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     

数据长度和信噪比对中频雷达风场计算的影响分析

计算相关函数是FCA(Full Correlation Analysis)风场算法的重要步骤.理论分析发现,信号与噪声之间的互相关函数不等于零是相关函数幅度校正产生误差的重要原因,而数据长度和信噪比都会对这一误差的分布产生影响.通过仿真计算验证了这一结论,并在统计分析后得到了数据长度和SNR值对互相关函数最大值延迟时间和幅值误差分布的影响关系.结合FCA计算中最大值延迟时间和幅值对FCA风场计算结果的影响关系,进一步得出了中频雷达数据长度和信噪比阈值的设定标准,以及互相关函数幅度校正的修正准则.     

Compressive sensing-based wind speed estimation for low-altitude wind-shear with airborne phased array radar

An important issue in low-altitude wind-shear detection is to estimate the wind speed of wind field. In this paper, a novel method for wind speed estimation with airborne phased array radar is proposed by combining space time adaptive processing and compressive sensing. The proposed method is able to achieve accurate wind speed estimate in the condition of limited number of sampling pulses, as demonstrated by numerical examples.     

Statistical moments of radar cross section

The radar cross section (RCS) for backscatter from a smooth closed convex surface reflector, as calculated from geometrical optics, is shown to have a mean value equal to A/4, where A is the total surface area of the reflector, and the mean is obtained by averaging over all aspects. Results are also given for the calculation of higher-order moments and probability density functions     

Ergodicity and fourth-order spectral moments

Relationships between ergodicity and structures of fourth-order spectral moments are investigated. In particular it is shown that second-order ergodicity of a random process is directly related to the distribution of these moments on the normal manifolds of the frequency domain. This result is illustrated by various examples     

Optimized estimation of moments for nonstationary signals

The behavior of nonstationary moment estimators that are based on linear time-invariant filtering is analyzed. The performance of such estimators is evaluated in terms of their time-averaged variance and time-averaged squared bias. Optimal estimators that minimize a convex combination of bias and variance are derived. The superiority of such optimally weighted filtering over the conventional (exponentially windowed) moment estimation technique is demonstrated by means of a simple example. The same example also serves to illustrate the difficulties encountered when the construction of optimal estimators relies on uncertain prior information, as well as to demonstrate the feasibility of overcoming such difficulties by using appropriately designed (robust) optimal estimators. We also include a brief discussion of the relevance of the proposed moment estimation technique to identification of linear time-variant systems and to estimation of time-variant spectra     

Lattice methods for spectral estimation

Lattice forms provide convenient parametrization of rational spectra of stationary processes. A comprehensive summary of lattice algorithms for estimating spectral parameters of AR, MA, and ARMA processes is presented. It is shown that various well-known spectral estimation techniques, such as the Maximum Entropy Method (MEM) and Maximum Likelihood Method (MLM), can be efficiently computed from lattice parameters. Algorithms are presented for the autocorrelation, pre-windowed, and covariance methods of forming the sample covariance matrix.     

Optimal kernels for nonstationary spectral estimation

Current theories of a time-varying spectrum of a nonstationary process all involve, either by definition or by difficulties in estimation, an assumption that the signal statistics vary slowly over time. This restrictive quasistationarity assumption limits the use of existing estimation techniques to a small class of nonstationary processes. We overcome this limitation by deriving a statistically optimal kernel, within Cohen's (1989) class of time-frequency representations (TFR's), for estimating the Wigner-Ville spectrum of a nonstationary process. We also solve the related problem of minimum mean-squared error estimation of an arbitrary bilinear TFR of a realization of a process from a correlated observation. Both optimal time-frequency invariant and time-frequency varying kernels are derived. It is shown that in the presence of any additive independent noise, optimal performance requires a nontrivial kernel and that optimal estimation may require smoothing filters that are very different from those based on a quasistationarity assumption. Examples confirm that the optimal estimators often yield tremendous improvements in performance over existing methods. In particular, the ability of the optimal kernel to suppress interference is quite remarkable, thus making the proposed framework potentially useful for interference suppression via time-frequency filtering     

Multidimensional spectral estimation

Methods of multidimensional power spectral estimation are reviewed. Seven types of estimators are discussed: Fourier, separable, data extension, MLM, MEM, AR, and Pisarenko estimators. Particular emphasis is given to MEM where current research is quite active. Theoretical developments are reviewed and computational algorithms are discussed.     

Maximum-entropy spectral analysis of radar clutter

The paper reviews a processor that uses the maximum-entropy spectral estimate to provide a set of Doppler-based features for classifying the different forms of radar clutter as encountered in an air traffic control environment. This enables vectoring aircraft around an area that is made hazardous by the presence of major weather disturbances or migrating flocks of birds. An overview is given of experimental results that demonstrate the practical viability of this Doppler processor.     

Ramp response radar imagery spectral content

The physical optics (PO) approximation is examined in the time domain to illustrate certain relationships between an area function interpretation of the physical optics scattering estimate and the span of interrogating frequencies required to produce an image of the object. The consequences of extending the normal physical optics integration limit to encompass the entire object are demonstrated using conducting spheres, disks, cone spheres, and hemispherical objects. Low frequency interrogating signals are stressed for imaging purposes with an interpretation of when such signals must be supplemented by higher frequencies.     

An estimation and verification of vessel radar cross sections for high-frequency surface-wave radar

The radar cross sections of both small and large ships for high-frequency surface-wave radar (HFSWR) were studied by using the numerical electromagnetics code, and by using measurements from an HFSWR system at Cape Race, Newfoundland, Canada. The results of the study indicated that Teleost, a 2405-ton Canadian Coast Guard ship, and large cargo container vessels (-36000 ton) have comparable RCS values at 3.1 and 4.1 MHz. This was verified by comparing Teleost signals with the reflections of seven cargo-container vessels, identified during an operational evaluation of the HFSWR. The conclusion of the study was that Teleost and the large cargo container vessels had an angle-averaged radar cross section (RCS) of -40 dBm/sup 2/, while small vessels (-1000 tons) could reasonably be characterized by an angle-averaged RCS of -30 dBm/sup 2/, in the lower end of the HF band (3-5 MHz).     

A two-dimensional Prony's method for spectral estimation

The problem of estimating the parameters of a model for bidimensional data made up by a linear combination of damped two-dimensional sinusoids is considered. Frequencies, amplitudes, phases, and damping factors are estimated by applying a generalization of the monodimensional Prony's method to spatial data. This procedure finds the desired quantities after an autoregressive model fitting to the data, a polynomial rooting, and a least-squares problem solution. The autoregressive models involved have a particular nature that simplifies the analysis. In fact, their characteristic polynomial factors into two parts so that many of their properties can be easily determined. Quick estimates of the parameters computed are found by using standard one-dimensional autoregressive estimation methods. An iterative procedure for refining the autoregressive parameters estimates which gives rise to better frequency estimates is also discussed. Some simulation results are reported     

Higher order spectral estimation for random fields

This paper is concerned with the nonparametric estimation of the higher order cumulant spectra of vector-valued stationary random fields onZ ^d by smoothing the periodograms, whereZ is the space of integers and the dimensiond1. We derive the asymptotic cumulant properties of the spectral estimates, and consider an application to multidimensional nonlinear systems identification. Numerical examples with simulated data are provided.     

Cumulant-based LP method for two-dimensional spectral estimation

A cumulant-based linear prediction (CBLP) method for two-dimensional (2-D) spectral estimation is presented. The main idea of the method is to compute the coefficients of two different single-quadrant prediction filters by applying the LP theory to a selected 2-D fourth-order mixed cumulant slice of the noisy signal. These coefficients are employed in formulating two different autoregressive spectral models. Both spectral models are combined to obtain the desired spectral estimate. The effectiveness of the proposed CBLP method is demonstrated through computer simulation     

On nonparametric spectral estimation

In this paper the Cramér-Rao bound (CRB) for a general nonparametric spectral estimation problem is derived under a local smoothness condition (more exactly, the spectrum is assumed to be well approximated by a piecewise constant function). Further-more, it is shown that under the aforementioned condition the Thomson method (TM) and Daniell method (DM) for power spectral density (PSD) estimation can be interpreted as approximations of the maximum likelihood PSD estimator. Finally the statistical efficiency of the TM and DM as nonparametric PSD estimators is examined and also compared to the CRB for autoregressive moving-average (ARMA)-based PSD estimation. In particular for broadband signals, the TM and DM almost achieve the derived nonparametric performance bound and can therefore be considered to be nearly optimal.This work was supported in part by the Swedish Foundation for Strategic Research (SSF) through the Senior Individual Grant Program.     

Multi-dimensional parametric spectral estimation

The approach taken toward estimating the power spectral density (PSD) function of multi-dimensional (m-d) data fields is sometimes too general considering that in many areas of application, the PSD is not arbitrary but is low order parametric. However, if the parametric form of such fields is not taken into account, then much is lost in estimating their power spectra. In this paper a new m-d (m = 3, 4) parametric spectrum estimation approach is introduced based on the minimum variance representations of m-d data fields. These representations are defined in integrated and compact linear predictive forms with their PSD interpretations being generally ARMA. For example, in the 3-d case it is shown that there are four possible models: causal, semicausal I, semicausal II, and noncausal. The selected model parameters for spectral estimation achieve the minimum covariance recursion error of a given finite length m-d data field. Spectra computed from short, long, noisy, narrow-band and wide-band data fields are compared with spectra computed by standard techniques and show improvement in resolution and in accuracy of spectrum matching.     

Data-adaptive evolutionary spectral estimation

We present a novel data-adaptive estimator for the evolutionary spectrum of nonstationary signals. We model the signal at a frequency of interest as a sinusoid with a time-varying amplitude, which is accurately represented by an orthonormal basis expansion. We then compute a minimum mean-squared error estimate of this amplitude and use it to estimate the time-varying spectrum at that frequency, all while minimizing the interference from the signal components at other frequencies. Repeating the process over all frequencies, we obtain a power distribution that is consistent with the Wold-Cramer evolutionary spectrum and reduces to Capon's (1969) method for the stationary case. Our estimator possesses desirable properties in terms of time-frequency resolution and positivity and is robust in the spectral estimation of noisy nonstationary data. We also propose a new estimator for the autocorrelation of nonstationary signals. This autocorrelation estimate is needed in the data-adaptive spectral estimation. We illustrate the performance of our estimator using simulation examples and compare it with the recently presented evolutionary periodogram and the bilinear time-frequency distribution with exponential kernels