The estimation of lower refractivity uncertainty from radar sea clutter using the Bayesian-MCMC method

The estimation of lower atmospheric refractivity from radar sea clutter(RFC) is a complicated nonlinear optimization problem.This paper deals with the RFC problem in a Bayesian framework.It uses the unbiased Markov Chain Monte Carlo(MCMC) sampling technique,which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework.In contrast to the global optimization algorithm,the Bayesian-MCMC can obtain not only the approximate solutions,but also the probability distributions of the solutions,that is,uncertainty analyses of solutions.The Bayesian-MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar seaclutter data.Reference data are assumed to be simulation data and refractivity profiles are obtained using a helicopter.The inversion algorithm is assessed(i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data;(ii) the one-dimensional(1D) and two-dimensional(2D) posterior probability distribution of solutions.     

Estimation of lower refractivity uncertainty from radar sea clutter using Bayesian-MCMC method

Estimation of lower atmospheric refractivity from radar sea clutter (RFC) is a complicated nonlinear optimization problem. This paper deals with the RFC problem in a Bayesian framework. It uses unbiased Markov Chain Monte Carlo (MCMC) sampling technique, which can provide accurate posterior probability distributions of the estimated refractivity parameters by using an electromagnetic split-step fast Fourier transform terrain parabolic equation propagation model within a Bayesian inversion framework. In contrast to the global optimization algorithm, the Bayesian-MCMC can obtain not only the approximate solutions, but also the probability distributions of the solutions, that is, uncertainty analyses of solutions. The Bayesian-MCMC algorithm is implemented on the simulation radar sea-clutter data and the real radar sea-clutter data. Reference data are assumed to be simulation data and refractivity profiles obtained with a helicopter. Inversion algorithm is assessed (i) by comparing the estimated refractivity profiles from the assumed simulation and the helicopter sounding data; (ii) the one-dimensional (1D) and two-dimensional (2D) posterior probability distribution of solutions.     

Monitoring of the ducting by a ground-based GPS receiver

In this paper, we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays. The vertical structure of the refractive environment is modeled using three parameters, i.e., duct height, duct thickness, and duct slope. The refractivity model is implemented with a priori constraints on the duct height, thickness, and strength, which might be derived from soundings or numerical weather-prediction models. A ray propagation model maps the refractivity structure into a replica field. Replica fields are compared with the simulation observed data using a squared-error objective function. A global search for the three environmental parameters is performed using genetic algorithm. The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated. This technique could provide near-real-time estimation of ducting effect. The results suggest that ground-based GPS provides significant atmospheric refractivity information, despite certain fundamental limitations of ground-based measurements. Radiosondes typically are launched just a few times daily. Consequently, estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates using radiosonde data alone.     

Monitoring of ducting by using a ground-based GPS receiver

In this paper,we describe the estimation of low-altitude refractivity structure from simulation and real ground-based GPS delays.The vertical structure of the refractive environment is modeled using three parameters,i.e.,duct height,duct thickness,and duct slope.The refractivity model is implemented with a priori constraints on the duct height,thickness,and strength,which might be derived from soundings or numerical weather-prediction models.A ray propagation model maps the refractivity structure into a replica field.Replica fields are compared with the simulation observed data using a squarederror objective function.A global search for the three environmental parameters is performed using a genetic algorithm.The inversion is assessed by comparing the refractivity profiles from the radiosondes to those estimated.This technique could provide near-real-time estimation of the ducting effect.The results suggest that ground-based GPS provides significant atmospheric refractivity information,despite certain fundamental limitations of ground-based measurements.Radiosondes are typically launched just a few times daily.Consequently,estimates of temporally and spatially varying refractivity that assimilate GPS delays could substantially improve over-estimates caused by using radiosonde data alone.     

Refractivity estimation from radar sea clutter

This paper addresses the problem of estimating lower atmospheric refractivity under the nonstandard propagation conditions frequently encountered in low altitude maritime radar applications. The vertical structure of the refractive environment is modeled by using a five-parameter model, and the horizontal structure is modeled as range-independent. The electromagnetic propagation in the troposphere is simulated by using a split-step fast Fourier transform based on parabolic approximation to the wave equation. A global search marked as a modified genetic algorithm (MGA) for the 5 environmental parameters is performed by using a genetic algorithm (GA) integrated with a simulated annealing technique. The retrieved results from simulated runs demonstrate the ability of this method to make atmospheric refractivity estimations. A comparison with the classical GA and the Bayesian Markov Chain Monte Carlo (Bayesian-MCMC) technique shows that the MGA can not only shorten the inverse time but also improve the inverse precision. For real data cases, the inversion values do not match the reference data very well. The inverted profile, however, can be used to synoptically describe the real refractive structure.     

无线电掩星滑动频谱方法和后传播方法的分析比较

本文详细介绍了滑动频谱方法,并通过模拟仿真和实测资料处理与后传播方法进行比较. 通过对模拟仿真信号反演发现:后传播方法和滑动频谱方法均能削弱大气多路径的影响,后传播方法在一定程度上优于滑动频谱方法;在模拟信号的相位中加入高斯噪声对后传播方法影响不大,但对滑动频谱方法影响较大,尤其在边界层以下. 分别用后传播方法和滑动频谱方法对2007年第71天至73天共约4500个COSMIC掩星数据进行处理. 将折射率反演结果与ECMWF分析场资料进行统计比较,结果显示:滑动频谱方法反演的掩星廓线深度大于后传播方法;后 关键词： GPS/LEO掩星 多相位屏模型 后传播方法 滑动频谱方法     

基于雷达海杂波的区域性非均匀蒸发波导反演方法

由于不同海域上空气象条件的不同, 海上蒸发波导在大尺度海面上空发生时通常是区域性非均匀的, 这一特性使得该环境中的电波传播特性相对于水平均匀的蒸发波导环境情况而明显不同, 因此, 进行区域性非均匀的蒸发波导探测反演对正确预测电波传播特性及提高雷达系统的工作性能具有重要的意义. 考虑到实际应用中蒸发波导信息获取手段的多样性, 将中尺度数值气象模式MM5预报的区域性蒸发波导修正折射率剖面作为先验信息, 提出了一种含该先验信息的区域性非均匀蒸发波导的雷达海杂波后验概率估计模型. 该模型使用主分量分析法对蒸发波导的水平非均匀性进行参数化建模, 然后通过贝叶斯理论将修正折射率剖面参数的先验概率分布、后验概率分布和似然函数联系起来, 利用雷达海杂波实现蒸发波导剖面参数的最大后验概率估计反演. 通过我国东海海域的实际区域性非均匀蒸发波导反演测试, 表明该模型能够以更高的精度实现区域性非均匀蒸发波导的反演.     

大气波导条件下雷达海杂波功率仿真

考虑近海面大气折射率垂直梯度的变化, 采用曲面波频谱估计方法(CWSE)计算掠射角, 并结合修正的GIT海表反射率模型和雷达距离方程对大气波导条件下雷达海杂波功率进行仿真, 最后通过数值实验及与实测数据比较, 验证了CWSE方法的可行性. 关键词： 大气波导 雷达海杂波 曲面波频谱估计     

Propagation modeling of ocean-scattered low-elevation GPS signals for maritime tropospheric duct inversion

The maritime tropospheric duct is a low-altitude anomalous refractivity structure over the ocean surface,and it can significantly affect the performance of many shore-based/shipboard radar and communication systems.We propose the idea that maritime tropospheric ducts can be retrieved from ocean forward-scattered low-elevation global positioning system(GPS) signals.Retrieval is accomplished by matching the measured power patterns of the signals to those predicted by the forward propagation model as a function of the modified refractivity profile.On the basis of a parabolic equation method and bistatic radar equation,we develop such a forward model for computing the trapped propagation characteristics of an ocean forward-scattered GPS signal within a tropospheric duct.A new GPS scattering initial field is defined for this model to start the propagation modeling.A preliminary test on the performance of this model is conducted using measured data obtained from a 2009-experiment in the South China Sea.Results demonstrate that this model can predict GPS propagation characteristics within maritime tropospheric ducts and serve as a forward model for duct inversion.     

红外大气折射率剖面分布模式

针对光电测量设备的大气折射误差实时修正以及红外激光传输研究等问题,利用2006年至2010年间在新疆戈壁地区获取的大气参数探空实验数据,计算得到了两个特定的波长,即1.32 m和4 m对应的大气折射率平均剖面分布,进而提出了一种实用的折射率剖面分布模式三参数指数分布模式。利用非线性最小二乘法,分别拟合得到了波长为1.32 m和4 m时的红外波在各季节内折射率的三参数指数剖面分布模式。采用统计得到的折射率剖面分布模式实时修正了光电设备的仰角测量数据,通过和实测模型的事后修正结果比较发现,二者的差值小于5,实现了对当地光学测量数据大气折射误差的实时、快速修正。     

Refractivity estimations from an angle-of-arrival spectrum

This paper addresses the probability of atmospheric refractivity estimation by using field measurements at an array of radio receivers in terms of angle-of-arrival spectrum.Angle-of-arrival spectrum information is simulated by the ray optics model and refractivity is expressed in the presence of an ideal tri-linear profile.The estimation of the refractivity is organized as an optimization problem and a genetic algorithm is used to search for the optimal solution from various trial refractivity profiles.Theoretical analysis demonstrates the feasibility of this method to retrieve the refractivity parameters.Simulation results indicate that this approach has a fair anti-noise ability and its accuracy performance is mainly dependent on the antenna aperture size and its positions.     

扩展卡尔曼滤波和不敏卡尔曼滤波在实时雷达回波反演大气波导中的应用

为了改善雷达回波反演大气波导(RFC)方面存在的单时次、单方位角反演的问题,提出利用扩展卡尔曼滤波和不敏卡尔曼滤波的反演算法对大气波导结构的多方位角实时跟踪反演. 在卡尔曼滤波方法中分别给出大气波导结构的参数化方程、观测方程、滤波算法的状态转移方程,最后导出滤波反演算法的迭代求解流程. 在大气波导结构不随时间变化和随时间变化的两种条件下,对扩展卡尔曼滤波和不敏卡尔曼滤波算法进行数值实验. 实验结果表明,不敏卡尔曼滤波更适用于RFC这高度非线性反演问题,它可能今后为大气波导结构多方位角实时跟踪反演的业务化运行提供理论基础与技术保证. 关键词： 大气波导 雷达回波 扩展卡尔曼滤波 不敏卡尔曼滤波     

GPS/LEO掩星正则变换反演方法

利用无线电全息方法, 如正则变换方法或全谱反演方法, 可以有效地解决大气多路径条件下GPS掩星信号的反演问题. 本文采用正则变换方法反演掩星资料, 模拟仿真反演结果显示正则变换方法可以准确地反演包含大气多路径效应的信号. 在模拟信号的相位中加入不同程度的高斯相位噪声后, 正则变换方法的反演结果会受到不同程度的影响. 用正则变换方法对2007年第71天至73天共约4500个COSMIC数据进行处理. 将其折射率反演结果和atmPrf资料 (利用全谱反演方法计算得到) 一起, 与对应的ECMWF 分析场资料进行统计比较, 结果表明: 在5 km以下, 正则变换方法计算的折射率的相对误差的平均值普遍大于atmPrf资料. 其原因可能为: 正则变换方法将信号从LEO轨迹后传播至辅助屏, 造成孔径缩小, 精度下降. 同时也讨论了信号截断对低对流层中反演精度和掩星个数的影响. 关键词： 无线电掩星 大气多路径 多相位屏技术 正则变换方法     

风浪因素对海洋波导雷达回波作用机理的研究

采用文氏谱模型描述近海海洋动力环境海面的粗糙特征, 并运用海浪谱理论得到风速和均方根高度偏差的关系. 进而应用修正的离散混合傅里叶变换方法和改进的雷达散射系数模型分别计算了电磁波传输损耗和雷达散射系数. 在此基础上, 通过数值计算分析了风浪因素对海洋波导环境雷达回波功率值的影响. 结果表明, 风浪因素对不同观测高度处的传输损耗的影响均不大; 风浪因素对雷达回波功率有显著影响, 并且相对于传输损耗, 雷达散射系数项受风浪因素影响较大因而导致较大的雷达回波功率的变化.     

利用粒子滤波从雷达回波实时跟踪反演大气波导

粒子滤波(particle filter,PF)是利用蒙特卡洛仿真方法处理递推估计问题的非线性滤波算法,这种方法不受模型线性和高斯假设的约束,是处理非线性非高斯动态系统状态估计的有效算法,适用于雷达回波反演大气波导(RFC)这类非线性非高斯问题.文中分别介绍了PF的基本思想和具体算法实现步骤,最后导出PF反演算法的迭代求解格式.数值试验结果表明,与扩展卡尔曼滤波(extended kalman filter,EKF)和不敏卡尔曼滤波(unscented kalman filter,UKF)相比,PF更适用于RFC这类高度非线性反演问题,可有效提高反演结果的稳定性和精度.     

Remote sensing of atmospheric duct parameters using simulated annealing

Simulated annealing is one of the robust optimization schemes. Simulated annealing mimics the annealing process of the slow cooling of a heated metal to reach a stable minimum energy state. In this paper, we adopt simulated annealing to study the problem of the remote sensing of atmospheric duct parameters for two different geometries of propagation measurement. One is from a single emitter to an array of radio receivers (vertical measurements), and the other is from the radar clutter returns (horizontal measurements). Basic principles of simulated annealing and its applications to refractivity estimation are introduced. The performance of this method is validated using numerical experiments and field measurements collected at the East China Sea. The retrieved results demonstrate the feasibility of simulated annealing for near real-time atmospheric refractivity estimation. For comparison, the retrievals of the genetic algorithm are also presented. The comparisons indicate that the convergence speed of simulated annealing is faster than that of the genetic algorithm, while the anti-noise ability of the genetic algorithm is better than that of simulated annealing.     

Multi-harmonic active structural acoustic control of a helicopter main transmission noise using the principal component analysis

This paper evaluates the feasibility and effectiveness, under controlled conditions, of active structural acoustic control of a helicopter main transmission in order to attenuate the vibration of the receiving roof panel and its sound radiation into the cabin. The vibroacoustic analysis of a typical helicopter drive train is conducted to extract the dominant tones generated by the various transmission stages. A finite element model of a Bell 407 transmission and simplified roof structure is developed in order to investigate various active control arrangements using piezoceramic actuators to control wave propagation in the gearbox supporting struts or receiving panel. The principal component analysis is used to extract the most significant control paths and reduce the control effort. A multiple frequency principal component least mean square (PC-LMS) algorithm is implemented on a laboratory setup and is used to successfully reduce up to seven gearbox tones simultaneously.     

GPS/LEO无线电掩星开环反演技术

在低对流层,传统的闭环模式容易造成较大的信号追踪误差. 开环模式通过内部或外部方式消除导航资料调制(navigation data modulation, NDM)对大气反演的影响,能够准确地恢复信号的相位. 内部和外部方式的区别是,前者通过信号相邻采样的内在联系移除NDM, 后者利用卫星导航位元数据进行处理. 通过内部和外部两种方式处理COSMIC (constellation observing system for meteorology, ionosphere and climate)掩星数据,利用全谱反演方法获得弯曲角,通过Abel积分变换计算折射率. COSMIC掩星个案分析表明,在低对流层,内部方式可能会导致信号的半周跳现象, 从而造成反演的折射率出现误差. 分别用上述两种方式对2007年第71天至73天共约3130个COSMIC掩星开环数据进行处理. 将折射率反演结果与ECMWF(european centre for medium-range weather forecasts)分析场资料进行统计比较,结果显示:外部处理方式的探测深度比内部方式低100 —200 m. 在热带的3 km以下,内部方式具有比外部方式稍大的折射率负偏差. 因此,外部方式能够得到比内部方式略优的反演结果.     

A new phase-screen method for electromagnetic wave propagation in turbulent flows using large-eddy simulation

Use of large-eddy simulation (LES) data in electromagnetic wave propagation modeling is not very common because of the high computational cost involved. A new phase-screen method is proposed to model radio wave propagation, in the atmospheric turbulence, using the resolved scale refractivity obtained from LES. The proposed method offers the same level of accuracy, as the one already existing in the literature, at much cheaper cost.     

Measurement of the variance of water surface slopes by a radar: Verification of algorithms

A full-scale experiment is carried out to study backscattering of a microwave radar signal by a rough water surface during flight over the Gorky water storage. A centimeter-wavelength Doppler radar with a knife-beam antenna oriented vertically downward was installed on the helicopter. The main goal of the experiment was a functional test of the modified radar system and new retrieval algorithms of the variance of surface slopes of a rough water surface and direction of the wind-wave propagation. The data analysis confirmed that the reflected power and the Doppler spectrum width depend on the direction of the wind-wave propagation. Two new algorithms were used for retrieval of the surface-slope variance. The processing of data showed that these algorithms make it possible to determine the variance of the scattering-surface slopes from a moving carrier without bounds on the flying height (such a capability was absent earlier). The direction of the wind-wave propagation is unambiguously determined by the Doppler spectrum width. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 5, pp. 399–412, May 2008.