基于RELAX的气象雷达回波参数化谱矩估计方法

气象雷达回波的功率、平均频率和谱宽等谱矩参数与气象目标的类型密切相关,如何准确估计一直是关注的问题。地杂波也是气象雷达面临的严重干扰。气象目标回波和地杂波的频谱呈现高斯谱的特征,其参数化模型可以利用来估计这些谱矩参数。提出了拟合信号功率谱的参数化谱矩估计方法,并采用RELAX的思想进行多个高斯谱信号混合时的谱矩参数估计。最后利用仿真气象雷达信号进行了实验和性能分析,实验结果表明提出的方法能准确估计出高斯功率谱的谱矩参数,且具有较高的分辨率。与脉冲对法相比可用于估计多个高斯谱混合的情况（比如地杂波和气象回波叠加在一起时）,与最大似然法相比降低了运算量。      

低信噪比下雷达回波谱矩快速估计方法

针对在低信噪比下机载气象雷达回波多普勒参数（谱矩）估计不准确的问题，本文在气象目标的雷达回波频谱服从高斯分布的基础上，给出了一种利用协方差矩阵分解的快速参数化谱矩估计算法。通过理论分析，推导出雷达回波的协方差矩阵具有范德蒙结构特性，进而将用于谱矩估计的代价函数转化为类傅里叶变换结构，然后进一步通过快速傅里叶变换和高斯加权滑窗计算代价函数，实现快速的谱矩估计。仿真实验结果表明，该方法在信噪比低于5 dB时仍可以有效估计雷达回波的谱矩参数，同时运算复杂度大大降低，而且在谱宽值较大情况下仍能保持较好的估计性能。      

Nonparametric estimation of mean Doppler and spectral width

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order     

The cumulant theory of cyclostationary time-series. II. Developmentand applications

For pt.I see ibid., vol.42, no.12, p.3387-3408 (1994). The development of the theory of nonlinear processing of cyclostationary time-series that is initiated in Part I is continued. A new type of cumulant for complex-valued variables is introduced and used to generalize the temporal and spectral moments and cumulants for cyclostationary time-series from real-valued to complex-valued time-series. The relations between the temporal and spectral moments and cumulants at the inputs and outputs of several signal processing operations are determined. Formulas for the temporal and spectral cumulants of complex-valued pulse-amplitude-modulated time-series are derived. Estimators for the temporal moments and cumulants and for the cyclic polyspectra are presented and their properties are discussed. The performance of these estimators is illustrated by several computer simulation examples for pulse-amplitude-modulated time-series. The theory is applied to the problems of weak-signal detection and interference-tolerant time-delay estimation     

利用RR-MWF的低信噪比下机载气象雷达回波谱矩估计方法

常规机载气象雷达采用脉冲对法估计谱宽实现湍流检测,当信噪比较低时脉冲对法的谱宽估计误差大。晴空湍流（clear air turbulence,CAT）含水量较少,雷达回波信噪比很低,因此常规机载气象雷达无法检测CAT。为提高低信噪比下机载气象雷达回波谱宽估计性能,提出了一种基于降秩多级维纳滤波器（Reduced-Rank Multistage Wiener Filter, RR-MWF）的回波谱矩估计方法。该方法在机载气象雷达引入空时体制的基础上,利用空时域联合处理对湍流回波进行处理,通过空时积累改善信噪比。在最小均方误差准则下,构造了适用于分布式气象目标的自适应RR-MWF权矢量和代价函数,估计回波谱矩。仿真实验表明,提出的RR-MWF估计器在信噪比低于10dB时明显优于常规的脉冲对法,可用于CAT检测。      

Exploitation of spectral redundancy in cyclostationary signals

It is shown that the cyclostationarity attribute, as it is reflected in the periodicities of (second-order) moments of the signal, can be interpreted in terms of the property that allows generation of spectral lines from the signal by putting it through a (quadratic) nonlinear transformation. The fundamental link between the spectral-line generation property and the statistical property called spectral correlation, which corresponds to the correlation that exists between the random fluctuations of components of the signal residing in distinct spectral bands, is explained. The effects on the spectral-correlation characteristics of some basic signal processing operations, such as filtering, product modulation, and time sampling, are examined. It is shown how to use these results to derive the spectral-correlation characteristics for various types of man-made signals. Some ways of exploiting the inherent spectral redundancy associated with spectral correlation to perform various signal processing tasks involving detection and estimation of highly corrupted man-made signals are described     

Time-frequency analysis of myoelectric signals during dynamic contractions: a comparative study

In this paper, we introduce the nonstationary signal analysis methods to analyze the myoelectric (ME) signals during dynamic contractions by estimating the time-dependent spectral moments. The time-frequency analysis methods including the short-time Fourier transform, the Wigner-Ville distribution, the Choi-Williams distribution, and the continuous wavelet transform were compared for estimation accuracy and precision on synthesized and real ME signals. It is found that the estimates provided by the continuous wavelet transform have better accuracy and precision than those obtained with the other time-frequency analysis methods on simulated data sets. In addition, ME signals from four subjects during three different tests (maximum static voluntary contraction, ramp contraction, and repeated isokinetic contractions) were also examined.     

Asymptotically efficient estimation of spectral moments

The article studies parametric estimation of spectral moments of a zero-mean complex Gaussian stationary process immersed in independent Gaussian noise. With the merit of the maximum-likelihood (ML) approach as motivation, this work exploits a Whittle's (1953) type objective function that is able to capture the relevant features of the log-likelihood function while being much more manageable. The resulting estimates are strongly consistent and asymptotically efficient. As an example, application to Doppler weather radar data is considered     

Parameter estimation and blind channel identification in impulsivesignal environments

New methods for parameter estimation and blind channel identification in impulsive signal environments are presented, where the signals/noise are modeled as symmetric α-stable (SαS) processes. First, we present methods for estimating the parameters (characteristic exponent α and dispersion γ) of a SαS distribution from a time series. The fractional lower order moments, with both positive and negative orders, and their applications to signal processing are introduced. Then we present a new algorithm for blind channel identification using the output fractional lower order moments, and the α-Spectrum, a new spectral representation for impulsive signals, is introduced. From the α-Spectrum, we establish the blind identifiability conditions of any FIR channel (mixed-phase, unknown order) with i.i.d. SαS (α>1) input. As a byproduct, a simple algorithm for recovering the phase of any type of a signal from the magnitude of its z-transform is presented. The novelty of our paper is in parameter estimation and blind identification of the FIR channel based on fractional lower order moments of its output data. Monte Carlo simulations clearly demonstrate the performance of the new methods     

A novel algorithm for voice conversion using Canonical Correlation Analysis

A novel algorithm for voice conversion is proposed in this paper. The mapping function of spectral vectors of the source and target speakers is calculated by the Canonical Correlation Analysis （CCA） estimation based on Gaussian mixture models. Since the spectral envelope feature remains a majority of second order statistical information contained in speech after Linear Prediction Coding （LPC） analysis, the CCA method is more suitable for spectral conversion than Minimum Mean Square Error （MMSE） because CCA explicitly considers the variance of each component of the spectral vectors during conversion procedure. Both objective evaluations and subjective listening tests are conducted. The experimental results demonstrate that the proposed scheme can achieve better performance than the previous method which uses MMSE estimation criterion.     

Estimation of the energy spectrums of reflections in pulse doppler weather radars. Part 3. Statistical analysis of the reconstruction techniques of continuous spectrums of the reflections from meteorological objects

This is the third paper in a series of papers dedicated to the peculiarities of estimation of the continuous energy spectrums of random processes of different nature, which are determined by their samples at discrete moments of time. In the article we justify the methodology and present the quantitative results of analytical and experimental investigation and comparison of statistical characteristics of classical and “parametric” methods of energy spectrums reconstruction for interperiod fluctuations of different nature reflections (including the ones from meteorological objects) in pulse radars. The methodology is followed by quantitative results which correspond to and obtained for a real-world “adaptive” case. Under the latter, a priori unknown echoes’ covariance matrix is replaced with different-kind estimates formed from finite-size training samples. Based on the results obtained, we substantiate the spectral estimation algorithms reasonable for utilization in different-purpose radars, in particular in pulse Doppler weather ones. Discussion of efficient ways for their practical implementation on a unified basis of adaptive lattice filters concludes the paper.     

Nonlinear transformations of random processes

This paper provides a general method of calculating the mean-square bandwidth (and other spectral moments) of an arbitrary zero-memory nonlinear transformation of a stationary random process. The method is valid when the original process is an arbitrary combination of other random processes. It can be used to determine the mean-square bandwidth (or the spectral moments) of the transformed process either before or after that process is passed through a bandpass filter. Five examples of the application of this method are provided simplifying and generalizing known results, as well as providing new results.     

基于相关向量机的信噪比估计算法

为了使已有PSK信号信噪比估计算法在平坦衰落信道下,能够同时满足估计范围大、估计精度高的要求,提出了一种基于相关向量机（RVM, relevance vector machine）的信噪比估计新算法。该方法在建立起信噪比与二阶、四阶矩之间关系的基础上,应用相关向量机建立估计模型,并通过训练学习,得到可靠的模型权值。实验表明,利用测试数据对信号信噪比进行估计时,相对于其他算法,该算法具有使用数据量少,估计范围广,在有效的估计范围内,估计精度较高,且适用于多种调制信号的特点。     

Spectral Caracterization via Fusing Modified Prony Method with High Resolution Nonparametric Spectral Estimators

In this paper, we present a new approach to high-resolution spectral characterization of the unknown number of spectral line components embedded in colored noise. The addressed method resolves the spectral analysis problem via intelligent fusing the two spectrum estimation paradigms: (i) the parametric line spectral estimation that employs the modified regularized Prony (MORP) method for multi-harmonic signal characterization and (ii) nonparametric spectral estimation. Two nonparametric high-resolution spectral estimation methods are proposed to be fused with the MORP: the minimum variance (MV) and maximum entropy (ME) techniques. Via aggregation of the developed model-based MORP and model-free MV/ME techniques into the fused MORP-MV/MORP-ME resulting method a substantial improvement of the spectral characterization performances is gained when those are applied to characterization/analysis of the composed distributed scenes that contain noised closely spaced spectral lines to be localized with high resolution and accuracy. The simulation results are presented to illustrate the performance enhancement gained with the proposed fused MORP-MV/MORP-ME method.     

Recovery of Spectral Moments from Overlaid Echoes in a Doppler Weather Radar

This paper presents a technique that enables the estimation of spectral moments of overlaid first and second trip weather echo signals in a pulsed Doppler radar. The transmitted pulses are phase coded with a sequence that allows manipulation of the signal spectrum in such a way that either the first or the second trip signal autocorrelation can be made zero, thus removing the bias error in mean velocity estimates due to overlaid echo. With a sufficiently large number of samples, desired mean velocities can be recovered using autocovariance processing provided that the interfering overlying echo power is not more than 10 dB higher than the desired echo power. Also presented is a spectral processing technique that, in conjunction with autocovariance processing, can recover all three spectral moments of both the first and second trip echoes, when their spectrum widths are narrow compared to the Nyquist interval and their power ratio is in the range ±15 dB. An algorithm is developed that can be easily implemented in existing Doppler radars, with the addition only of a lowpower switchable phase shifter and associated drive circuit.     

Effective Bandwidths for LANDSAT-4 And LANDSAT-D' Multispectral Scanner And Thematic Mapper Subsystems

The spectral bands of the Multispectral Scanner and Thematic Mapper subsystems of Landsat-4 and Landsat-D' have been analyzed using a bandwidth normalization technique based on analysis of the moments of the spectral responsitivy curves. The results include the effective wavelength, the bandpass, the wavelength limits, and the normalized responsivity for each spectral channel. In addition, temperature coefficients for TM PF Channel 6 have been derived. The moments normalization method employed yields sensor parameters whose derivation is independent of source characteristerics (i.e., incident solar spectral irradiance, atmospheric transmittance, or ground reflectance). The errors expected using these parameters are lower that those expected using other normalization methods.     

Assembly yield prediction of plastically encapsulated packages with a large number of manufacturing variables by advanced approximate integration method

An advanced approximate integration scheme called eigenvector dimension reduction (EDR) method is implemented to predict the assembly yield of a plastically encapsulated package. A total of 12 manufacturing input variables are considered during the yield prediction, which is based on the JEDEC reflow flatness requirements. The method calculates the statistical moments of a system response (i.e., warpage) first through dimensional reduction and eigenvector sampling, and a probability density function (PDF) of random responses is constructed subsequently from the statistical moments by a probability estimation method. Only 25 modeling runs are needed to produce an accurate PDF for 12 input variables. The results prove that the EDR provides the numerical efficiency required for the tail-end probability prediction of manufacturing problems with a large number of input variables, while maintaining high accuracy.     

A recursive maximum likelihood algorithm for ARMA spectral estimation

A spectral estimation technique is presented for autoregressive moving-average (ARMA) processes. The technique is based on a parameter estimation technique known as the rec ursive maximum likelihood (RML) method. The recursive spectral estimation algorithm is presented and its asymptotic properties are discussed. Simulation results are presented to illustrate the performance of the estimator for various types of data.     

Spectral moment matching in the maximum entropy spectral analysis method (Corresp.)

The formula for the spectral moments is expanded in a series consisting of autocorrelation terms. By using the autocorrelation extrapolation inherent in the maximum entropy method (MEM) for spectral analysis, it is found that good estimates of the moments can be found from a very Iow order autoregressive model.     

Performance of normalized correlation estimators for complexprocesses

Direct and fast techniques for estimating normalized second-order moments of complex processes are discussed. First, the accuracy of the direct estimate is explicitly given in terms of bias and covariance for the Gaussian processes. Then, a class of estimators based on the complex invariance property is considered. Their theoretical accuracy is given for some cases of paramount interest from a computational point of view in the Gaussian case. In particular, applications in the areas of autoregressive spectrum analysis and spectral centroid estimation are presented. General analytic results and simple expression for immediate evaluation are provided