mode resonances in the tests and their influence on the hydrodynamics loads of a damaged ship. Detailed physical investigations are presented at these resonance frequencies for the damaged section. Effect of filling level in the damage compartment, damage-opening length and air compressibility in the airtight compartment is examined. Nonlinear effects are documented and appear dominant, especially, for lowest filling level where we have shallow-water depth conditions in the damaged compartment. Resonance phenomena that can lead to significant local loads are identified for the shallow water condition. Air compressibility in the airtight compartment and floodwater act as a coupled system and influence inflow/outflow of floodwater in the compartment. It has a significant effect on local floodwater behavior in the damaged compartment.     

Numerical analysis of a propeller during heave motion in cavitating flow

In practical maritime conditions, ship hulls experience heave motion due to the action of waves, which can further drive the ship’s propellers to oscillate relative to the surrounding water. In order to investigate the motion of a propeller working behind a surface vessel sailing in waves, a numerical simulation is conducted on a propeller impacted by heave motion in cavitating flow using the Reynolds-averaged Navier-Stokes (RANS) method. The coupling of the propeller’s rotation and translation is fulfilled using equations of motion defined for this purpose. The heave motion is simplified as a periodic motion based on a sinusoidal function. The numerical transmission of information from the unsteady flow field is achieved using the overset grid approach. In this manner, the unsteady thrust coefficient and torque coefficient of propellers in different periods of heave motion are analyzed. A comparative study is implemented on the unsteady cavitation performance and wake characteristics of propeller. With the propeller’s heave motion, the flow field non-uniformity constantly changes the load on the propeller during each revolution period and each heaving period, the propeller load and the wake field are closely related to the variation of heave motion period. The results obtained from the numerical simulation are expected to serve as a useful theoretical reference for the numerical analysis of a propeller in a heave motion.     

用圆中数滤波器排除卫星散射计风场反演中的风向模糊

由卫星散射计测量得到的归一化雷达截面积σ^0值以及这些σ^0值关联海面风速风向的经验模型函数可以反演海面的风矢量。但是对应一分辨面元上测量的σ^0值并不是唯一的风矢量解与之对应,选择一个风矢量解来表示真风矢量的处理过程就叫模糊排除或称消去伪解。本文引入一种圆中数滤波技术,在由模拟的ERS－1散射计数数据反演风场中,不附加任何其他信息的情况下,圆中数滤波器改进风向模糊排除方法,很好地重现模拟的海面真风矢量。