A backscattering model for ocean surface

A surface scattering model based on an approximate solution of the integral equations for the surface tangential fields has been developed for non-Gaussian distributed, finitely conducting surfaces. It consists of two parts. One part is proportional to the surface roughness spectrum, and the other to the surface bispectrum. The bispectrum part comes into the model when the third-order surface statistics are included. While the second-order statistics account for the wind directional dependence, the third-order statistics account for the dependence on the sense of direction of the wind. Thus, it is the critical part for explaining the difference between upwind and downwind observations. In general, the bispectrum is a complex quantity and the asymmetric effect of the sea surface is represented by its imaginary part. The model characteristics, such as polarization and azimuthal dependence, are illustrated through numerical calculations. The predictions of the model are compared with field measurements, and excellent agreement is obtained     

Incoherent bistatic scattering from the sea surface at L-band

A bistatic electromagnetic wave scattering model for the sea surface is developed to examine its wind dependence property over a wide range of incident angles along the specular direction. This is done by combining an existing scattering model with a sea spectrum recently reported in the literature. In general, electromagnetic wave scattering from a rough surface is dependent on the Fourier transform of the nth power of its height correlation function which can be computed numerically from the surface spectrum. This transform relation indicates that scattering is sensitive not only to the surface spectrum but also to its convoluted properties. Generally, surface scattering is sensitive only to a portion of the surface correlation measured from the origin. The size of this portion is a function of three variables (the incident angle, the surface height standard deviation, and the exploring wavelength) and the rate of decay of the correlation function. The decay rate near the origin of the sea surface correlation is very small, so much so that at L-band this portion is too wide for a two-term approximation of the correlation function. This is true in spite of the fact that the sea surface has a very large rms height. Thus, a scattering model based on geometric optics is generally not applicable at L-band especially at large angles of incidence. An additional finding is that in specular scattering wind dependence is stronger at larger angles of incidence for incident angles between 0 and 70° over the wind speed range of 4 m/s-20 m/s     

Approximate information content of a signal with bispectral constraints

The information content of a signal constrained only by its autocorrelation function or by the total power at each of its Fourier frequencies is well known. This paper addresses the information content of a signal constrained by both the power at each Fourier frequency and by its bispectrum. It is found that the amount by which the information content of a signal with a known power spectrum is reduced when bispectral constraints are imposed is primarily determined by its bicoherence. Approximate solutions for the signal distribution function and signal entropy are obtained in the limit of small bicoherence values using a perturbation theory approach. In the limit of bicocoherence values approaching unity, approaches based on a "mean field" argument also yield expressions for the signal information content. Estimates of the reduction in information content by a quadratic distortion are made. Signal distribution functions are used to develop a non-linear signal detection algorithm similar to the North filter.     

Experience with bicoherence of electrical power for conditionmonitoring of wind turbine blades

The authors explore the application of the normalised bispectrum or bicoherence to the problem of condition monitoring of wind turbine blades. Background information is provided on this type of condition monitoring, how it differs from more conventional condition monitoring of turbo machinery, and the motivation for selecting bicoherence. Bicoherence is defined and compared with the power spectral density. Complications in collecting suitable data, and estimating the bicoherence from that data are investigated; including the requirements of very long stationary data sets for consistent estimates, and computational difficulties in handling such large data sets. Bicoherence is then applied to electrical power output data obtained from a 45 kW wind turbine. The turbine is operated in three configurations to represent normal and fault conditions. A blade with less flapwise stiffness but identical outer dimensions to the matched set of blades was fitted to simulate a damaged blade. Comparison of the results from the power spectral density and bicoherence indicates how the bicoherence might be employed for condition monitoring purposes. Slices of the bicoherence with one frequency fixed at the rate of rotation show clear differences between the configurations and substantially reduce the computational effort required to calculate the estimate     

Testing for linearity of noisy stationary signals

Existing approaches to nonlinear signal detection via testing for linearity of a stationary non-Gaussian time series may fail if the data are contaminated with noise. These tests are based upon the skewness function (or bicoherence) of the time series which is a constant for linear processes in the absence of any measurement noise. In this paper a modification to the Subba Rao and Gabr (1980) approach is proposed by defining a scaled skewness function based upon the data bispectrum and a bispectrum-based power spectrum estimate. Under the null hypothesis, the modified skewness function of the noisy data is a constant. It is shown that this modified skewness function satisfies all the desired properties to qualify as a test statistic for the Subba Rao and Gabr test. On the other hand modifications to the Hinich (1982) test are not obvious. Computer simulation results are presented in support of the proposed approach     

海洋环境对雷达海杂波后向散射特性影响分析

为分析海洋环境对雷达海杂波后向散射特性的影响,建立了一种基于修正复合模型方法的雷达海杂波后向散射关系模型。雷达入射余角较大时,主要散射形式为镜面散射;入射余角较小时,主要散射形式为Bragg散射。考虑了逆顺风条件下后向散射系数的差异性,改进了原有模型Bragg散射的方向海谱部分,增加了风向因子。利用模型对不同入射角条件下海洋环境因素与后向散射系数的关系进行了仿真计算。计算结果表明,当海面作为雷达波的反射面时,雷达后向散射特性十分复杂,风速、风向、海浪、降水、海面油污等海洋环境因素都会对其产生影响。其中,风速和有效波高对海面后向散射的影响最大,风向次之,降水再次之,而海面油污的影响最小。      

Dual-polarization measurements at C-band over the ocean: results from airborne radar observations and comparison with ENVISAT ASAR data

This paper presents an analysis of measurements of the normalized radar cross-section (NRCS) in vertical and horizontal polarizations over the ocean obtained from the C-band airborne radar STORM. The dataset was collected during the experiment called "Validation with a Polarimetric Airborne Radar of ENVISAT SAR over the Ocean (VALPARESO)", which took place during the calibration/validation phase of the ENVISAT Advanced Synthetic Aperture Radar (ASAR). From this dataset, the properties of the polarization ratio are discussed and in particular its dependencies with radar geometry (incidence and azimuth angle) as well as with meteorological conditions (wind and sea state). The polarization ratio is found to be dependent on incidence and azimuth angles. Its dependence with incidence angle is found to be significantly different from empirical models previously proposed in the literature. It also exhibits some correlation with surface conditions (wind and wave) with a more important correlation with significant wave steepness. Two new analytical formulations are proposed to model the polarization ratio, one as a function of incidence angle only, the second one with additional dependence with azimuth angle. It is shown that it is necessary to consider an azimuth-dependent polarization ratio for incidence angles larger than 30/spl deg/. Comparisons with the polarization ratio from ENVISAT ASAR images are used to assess this model.     

Statistical approach to quantify the presence of phase coupling using the bispectrum

The bispectrum is a method to detect the presence of phase coupling between different components in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index, which is essentially a normalized bispectrum. The major drawback of the bicoherence index (BCI) is that determination of significant phase coupling becomes compromised with noise and low coupling strength. To overcome this limitation, a statistical approach that combines the bispectrum with a surrogate data method to determine the statistical significance of the phase coupling is introduced. Our method does not rely on the use of the BCI, where the normalization procedure of the BCI is the major culprit in its poor specificity. We demonstrate the accuracy of the proposed approach using simulation examples that are designed to test its robustness against noise contamination as well as varying levels of phase coupling. Our results show that the proposed approach outperforms the bicoherence index in both sensitivity and specificity and provides an unbiased and statistical approach to determining the presence of quadratic phase coupling. Application of this new method to renal hemodynamic data was applied to renal stop flow pressure data obtained from normotensive (N = 7) and hypertensive (N = 7) rats. We found significant nonlinear interactions in both strains of rats with a greater magnitude of coupling and smaller number of interaction peaks in normotensive rats than hypertensive rats.     

Detection of quadratic phase coupling from human EEG signals using higher order statistics and spectra

Interactions among neural signals in different frequency components have become a focus of strong interest in biomedical signal processing. The bispectrum is a method to detect the presence of quadratic phase coupling (QPC) between different frequency bands in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index (BCI), which is essentially a normalized bispectrum. The main disadvantage of the BCI is that the determination of significant QPC becomes compromised with noise. To mitigate this problem, a statistical approach that combines the bispectrum with an improved surrogate data method to determine the statistical significance of the phase coupling is introduced. The method was first tested on two simulation examples. It was then applied to the human EEG signal that has been recorded from the scalp using international 10–20 electrodes system. The frequency domain method, based on normalized spectrum and bispectrum, describes frequency interactions associated with nonlinearities occurring in the observed EEG.     

修正双尺度模型在非高斯海面散射中的应用

基于海浪在水平及垂直方向上的倾斜效应,应用修正的双尺度模型求解非高斯海面的电磁散射,在经典的一阶微扰散射系数上添加了一个附加散射系数项,它与非高斯海面的双谱函数成正比,且该项反映了海面后向散射系数在逆风和顺风向上观测结果的不对称性.在修正模型中还考虑了遮蔽函数、曲率效应等因素对散射结果的影响.最后应用修正的双尺度模型数值计算并讨论了非高斯海面后向电磁散射特性,修正模型下的计算结果与实验数据有较好的吻合.     

Modeling arbitrary polynomial bispectra in one and two dimensions

The authors propose a novel model, called a system with multiplicity (SWM), which is a refinement of the model proposed by Sakaguchi and Sakai (1989), to represent arbitrary polynomial bispectra. It is shown that an arbitrary polynomial bispectrum of a 1-D signal can always be realized using an SWM with FIR (finite impulse response) components. An algorithm is then developed for the identification of SWM that will match a given polynomial bispectrum. The authors address the problem of simultaneously matching an arbitrary polynomial bispectrum and a rational power spectrum function using an SWM. It is shown that this can always be accomplished by including another LSI component that is driven by a Gaussian input to the system. Experimental results for matching an estimated bispectrum as well as simultaneously matching a polynomial bispectrum and a power spectrum of some 1-D signals are presented. It is shown that in two dimensions an arbitrary polynomial bispectrum cannot always be uniquely modeled using an SWM with 2-D FIR components having different extents     

海面油膜的偏振反射特性仿真实验

为了给海面溢油污染识别检测提供理论基础,根据菲涅尔反射公式的偏振反射系数,结合偏振双向反射率因子和粗糙海面的概率密度分布函数,建立了完善的pBRDF模型,仿真在不同太阳入射角度、不同探测器观测角度以及不同海面风速风向等条件下海水和油膜的偏振反射分布函数。结果表明:海水和油膜太阳天顶角为53°和56°时P偏振反射率分别为1.0×10^-5和2.5×10^-5,S偏振反射率随着太阳天顶角的增加而增加;海面风速越大偏振反射率峰值越小;海面风向只改变pBRDF的空间位置;海水和油膜线偏振度空间分布有明显差异。搭建实验平台相机以40°拍摄时,得出海水和油膜的线偏振度分别在0.2~0.4, 0.5~0.7之间,同时表明利用偏振探测获取目标场景的偏振度和偏振角图可提高图像质量。     

折射率和粒子尺度对大气气溶胶光散射特性的影响

采用Mie散射方法计算了小尺度范围内,0.65 m波长大气气溶胶粒子光学特性与折射率、粒子尺度参数的关系,并分析了折射率虚部对气溶胶粒子散射相函数的影响。结果表明:在小尺度范围内,气溶胶粒子散射特性受折射率、尺度参数影响较大,折射率实部和尺度参数对消光效率因子等非散射角散射参量的影响存在一定程度的对称性。同时还发现,在特殊散射角位置,无论对于单粒子还是对于多分散粒子群系统,气溶胶粒子（群）的散射相函数与折射率虚部基本无关,不同折射率虚部的散射相函数在前向散射方向存在交点,交点位置随粒子尺度参数的变化基本为高斯分布。随着粒子尺度参数的增大,交点位置向前向小角方向移动,并逐步趋于离散。这一结论对了解大气气溶胶粒子的散射效应具有一定的参考意义。     

基于高频雷达二阶海洋回波的风速反演算法研究与应用

基于高频电磁波与海洋表面的散射机制,以雷达二阶散射截面方程为理论依据。首先,进行了从高频雷达二阶海洋 回波谱中反演饱和风速的算法理论近似,讨论算法运用的前提条件;其次进行了饱和风速与二阶谱峰频率的关系式推导;然后,利用高频地波雷达模拟海洋回波谱数据对算法进行了可行性验证,证明该算法特定风速范围内有较好的反演结果; 最后,将算法应用于实测高频地波雷达海洋回波多普勒谱进行了饱和风速反演,并进行了反演结果分析与误差分析。 结果分析表明:该算法在满足理论近似条件的前提下能有效提取海面饱和风速信息。     

利用微波散射特性重建海面波高谱

本文利用电磁散射理论进行海面微波后向散射特性的数值分析,并与机载散射计所获得的实验数据匹配重建反映风场的海面波高谱。从而得到散射系数与风速的关系曲线,只要测得海面后向散射系数就能确定海面风速,这对于海洋微波遥感具有一定实际指导意义。     

A theoretical study of sea surface up/down wind brightnesstemperature differences

The small slope approximation (SSA) for polarimetric thermal emission from a rough surface is applied to study the up/down wind difference of sea surface brightness temperatures. A complete third-order theory is used, with results expressed in terms of an integral over the sea surface bispectrum. An approximation is developed to obtain emission contributions for surface length scales much larger than the electromagnetic wavelength and in this limit, the up/down wind brightness temperature difference is determined entirely by a combination of third moments of surface slope. Polarization dependencies in this limit however do not match those obtained from the Jet Propulsion Laboratory (JPL) WindRAD empirical model. Another approximation is derived to capture up/down wind emission asymmetry due to short waves which are modulated by longer waves. In this case, an integral of emission "weighting functions" over a pair of "reduced" bispectra is obtained, and examination of the weighting functions shows the importance of surface length scales comparable to the electromagnetic wavelength. The polarization dependencies of these weighting functions illustrate the possibility of matching the WindRAD model, but the absence of an effective hydrodynamic model for short gravity-capillary wave modulation by longer waves limits detailed comparisons     

REBUILDING THE SEA WAVE HEIGHT SPECTRUM BY USING MICROWAVE SCATTERING CHARACTERISTICS

The microwave back-scattering characteristics are numerically analysed by the elec-tromagnetic scattering theory,and the sea wave height spectrum that reflects the wind field isrebuilt by comparing the calculated data with experimental data which were measured by airbornescatter.According to the wave height spectrum,the relationship between the back-scattering co-efficients and wind speeds can be obtained.Once the back-scattering coefficients of the sea surfaceare measured,then the wind speeds over the sea surface can approximately be determined.It isuseful for the microwave remote sensing in ocean.     

Performance Study of Adaptive Filtering in Bispectrum Signal Reconstruction

The problem of reconstructing a signal waveform when the observed realizations are corrupted by intensive noise and random shifts is considered in this paper. Several ways of performing bispectrum filtering are proposed and investigated. First, it is shown that the signal reconstruction is more efficient if one applies smoothing to the recovered real and imaginary parts of the Fourier spectrum separately instead of filtering the magnitude and phase spectra recovered from a bispectrum estimate. Second, several nonadaptive filters are studied, and it is demonstrated that the proper choice of the filter type and its parameters is critical. Some adaptive filtering techniques based on the Z-parameter and on local polynomial approximation (LPA)-intersection of confidence intervals (ICI) are discussed. The performances of nonadaptive and adaptive filtering techniques in the bispectrum-based signal reconstruction are studied using the mean-squared error as the criterion. It is shown that the use of LPA-ICI and other adaptive filters provides improvement of signal reconstruction in comparison to the conventional bispectrum method and the combined bispectrum filtering methods proposed earlier for nonadaptive filters. The benefits achieved are mainly observed for low (smaller than unity) signal-to-noise ratios.     

地海交界分区域复合粗糙面的布儒斯特效应研究

通过随机粗糙面建模理论, 研究地海交界分区域复合粗糙面的布儒斯特效应.采用蒙特卡罗方法, 利用高斯谱函数模拟陆地粗糙面, 利用Pierson-Moskowitz(PM)海洋谱模拟海面部分, 运用加权反正切函数滤波处理以平滑交界, 构建了地海交界分区域复合粗糙面的几何模型.考虑到粗糙陆地表面与海面各自内部面元的耦合作用以及区域之间和交界处面元的相互耦合, 提出了一种基于地海交界分区域面元的迭代物理光学法, 快速求解地海交界分区域复合粗糙面的镜向散射, 分别就陆地粗糙面的均方根高度、相关长度, 海面的风速、风向对其布儒斯特效应的影响进行了分析, 发现了地海交界分区域复合粗糙面上的“布儒斯特融合效应”, 并发现陆地粗糙面的均方根高度与海面风速能够显著影响布儒斯特角的“融合”现象.本研究为探测地海交界区域的真实环境提供了理论基础, 数值仿真结果对抗多径干扰、雷达目标的探测与识别、遥感信息处理具有借鉴意义.     

一维改进分形海面模型及海谱分析

针对经典分形模型的功率谱在空间波数小于基波波数时不能满足正幂率的问题,提出了一种统计模型和归一化带限Weierstrass分形模型相结合的一维粗糙海面模型,得到改进分形表面功率谱,并且和PM谱进行了对比,对分形维数、频率幅度尺度因子、风速等参量对一维海面轮廓的影响做了进一步分析.研究表明:在不同风速下表面功率谱和PM变化趋势是一致的,证明了改进方法的正确性.海面形状具有大尺度涌浪和小尺度张力波的特性,并且统计模型和分形模型的性质在改进模型中依然适用,验证了模型的合理性.