一个稳态Kalman滤波风暴潮数值预报模式

利用Kalman滤波资料同化技术将海洋站水位观测资料融入二维线性风暴潮模式中,研制具有资料同化能力的风暴潮预报模式,改进风暴潮模式计算结果.通过在风暴潮模式的动量方程中加入模式噪声项来修正模式本身和气象强迫力的不确定性.确定性模式的输出通过带有观测噪声的观测方程与可利用的海洋站的潮位观测资料联系起来.假定初始的模式噪声和观测噪声满足均值为0的高斯分布,用迭代法得到计算区域的状态向量的稳态Kalman滤波,进而得到风暴潮模式输出的最优线性校正结果.利用这种资料同化技术,对1956年发生在东海的一次强风暴潮过程进行了后报试验,结果表明,该同化方法对短期风暴潮水位后(预)报有一定的改进.     

Assimilation of the climatic hydrological data in the σ-coordinate model of the black sea by the algorithm of adaptive statistics

We realize the algorithm of adaptive statistics of forecasting errors for the assimilation of the climatic fields of temperature and salinity in the σ-coordinate model of the dynamics of the Black Sea. The principal relations of this algorithm and its simplified version based on the Kalman filter are presented. The distinctive features of realization of the algorithm specified by the model are discussed. We also present the results of comparison of the hydrophysical fields of the Black Sea reconstructed according to the algorithm of adaptive statistics and a simplified scheme of assimilation of the climatic data. It is shown that the dependence of sources in the transport equations (heat and salt diffusion) on the four-dimensional variances of forecasting errors and threedimensional measurement errors enables one to reconstruct the mutually adapted climatic parameters of the sea more exactly.     

A numerical storm surge forecast model with Kalman filter

ImUcrIONThe deterministic storm stirge nurnrical fOrecast Tnedel has played an imPOrtant role inroutine storm surge real-time fOrecast. But somtimes the error of forecast is still large by usingdeterministic medels (Je1esnianshi et al., l992). The source of these errors mainly comesfrom (1 ) errors of wind stress and medel's open boundary, (2) non--optimized medel param-eter, (3) error of model equations, (4) error of medel's numrical methed, etc. The effec-ti ve methed to solve this probl…     

SINS/DGPS矢量重力测量系统滤波技术研究

以单通道捷联惯性导航系统的速度误差和姿态误差方程为状态方程,以陀螺仪误差和垂线偏差为过程噪声,以DGPS的速度与捷联惯导的速度之差为观测量,建立Kalman滤波模型,经滤波得到高精度实时导航信息。从导航信息中提取水平重力信息,进而得到垂线偏差。对高精度惯性元件构建的惯导系统进行数值仿真,仿真结果表明,组合系统可以有效提高实时导航和姿态精度,经50s平均后,可以得到精度为2″的垂线偏差。     

关于Boussinesq型水波方程理论和应用研究的综述

Boussinesq型方程是研究水波传播与演化问题的重要工具之一,本文就1967-2018年常用的Boussinesq型水波方程从理论推导和数值应用两个方面进行了回顾,以期推动该类方程在海岸(海洋)工程波浪水动力方向的深入研究和应用。此类方程推导主要从欧拉方程或Laplace方程出发。在一定的非线性和缓坡假设等条件下,国内外学者建立了多个Boussinesq型水波方程,并以Stokes波的相关理论为依据,考察了这些方程在相速度、群速度、线性变浅梯度、二阶非线性、三阶非线性、波幅离散、速度沿水深分布以及和(差)频等多方面性能的精度。将Boussinesq型水波方程分为水平二维和三维两大类,并对主要Boussinesq型水波方程的特性进行了评述。进而又对适合渗透地形和存在流体分层情况下的Boussinesq型水波方程进行了简述与评论。最后对这些方程的应用进行了总结与分析。     

Characteristics of Vibrational Wave Propagation and Attenuation in Submarine Fluid-Filled Pipelines

As an important part of lifeline engineering in the development and utilization of marine resources, the submarine fluid-filled pipeline is a complex coupling system which is subjected to both internal and external flow fields. By utilizing Kennard’s shell equations and combining with Helmholtz equations of flow field, the coupling equations of submarine fluid-filled pipeline for n=0 axisymmetrical wave motion are set up. Analytical expressions of wave speed are obtained for both s=1 and s=2 waves, which correspond to a fluid-dominated wave and an axial shell wave, respectively. The numerical results for wave speed and wave attenuation are obtained and discussed subsequently. It shows that the frequency depends on phase velocity, and the attenuation of this mode depends strongly on material parameters of the pipe and the internal and the external fluid fields. The characteristics of PVC pipe are studied for a comparison. The effects of shell thickness/radius ratio and density of the contained fluid on the model are also discussed. The study provides a theoretical basis and helps to accurately predict the situation of submarine pipelines, which also has practical application prospect in the field of pipeline leakage detection.     

A type of new conserved quantity deduced from Mei symmetry for Appell equations in a holonomic system with unilateral constraints

A type of new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints is investigated. The expressions of new structural equation and new conserved quantity deduced from Mei symmetry of Appell equations for a holonomic system with unilateral constraints expressed by Appell functions are obtained. An example is given to illustrate the application of the results.     

Towfish orientation and position estimation

The towfish location and orientation problems that arise in using side-scan sonar to detect objects on the sea bottom are treated separately. Data which locate the towfish relative to the ship are usually deteriorated by multipath receptions and other effects. In order to overcome this serious degradation in the location measurements, a modified Kalman filter is proposed. An estimate of the state transition matrix for this filter is derived, and a means of switching between two Kalman gains is suggested. The feasibility of the proposed filter is justified by a case study. Improved estimates of towfish pitch and heading measurements are obtained by a separate system employing model identification and subsequent Kalman filtering. Application of these methods to data from similar towed side-scan sonar systems should yield significant gains in object location accuracy     

Assimilation of the data of observations and adaptive prediction of the natural processes

We propose a dynamical model for the prediction of random components of natural processes. The model is based on the system concept of adaptive balance of causes (ABC-model) and contains dynamic equations for the coefficients of influence adapted to the correlations existing in the predicted processes. To improve the accuracy of predictions, we consider two possible schemes of assimilation of the data of observations in the equations of the ABC-model, namely, the Kolmogorov and Kalman schemes. Both schemes are oriented toward the application of sample correlation coefficients for the prediction of time series of measurements and, hence, take into account the nonstationarity of actual natural processes. We present some examples of prediction of the simulated time series clarifying the algorithms of assimilation of the data of observations. A conclusion is made that the methods of systems modeling and adaptive prediction of random processes by the ABC-method are quite promising.     

扩展卡尔曼滤波与采样卡尔曼滤波性能比较

详细研究了卡尔曼滤波在非线性系统中的应用,在分析扩展卡尔曼滤波理论的基础上,指出了其在非线性系统应用中的缺陷,阐述了采样卡尔曼滤波(UKF)思想,通过事例和仿真说明了这种新型卡尔曼滤波理论的优越性能。     

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.     

On the equations of rolling motion of a ship with a flooded compartment

This paper deals with obtaining the governing equations of rolling motion of a ship with a flooded compartment. The equations of motion are obtained through the variational formulation in the form of Hamilton-Ostrogradskii equation by taking the ship, the fluid in the flooded compartment and the sea as a single mechanical system. Since no specification concerning ships or flooded compartments has been made, the obtained equations are applicable to any sea-going vessel. As an application, the equation of rolling motion of a ship with a prismatic flooded compartment is obtained by choosing a suitable velocity potential for the fluid motion in the compartment.     

Intrusion of less saline shelf water into the Kuroshio subsurface layer in the East China Sea

The possible origin and cause of the less saline shelf water detected in the Kuroshio subsurface layer around the shelf edge of the East China Sea are investigated using observational results obtained in May 1998–2001 in conjunction with a dataset archived by Japan Oceanographic Data Center and a numerical model. The observations show that subsurface intrusions of less saline water are always detected in May in layers above 24.5σθ isopycnal surface, and that salinity inversions (i.e., areas in which the less saline water lies beneath the saline water) are detected around the trough of the Kuroshio frontal eddy (or wave). Analyses of the archived dataset reveal that the isopycnal surface of 24.5σθ is the deepest layer of the Kuroshio pycnocline outcropping to the sea surface on the shallow shelf in early spring. Outcropping isopycnals above 24.5σθ encounter a less saline water plume originating from the Changjiang, especially in the western East China Sea. Thereafter, the less saline water moves along isopycnal layers and reaches the Kuroshio front around the shelf edge. Numerical models demonstrate that, when the frontal wave captures the less saline water, the shelf water takes the form of a salinity inversion in the trough because isohalines in the frontal wave have a phase lag between the upper and lower layers in consequence of the baroclinic instability.     

Towed array shape estimation using Kalman filters-theoreticalmodels

The dynamical behavior of a thin flexible array towed through the water is described by the Paidoussis equation. By discretizing this equation in space and time a finite-dimensional state-space representation is obtained where the states are the transverse displacements of the array from linearity in either the horizontal or vertical plane. The form of the transition matrix in the state-space representation describes the propagation of transverse displacements down the array. The outputs of depth sensors and compasses located along the array are shown to be related in a simple, linear manner to the states. From this state-space representation a Kalman filter which recursively estimates the transverse displacements and hence the array shape is derived. It is shown how the properties of the Kalman filter reflect the physics of the propagation of motion down the array. Solutions of the Riccati equation are used to predict the mean square error of the Kalman filter estimates of the transverse displacements     

Transformed equations of motion for underwater vehicles

A method for dynamics investigation and coupling detection between velocities of autonomous underwater vehicles (AUVs) is presented in this paper. The method is based on transformation of equations of motion, which are usually used for an underwater vehicle, into equations with a diagonal mass matrix. The obtained equations contain quasi-velocities and allow one to give a further insight into the AUV dynamics especially for an underactuated system. Some advantages of the proposed approach are discussed, too. An analytical example for a 3-DOF AUV shows possible application of the transformed equations. Moreover, the given approach is validated via simulation on a 6-DOF vehicle.     

Inferred variables in data assimilation: quantifying sensitivity to inaccurate error statistics

The ability of data assimilation systems to infer unobserved variables has brought major benefits to atmospheric and oceanographic sciences. Information is transferred from observations to unobserved variables in two ways: through the temporal evolution of the predictive equations (either a forecast model or its adjoint) or through an error covariance matrix (or a parametrized approximation to the error covariance). Here, it is found that high frequency information tends to flow through the former route, low frequency through the latter. It is also noted that using the Kalman Filter analysis to estimate the correlation between the observed and unobserved variables can lead to a biased result because of an error correlation: this error correlation is absent when the Kalman Smoother is used.     

基于灰关联分析方法卡尔曼滤波器的精度效能评估

针对综导系统卡尔曼滤波器的特点,深入研究了灰关联分析法在滤波器精度效能评估中的应用。给出卡尔曼滤波器进行灰关联分析的方法和步骤,并对某一类型的滤波器进行精度效能评估。仿真结果表明了该方法的可行性和有效性。     

Dispersion and stability analyses of the linearized two-dimensional shallow water equations in Cartesian coordinates

In the present study, a Fourier analysis is used to develop expressions for phase and group speeds for both continuous and discretized, linearized two-dimensional shallow water equations, in Cartesian coordinates. The phase and group speeds of the discrete equations, discretized using a three-point scheme of second order, five-point scheme of fourth order and a three-point compact scheme of fourth order in an Arakawa C grid, are calculated and compared with the corresponding values obtained for the continuous system. The three-point second-order scheme is found to be non-dispersive with grid resolutions greater than 30 grids per wavelength, while both the fourth-order schemes are non-dispersive with grid resolutions greater than six grids per wavelength. A von Neumann stability analysis of the two- and three-time-level temporal schemes showed that both schemes are stable. A wave deformation analysis of the two-time-level Crank–Nicolson scheme for one-dimensional and two-dimensional systems of shallow water equations shows that the scheme is non- dispersive, independent of the Courant number and grid resolution used. The phase error or the dispersion of the scheme decreases with a decrease in the time step or an increase in grid resolution.     

融合法及其在数据同化中的应用研究

根据预报值具有最小方差这一要求,详细推导了融合法在观测数据为一维、多维和维数不同的情况下的具体同化表达形式,同时还给出了不同情况下与同化表达式相对应的预报误差公式.利用这些公式,可以用融合法处理常见的海洋观测数据的同化问题.在陆架海模式HAMSOM基础上,以4月份的渤海海表温度为例,我们验证了同化公式的正确性,并给出了同化后较好的同化结果。最后将融合法的同化结果与卡尔曼滤波同化结果进行了对比.比较表明,融合法使用起来更简单,且能有效地处理常见的海洋观测数据.     

Velocity-Aided Underwater Navigation System Using Receding Horizon Kalman Filter

This paper discusses the problems related to constructing a receding horizon filter for underwater inertial navigation systems which are subject to external disturbances. Noises are assumed to be bounded, additive, and contained in both state and measurement equations. An estimator is designed according to the sliding-window strategy to minimize the receding horizon estimation cost function. The derived filter is applied to a velocity-aided inertial navigation system. Simulations show that the derived filter is more accurate than the standard Kalman filter (KF) for underwater navigation systems subject to temporary unknown disturbances