ARMA Time Series Modeling: an Effective Method

The ability to generate rational models of time series plays an important role in such applications as adaptive filtering, spectral estimation, digital control, array processing, and forecasting. A method for effecting an autoregressive moving average (ARMA) model estimate is presented which possesses a number of admirable properties: 1) it has an elegant algebraic structure, 2) its modeling performance in spectral estimation applications has been empirically found to typically exceed that of such contemporary techniques as the periodogram, the Burg method, and the Box-Jenkins method on a variety of problems, 3) it is implementable by computationally efficient algorithms, and 4) it is based on pseudomaximum likelihood concepts. Taken in combination, these properties mark this method as being an effective tool in challenging applications requiring high modeling performance in a real time setting.     

Emulating random process target statistics (using MSF)

The topics of matrix spectral factorization (MSF) in conjunction with results from realization theory are applied here in simulating a stationary multi-input/multi-output (MIMO) linear system from a specified power spectral density matrix. MSF provides the appropriate transfer function matrix and realization theory specifies the corresponding parameters of a linear system having this transfer function This approach can be used to correctly capture the cross correlations that exist in a multichannel vector random process (representing a particular radar target signature). Aspects of the solution to this problem are illustrated using an original representative example problem with a closed-form answer. Existing software programs for accomplishing MSF are identified and one has been successfully validated using the known closed-form solution mentioned above. A streamlined realization algorithm (offered here as the primary theoretical contribution) can be used along with the MSF computer program and can now be applied to actual radar data. Besides multichannel spectral estimation, several other important applications of this same MSF solution methodology are summarized in Appendix B including extending applicability to the complex case (to handle radar polarization issues related to coherent phase processing), and finally in reexpressing second order statistics of a multichannel autoregressive moving average (ARMA) process as those of a simpler but mathematically equivalent autoregressive (AR) process of slightly higher dimensions (as another original application of the same major result offered here)     

Angular Spectra in Radar Applications

Recent advances in the art of estimating spectral densities have led to speculation that these same techniques could be used to improve angular resolution in radar applications. An improvement in angular resulution would be particularly helpful in sepingrating low angle returns from their surface reflected images. Despite the duality between time and space, however, it turns out that the low angle radar problem is different from the usual spectral estimation problem in a rather fundamental way. The unfortunate result is that the improved spectral estimation techniques are of little, if any, value in solving the low angle tracking problems.     

Spectral Analysis and Subtraction of Noise in Radar Signals

A new method of maximum entropy spectral estimation called the revised maximum entropy method (MEM) is formulated and is applied to the spectral analysis of the echo signals from atmospheric turbulence observed by an incoherent scatter radar. The revised MEM is shown free from many demerits of the other methods for spectral analysis. Further it makes it possible to subtract the white noise usually contained in the data during the processing. Some examples of spectral estimation are shown for the actual radar signals and the simulated data. Another application of the revised MEM is the subtraction of the clutter component which is difficult to do by linear filtering. The method is successfully applied to several data abounding with the clutter to obtain the spectra of the echo signals with less clutter distortion.     

Comparison of various periodograms for sinusoid detection andfrequency estimation

With the advent of the fast Fourier transform (FFT) algorithm, the periodogram and its variants such as the Bartlett's procedure and Welch method, have become very popular for spectral analysis. However, there has not been a thorough comparison of the detection and estimation performances of these methods. Different forms of the periodogram are studied here for single real tone detection and frequency estimation in the presence of white Gaussian noise. The threshold effect in frequency estimation, that is, when the estimation errors become several orders of magnitude greater than the Cramer-Rao lower bound (CRLB), is also investigated. It is shown that the standard periodogram gives the optimum detection performance for a pure tone while the Welch method is the best detector when there is phase instability in the sinusoid. As expected, since the conventional periodogram is a maximum likelihood estimator of frequency, it generally provides the minimum mean square frequency estimation errors     

Streamlining measurement iteration for EKF target tracking

The estimation problem is defined, and a review of how the linear estimation approach of Kalman filtering is extrapolated to form an extended Kalman filter (EKF), applicable for state estimation in nonlinear systems is presented. A mechanization of an EKF variation known as an iterated EKF, offering improved tracking performance, is treated. A streamlined version of an iterated EKF that has a lesser computational burden (fewer operations per cycle or time step) than prior formulations is offered. A nonlinear filtering application example, to be used as a testbed for this new approach, is described, and the detailed modeling considerations as needed for exoatmospheric random-variable radar target tracking are discussed. The performance of the streamlined mechanization is illustrated in this radar target tracking example, and comparisons are made with the performance of an EKF without measurement iteration     

Resolution of signal sources via spectral moment estimation

In different practical situations it is desired to estimate the number of signal sources and their positions in space or in frequency domain. The first problem is known as the detection or the order estimation and the second one as the resolution. For the resolution problem techniques such as nonlinear least squares (NLSM), high-order Yule-Walker method (HOYW), multiple signal classification (MUSIC), Pisarenko harmonic retrieval method, min-norm method, estimation of signal parameters by rotational invariance technique (ESPRIT), were proposed (Marple, 1987 and Stoica and Moses, 1997). All these high-resolution methods are based on the analysis of the signal covariance matrix. But the covariance matrix is not the only choice to represent the signal spectrum. In different applications (weather radars, synthetic aperture radar (SAR) signal processing, ultrasound imaging in medicine, atmospheric turbulence measurements) the signal spectrum can be modeled through its algebraic moments. Recently a number of efficient nonparametric methods have been proposed to estimate the algebraic spectral moments (Monakov, 1999). The presented paper is an attempt to solve the direction of arrival (DOA) problem via estimation of the algebraic spectral moments. A method proposed in the article is comparable in its accuracy with the MUSIC method. At the same time its computational burden is much lower. The method permits to estimate the signal power of sources easily to complete the full spectral line analysis. Additionally the method shows good robustness in situations when signal sources have noticeable spatial extend     

Super resolution SAR imaging via parametric spectral estimationmethods

Super resolution synthetic aperture radar (SAR) image formation via sophisticated parametric spectral estimation algorithms is considered. Parametric spectral estimation methods are devised based on parametric data models and are used to estimate the model parameters. Since SAR images rather than model parameters are often used in SAR applications, we use the parameter estimates obtained with the parametric methods to simulate data matrices of large dimensions and then use the fast Fourier transform (FFT) methods on them to generate SAR images with super resolution. Experimental examples using the MSTAR and Environmental Research Institute of Michigan (ERIM) data illustrate that robust spectral estimation algorithms can generate SAR images of higher resolution than the conventional FFT methods and enhance the dominant target features     

Design of a practical tracking algorithm with radar measurements

The extended Kalman filter (EKF) has been widely used as a nonlinear filtering method for radar tracking problems. However, it has been found that if cross-range measurement errors of the target position are large, the performance of the conventional EKF degrades considerably due to nonnegligible nonlinear effects. A new filtering algorithm for improving the tracking performance with radar measurements is developed based on the fact that correct evaluation of the measurement error covariance is possible in the Cartesian coordinate system. The proposed algorithm may be viewed as a modification of the EKF in which the variance of the range measurement errors is evaluated in an adaptive manner. The filter structure facilitates the incorporation of the sequential measurement processing scheme, and this makes the resulting algorithm favorable to both estimation accuracy and computational efficiency. Computer simulation results show that the proposed method offers superior performance in comparison to previous methods. Moreover, our developed algorithm provides some useful insight into the radar tracking problem     

一种新的周期性运动部件调制谱估计方法

目标内部运动部件对雷达回波产生的周期性运动部件调制 (PMPM )为目标识别提供了丰富的特征信息。但由于大多数雷达均采用多目标工作方式 ,因此 ,通常情况下只能从雷达获得不连续的目标回波脉冲串 ,这极大增加了根据目标回波频谱提取PMPM特征的难度。针对含PMPM目标回波频谱具有简单结构这一特点 ,提出了基于最小熵准则的交替迭代反卷积方法(AIDME)用于扩展目标雷达回波频谱估计。结果表明 :与傅里叶谱分析方法相比 ,该方法能够有效消除卷积核函数的不利影响 ,获得逼近目标回波真实谱的良好谱估计结果     

Disturbance estimation and compensation in linear systems

Discrete-time estimation and compensation are discussed as a solution to the problems encountered when disturbances are present and degrade the performance of continuous automatic control systems. The method described, under a mild set of conditions, allows the designer to locate the closed-loop system poles substantially anywhere and provide disturbance rejection as large as desired by increasing the dimensions of the disturbance estimator. This estimation/compensation scheme results in a gain characteristic, below some frequency (ω_c ), with a slope of q×20 dB/decade. The value of q and ω_c can be chosen by the designer, within the physical limitations of the problem, so that the system error resulting from either deterministic or stochastic disturbances is sufficiently reduced. The method has been investigated for use with known linear, time-invariant systems     

NOMA异步干扰消除技术

由于NOMA(Non-Orthogonal Multiple Access,非正交多址接入)技术能够提高系统的吞吐量和频谱效率,因而在空间信息传输中具有广阔的应用前景.针对N O MA在传输过程中必然面临的同步问题以及不同用户信号间的彼此干扰问题,提出了N O MA异步干扰消除方案.首先采用过采样使得输出符号之间的噪声分量彼此独立,然后利用过采样输出序列间良好的结构性,分别采用SIC(Successive Interference Cancellation,串行干扰消除)、BP(Belief Propagation,置信度传播)、MLSD(Maximum Likelihood Sequence Detection,最大似然序列检测)等对采样输出的序列进行信号检测.仿真结果表明,符号异步NOMA相比于同步NOMA具有更好的误码性能.     

Efficient implementation of Capon and APES for spectral estimation

Both the Capon and APES estimators can be shown to belong to the class of matched-filterbank spectral estimators and can be used to obtain complex spectral estimates that have more narrow spectral peaks and lower sidelobe levels than the fast Fourier transform (FFT) methods. It can also be shown that APES has better statistical performance than Capon. In this paper, we address the issue of how to efficiently implement Capon and APES for spectral estimation     

The Resolution Performance of Range Estimators

The theoretical basis and methods of implementation of a moment algorithm for the range separation estimation of two closely spaced point targets are presented. Moment estimation and noise filtering techniques introduced here result in a considerable improvement over Baum's algorithm. The error bounds are established and it is shown that the spectral moment estimator exhibits optimum (zero bias, minimum variance) performance when the target separation normalized to the standard deviation of the Gaussian pulse is 2?1.5. Monte Carlo simulation is performed to verify the approximations made and to demonstrate the feasibility of the working models.     

空间谱估计经典算法性能比较

空间谱估计是阵列信号处理的一个重要研究方向。空间谱估计理论与技术已日趋成熟，近几十年的经典谱估计技术包括：常规波束形成（CBF）、Capon谱估计、多重信号分类（MUSIC）、旋转不变子空间算法（ESPRIT）、最大似然（ML）、子空间拟合（SF），及这些算法的扩展和变形。上述算法在各个分散的文章中均有具体深入的理论分析和研究，亦有类似的2种或3种算法的性能比较，但是针对这些所有算法的性能比较，就笔者所知尚无公开报道，而使工程实现时对算法的选择没有依据。本文对这些经典算法做了简介，列出各个算法的优缺点，并对性能进行仿真比较，能直观地得到各个算法的性能对比，给工程实现算法选择提供理论依据。     

基于稀疏表示的多雷达信号二维融合处理

多雷达信号融合通过对多视角和多频带雷达信号进行相干融合,可以提高图像的距离和方位向分辨率.为了克服基于谱估计的多雷达信号融合方法稳健性严重依赖于散射点个数估计精度和二维极点配对精度的问题,在深入研究逆合成孔径雷达(ISAR)信号的基础上,构造了多雷达信号二维融合的线性表示模型,将融合处理转化为一个信号表示问题;充分挖掘...     

高光谱图像压缩感知投影与复合正则重构

压缩感知理论提供了一种新的数据获取和压缩思路,能有效地把计算负担从编码端转移到解码端。高光谱数据具备数据稀疏性、空间相关性和谱间相关性,结合这3类先验知识,提出了一种基于复合正则化的高光谱图像压缩感知投影与重构方法。该方法的编码端只需要一个简单的投影操作;在重构算法实现中,基于变量分裂的思想,把具备多个正则项的优化问题转化成多个简单的优化问题,并用迭代方式求解。实验结果表明,本文算法在高光谱图像重构上能获得更高的峰值信噪比和更好的重构效果。该方法具备极低的编码复杂度,适用于资源受限的机载和星载高光谱成像平台。     

Optimum Linear Estimation of Stochastic Signals in the Presence of Multiplicative Noise

This paper considers optimum (MMSE) linear recursive estimation of stochastic signals in the presence of multiplicative noise in addition to measurement noise. Often problems associated with phenomena such as fading or reflection of the transmitted signal at an ionospheric layer, and also situations involving sampling, gating, or amplitude modulation, can be cast into such formulation. The different kinds of estimation problems treated include one-stage prediction, filtering, and smoothing. Algorithms are presented for discrete time as well as for continuous time estimation.     

The Proper Computation of the Matrix Pseudoinverse and its Impact in MVRO Filtering

There have been two new algorithms of fairly recent origin offered for the calculation of the matrix pseudoinverse. Unfortunately, nonpathological counterexamples can be constructed, as offered herein, that demonstrate the questionable nature of these two algorithms; however, a resolution is offered here to help prevent possible uncritical propagation of the questionable algorithms. As a rigorous alternative, a well-established technique (endorsed by numerical analysts) is reviewed for calculating the correct matrix pseudoinverse using a computer. Additionally, this technique possesses existent independently verified/validated and assessible software code for a convenient implementation. However, historical loose ends in calculating the associated condition number are singled out here as cause for concern and as a topic for future resolution and refinement. Finally, as the primary motivation for considering these issues, an application example is offered from estimation theory in the implementation and analysis of a minimum variance reduced-order (MVRO) filter having proper performance that critically hinges on the correct computation of the matrix pseudoinverse. While examples of applying MVRO to navigation applications were provided almost a decade ago, a clear indication of the somewhat restrictive conditions of applicability were wanting and so are elucidated here since there appears to be a resurgence of interest in this analytic technique. Another contribution is in providing a tally of the drawbacks to be incurred in using MVRO as well as its previously publicized benefits.     

Adaptive on-line flux estimation in field-oriented control of an IM

An adaptive technique for the online estimation of the rotor field vector to use as a feedback for the field-oriented control of an induction machine (IM) is described. This method makes use of the stator voltage and rotor speed measurements. It uses the least square estimation technique for identifying the machine parameters to be used in the estimation of the field vector. The position and magnitude of the flux vector are identified during the normal operation of the machine by applying some special constraints to the forcing function. This constraint is applied only for a short duration to make some measurements, and the machine performance is not affected. Extensive simulation of the system has been carried out, and the results are presented