Target localization and tracking from Doppler-shift measurements

It is possible to localize a nonmaneuvering moving source radiating a constant frequency tone from measurements of the Doppler-shifted frequency at several sensors. Due to the nonlinear nature of the problem, it is necessary to find the solution by grid searches. However, if measurements of the rates of frequency changes are available, the search is only in three dimensions instead of the normal five in source frequency, its x-y positions, and speeds. The validity of combining frequency and frequency-rate measurements is confirmed with simulation studies. The overall system includes a least-squares track-sort algorithm to differentiate the true track from the extraneous track, and a Kalman tracker for the prediction of future source positions, thereby reducing the grid search size. An error analysis relating localization accuracy to uncertainties in frequency measurements and sensor positions is also given     

On the effectiveness of constant coefficients roll motion equation

As known, the rolling motion characteristics, amplitudes and accelerations, greatly influence the ability of a ship to operate and survive in bad weather. On the other hand, traditional computer codes for seakeeping calculations fail the forecasting of large amplitude rolling. There is a great need of using semi-empirical damping models and coefficients. This stresses the importance of campaigns of measurements as described in the paper, to get a deeper insight into the physical-mathematical modelling of the different contributions to rolling equation.Experimental tests on nonlinear rolling in a regular beam sea of a Ro-Ro ship model have been conducted by varying both the wave steepness and the wave frequency. The use of a parameter estimation technique, based on the least squares fitting of the stationary numerical solution of the nonlinear rolling motion differential equation, allowed to obtain informations on the damping model and on the linear and nonlinear damping coefficients. These exhibit a quite strong dependence on frequency that reduces the efficiency of constant coefficients rolling equation to simulate large amplitude nonlinear rolling. The results indicate that a good quality prediction model of nonlinear rolling cannot be based on constant coefficients time domain simulations. These can infact lead to incorrect estimates of rolling amplitudes even when the parameters have been obtained through high level parameter estimation procedures based on experimental data. The analysis indicates also a marked dependence of the effective wave slope coefficient on wave amplitude. The introduction of both these dependences on the rolling equation allows to reproduce the experimental results with great accuracy even at large amplitudes.     

Target parameter estimation using measurements acquired with a small number of sensors

A performance prediction procedure is developed and applied to the evaluation of a passive tracking technique intended primarily for the localization of targets in the near field or vicinity of the sensors. The analysis is sufficiently general to be applied to underwater and air acoustics, passive radar, and electromagnetic direction finding systems. Since near field applications are of primary concern, localization parameter identifiability with a single pair of omni-directional sensors is established with the aid of the Fisher Information Matrix (FIM). The Fisher Information Matrix is also used to determine upper bounds on localization performance, and the corresponding uncertainty ellipses associated with target position are evaluated for various tracking scenarios and types of measurements. Emphasis is placed on the use of measurements such as time difference of arrival and frequency difference of arrival obtained with two sensors, and frequency estimates obtained with a single sensor. It is shown that under certain conditions the time difference of arrival measurements yield full localization information, even though the conditioning can be marginal. Additional measurements, such as frequency, are shown to improve localization performance significantly. Bearing measurements obtained with a closely spaced cluster of a few sensors are also considered.     

An Empirical Method to Derive Ocean Waves From Second-Order Bragg Scattering: Prospects and Limitations

High-frequency (HF) radar wave processing is often based on the inversion of the Barrick-Weber equations, introduced in 1977. This theory reaches its limitations if the length of the Bragg-scattering wave raises to the order of the significant waveheight, because some assumptions are no longer met. In this case, the only solution is moving to lower radar frequencies, which is not possible or desirable in all cases. This paper describes work on an empirical solution which intends to overcome this limitation. However, during high sea state, the first-order Bragg peaks sometimes could not be clearly identified which avoids the access to the second-order sidebands. These cases cause problems to the algorithm which have not been solved yet and currently limit the maximum significant waveheight to about the same values as reported for the integral inversion method. The regression parameters of the empirical solution calibrated from the European Radar Ocean Sensing (EuroROSE) data set are constant values for the complete experiment and when applied to the HF radar data they reconstruct the measurements by a colocated wave buoy quite well. When including a radar-frequency-dependent scaling factor to the regression parameters, the new algorithm can also be used at different radar frequencies. The second-order frequency bands used for the empirical solution are sometimes disturbed by radio interference and ship echoes. Investigations are presented to identify and solve these situations     

Kalman filtering of vessel motions for ocean wave directional spectrum estimation

This paper proposes a high-speed iterative procedure for estimating the ocean wave directional spectrum from vessel motion data. It uses as input data, the measurements from motion sensors that are commonly available on dynamically positioned vessels and which may easily be installed on any ship. Because the necessary sensors are relatively inexpensive or may already be installed, it becomes an ideal solution to provide initial estimates to offline estimation procedures and to give spectral updates under quickly changing weather conditions. The Kalman filtering algorithm, for iterative harmonic detection, and frequency domain vessel response data are used in the estimation procedure. The results and conclusions are still based on synthesized data, but very promising.     

A closed-form solution to bearings-only target motion analysis

Bearings-only target motion analysis is a nonlinear state estimation problem in which the noise corrupted angle of arrival measurements of an emitted signal are used to obtain estimates of the source's range, bearing, course, and speed. The estimation process is complicated by unusual observability properties that render the quality of the estimate highly dependent on both the measurement noise levels and the source-observer geometry. Solutions that use recursive Kalman filtering approach or batch-style algorithms have been reported. The nonlinear batch style estimators for this process require iterative solution methods and under certain scenarios can be sensitive to initial conditions. Pseudolinear solutions that alleviate some of the difficulties with the iterative batch algorithms have been proposed. Although early versions of the pseudolinear filter suffered from biased estimates, subsequent improvements appear to have reduced the bias problem. This paper discusses a new pseudolinear solution based on the observable parameters from individual data segments defined by periods of constant observer velocity (termed “legs”). This solution is a true closed-form solution to the bearings-only target motion analysis problem. Although theoretically interesting, the technique does suffer under conditions of poor observability. A practical pseudolinear estimate, that does not suffer from the same observability problems, is developed and related to the first solution. Algorithm performance results, obtained from computer simulation, are presented. For the scenarios examined, the technique provides good state estimates under conditions of high observability. As observability conditions deteriorate, the solution does develop biases. However, it may still be useful for initializing an iterative nonlinear batch-style estimation algorithm     

Nonlinear Dynamic Behaviors of A Floating Structure in Focused Waves

Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional (2-D) box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile (CIP)-based Cartesian grid model, in which a more accurate VOF (Volume of Fluid) method, the THINC/SW scheme (THINC: tangent of hyperbola for interface capturing; SW: Slope Weighting), is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.     

Moving shoreline boundary condition for nearshore models

The paper develops and analyzes two fully nonlinear boundary conditions that incorporate the motion of the shoreline in nonlinear time domain nearshore models. A moving shoreline essentially means the computational domain is changing with the solution of the flow. The problem is solved in two steps. The first is to establish an equation that determines the motion of the shoreline based on the local momentum balance. The second is to develop and implement into a shoreline model the capability of accommodating a changing computational domain. The two models represent two different ways of addressing this step: one is to track the position of the shoreline in a fixed grid by establishing a special shoreline point which generally is not a fixed grid point. The second is by a coordinate transformation that maps the changing domain onto a fixed domain and solves the basic equations in the mapped domain. The two shoreline conditions are tested against three known solution for nonlinear shoreline motion. Two are the 1-D solutions to the nonlinear shallow water (NSW) equations by Carrier and Greenspan [J. Fluid Mech. 4 (1958) 97], one representing the response to a transient change in the offshore water level, the other the motion due to a periodic standing wave, both on slopes steep enough to allow full reflection. The third is the 2-D horizontal (2DH) computational solution by Zelt [Coast. Eng. 15 (1991) 205] for the run-up of a solitary wave on a cusped beach. In all cases, both models are shown to behave well and give high accuracy results for suitably chosen grid and time spacings.     

Picard iterations for a finite element shallow water equation model

ADCIRC, a finite element circulation model for shelves, coasts and estuaries, will be used for variational data assimilation. The nonlinear Euler–Lagrange (EL) problem will be solved using the iterated indirect representer algorithm. This algorithm makes such large, nonlinear but functionally smooth optimization problems feasible by iterating on linear approximations of the nonlinear problem (Picard iterations) and by making preconditioned searches in the “data subspace” at each iterate. Before solving the nonlinear EL using such Picard iterations, it essential that the iteration scheme be carefully examined within the framework of the nonassimilative or forward problem.The purpose of this paper is (1) to detail a Picard iteration procedure for ADCIRC, including the problematic bottom friction term; (2) to examine the ability of the iteration scheme to recover the nonlinear forward solution from deficient background fields; and (3) to present a study of different interpolation methods for reducing the memory/disk requirements of the iteration scheme. The iteration scheme is shown to be quite robust in its ability to recover the nonlinear solution from a variety of deficient background fields. A new cubic Hermitian interpolation method is shown to be a more effective alternative to standard linear interpolation for reducing memory/disk requirements, especially for high frequency overtides.     

Design and application of a semi-automated filtration system to study the distribution of particulate organic carbon in the water column of a coastal upwelling system

The processes controlling the production, transport and ultimate fate of particulate organic carbon (POC) in marine systems play a major role in the global carbon cycle. Direct measurements of POC concentrations in oceanic waters have been used extensively to investigate these processes, but because of the time-intensive effort associated with manual collection and filtration of water samples, this approach often results in limited temporal or spatial coverage. To increase the frequency of POC measurements, we designed and built a semi-automated filtration system (SAFS) that can be linked to a ship's underway surface water flow system and/or a towed profiling vehicle with pumping capabilities. Our results show that, compared to manual filtration, SAFS provides the ability to easily perform filtrations at high enough frequency to measure POC concentrations at spatial and temporal resolutions that are closer to those possible with in situ sensors. When combined with optical measurements, SAFS allows for the characterization of several distinct pools of particles within different geographical and depth regions of the water column off the Oregon Coast. These initial applications yielded data that provide considerable insight into the sources and character of particles in the water column and prove that this approach can be used to gain valuable information on the biogeochemistry of this and other similar ocean margins.     

A three-dimensional hydrostatic model for coastal and ocean modelling using a generalised topography following co-ordinate system

A three-dimensional hydrostatic model is presented that combines a generalised vertical co-ordinate system with an efficient implicit solution technique for the free surface. The model is capable of maintaining high resolution in the surface and/or bottom boundary layers as well as dealing with steep topography. Horizontal diffusion is calculated using the Smagorinsky formulation and a k–ε turbulence model is used in the vertical. In addition the model uses higher-order advection routines. An important aspect in three-dimensional models is the choice of vertical discretisation. If one is mostly interested in problems which are governed by boundary layer flows, a terrain following or sigma co-ordinate system seems attractive. This paper focuses on the development of a generalised sigma-type grid in a three-dimensional hydrostatic model. The generalised grid offers a wide range of possibilities including grid refinement toward the bed or surface, a mixed layer transformation, and a constant layer transformation where the lowermost or uppermost grid cells can be specified to have a constant height above the bed or below the surface. A number of tests are presented which show that the model is capable of simulating both shallow nearshore, estuarine flows as well as large-scale geophysical flows. These include an extreme flooding event in the shallow North Sea and the Odden ice tongue formation in the Greenland Sea.     

基于AIS信息校准的双频地波雷达的船只融合跟踪

高频地波雷达（HFSWR）和自动船只确认系统（AIS）是船只跟踪的重要传感器。高频地波雷达可以用来跟踪探测区域的所有船只,而AIS只能用来确认合作船只的信息。由于海杂波的干扰,使用单频率地波雷达的船只跟踪会淹没在布拉格峰值的盲区里,改变探测频率是克服这一缺点的有效手段。在这种背景下,我们提出一种基于AIS校准的双频雷达融合探测算法。因为不同频率的地波雷达测量与AIS的测量值存在系统误差,所以AIS信息可以用来估计和校准地波雷达的每个频率的系统误差。首先,将合作目标的点迹测量与地波雷达的点迹测量通过JVC分配算法进行点迹关联。从合作船只的点迹关联结果中,双频雷达的系统误差可以估计和校准。其次,基于校准的双频雷达数据,使用融合JPDA-UKF算法进行船只跟踪。通过真实探测的数据的实验结果显示所提算法可以实时跟踪船只,相比单频率跟踪可以进一步提高跟踪能力和跟踪精度。     

Comments on `Theory and application of calibration techniques foran NDBC directional wave measurements buoy' by K.E. Steele, et al.:nonlinear effects

For original paper see ibid., vol. OE-10, no.4, p.382-96 (1985). The authors of the above mentioned paper present an extensive set of linear calibration techniques that are applied to National Data Buoy Center wave-buoy sensor spectral output before calculating and disseminating directional wave spectra. The commentators identify and estimate the nonlinear effects that produce biases still present in the output, due both to wave nonlinearities themselves and to constraints on the buoy and mooring system to the driving forces. Simple models show that these nonlinearities can produce spectral energy biases of 5-15% at and above the spectral peak frequency, and even greater errors below it. NDBC presently records wave data from vertically stabilized and fixed accelerometers and slope sensors. Calculations show that these sensors all incur bias due to wave nonlinearities: this is greater for vertically stabilized accelerometers and least for slope sensors. Effects of the resulting inconsistencies between the different sensors are most pronounced below the spectral peak where the nonlinear terms dominate; these effects are illustrated with measured data     

An improved model for the dielectric constant of sea water at microwave frequencies

The advent of precision microwave radiometry has placed a stringent requirement on the accuracy with which the dielectric constant of sea water must be known. To this end, measurements of the dielectric constant have been conducted atS-band andL-band with a quoted uncertainty of tenths of a percent. These and earlier results are critically examined, and expressions are developed which will yield computations of brightness temperature having an error of no more than 0.3 K for an undisturbed sea at frequencies lower thanX-band. At the higher microwave and millimeter wave frequencies, the accuracy is in question because of uncertainties in the relaxation time and the dielectric constant at infinite frequency.     

HF radar data quality requirements for wave measurement

HF radar wave measurements are presented focussing on theoretical limitations, and thus radar operating parameters, and quality control requirements to ensure robust measurements across a range of sea states. Data from three radar deployments, off the west coast of Norway, Celtic Sea and Liverpool Bay using two different radar systems, WERA and Pisces, and different radio frequency ranges, are used to demonstrate the wave measurement capability of HF radar and to illustrate the points made. Aspects of the measurements that require further improvements are identified. These include modifications to the underlying theory particularly in high sea states, identification and removal of ships and interference from the radar signals before wave processing and/or intelligent partitioning to remove these from the wave spectrum. The need to match the radio frequency to the expected wave peak frequency and waveheight range, with lower radio frequencies performing better at higher waveheights and lower peak frequencies and vice versa, is demonstrated. For operations across a wide range of oceanographic conditions a radar able to operate at more than one frequency is recommended for robust wave measurement. Careful quality control is needed to ensure accurate wave measurements.     

一种优化模糊度搜索方法的研究

对于高精度测量和导航,GPS载波相位整周模糊度的快速求解仍然是一个难点,尤其对于单频接收机。提出一种快速求解整周模糊度的方法,其基本思想采用分步求解,首先应用最小二乘模糊去耦调节法(LAMBDA)搜索出来的模糊度作为初始值,然后应用卫星分组方法降低搜索维数,并应用极大似然准则,构造搜索函数,最后应用最优化原理,搜索出最优的模糊度参数,并从三个方面对其进行检验,即RATIO检验,OVT检验,多项式拟合残差检验。为验证该算法,我们用单频GPS接收机进行了实验,利用本文方法在11 S以内正确确定了模糊度,其基线长误差小于3MM,表明该方法不但可以改进模糊度的搜索速度,而且可以进一步提高其可靠性和成功率。该方法可广泛应用于定向及姿态测量。     

Fourier filtering and coefficient tapering at the North Pole in OGCMs

This article considers how some of the measures used to overcome numerical problems near the North Pole affect the ocean solution and computational time step limits. The distortion of the flow and tracer contours produced by a polar island is obviated by implementing a prognostic calculation for a composite polar grid cell, as has been done at NCAR. The severe limitation on time steps caused by small zonal grid spacing near the pole is usually overcome by Fourier filtering, sometimes supplemented by the downward tapering of mixing coefficients as the pole is approached; however, filtering can be expensive, and both measures adversely affect the solution. Fourier filtering produces noise, which manifests itself in such effects as spurious static instabilities and vertical motions; this noise can be due to the separate and different filtering of internal and external momentum modes and tracers, differences in the truncation at different latitudes, and differences in the lengths of filtering rows, horizontally and vertically. Tapering has the effect of concentrating tracer gradients and velocities near the pole, resulting in some deformation of fields. In equilibrium ocean models, these effects are static and localised in the polar region, but with time-varying forcings or coupling to atmosphere and sea ice it is possible that they may seriously affect the global solution. The marginal stability curve in momentum and tracer time-step space should have asymptotes defined by diffusive, viscous, and internal gravity wave stability criteria; at large tracer time steps, tracer advection stability may become limiting. Tests with various time-step combinations and a flat-bottomed Arctic Ocean have confirmed the applicability of these limits and the predicted effects of filtering and tapering on them. They have also shown that the need for tapering is obviated by substituting a truncation which maintains a constant time step limit rather than a constant minimum wave number over the filtering range.     

The role of the gravity-wave dispersion relation in HF radar measurements of the sea surface

Recent experimental and theoretical findings raise interesting questions about the applicability of the normal gravity-wave dispersion relation at wave frequencies that exceed the spectral peak frequency. The use of the dispersion relation in analysis of HF radar Doppler sea echo is examined in this paper. Drawing on the results of perturbation theory for wave-wave nonlinear interactions, we show that this relation, so essential to echo interpretation in terms of current and wave information, can be employed with no degradation in accuracy for current measurement when the dominant wave frequency is considerably less (by as much as 10) than the radar Bragg resonance frequency. This finding is supported by comparisons of currents measured by HF radar with "surface truth;" the first-order echo must only be identifiable in order to be used accurately. Wave-height directional spectral information can be extracted from the second-order echo at a given radar frequency up to the point (in wave height) where the perturbation solution employed in the inversion process fails; then a lower radar frequency must be used. On the other hand, most conventional wave measuring instruments should not use the dispersion relation for interpretation of data well beyond the spectral peak, because they do not observe wave height as a function of both space and time independently, as does HF radar.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.     

Internal wave generation in an improved two-dimensional Boussinesq model

A set of Boussinesq-type equations with improved linear frequency dispersion in deeper water is solved numerically using a fourth order accurate predictor-corrector method. The model can be used to simulate the evolution of relatively long, weakly nonlinear waves in water of constant or variable depth provided the bed slope is of the same order of magnitude as the frequency dispersion parameter. By performing a linearized stability analysis, the phase and amplitude portraits of the numerical schemes are quantified, providing important information on practical grid resolutions in time and space. In contrast to previous models of the same kind, the incident wave field is generated inside the fluid domain by considering the scattered wave field in one part of the fluid domain and the total wave field in the other. Consequently, waves leaving the fluid domain are absorbed almost perfectly in the boundary regions by employment of damping terms in the mass and momentum equations. Additionally, the form of the incident regular wave field is computed by a Fourier approximation method which satisfies the governing equations accurately in water of constant depth. Since the Fourier approximation method requires an Eulerian mean current below wave trough level or a net mass transport velocity to be specified, the method can be used to study the interaction of waves and currents in closed as well as open basins. Several computational examples are given. These illustrate the potential of the wave generation method and the capability of the developed model.