An adaptive filtering approach to spectral estimation and SARimaging

We present an adaptive FIR filtering approach, which is referred to as the amplitude and phase estimation of a sinusoid (APES), for complex spectral estimation. We compare the APES algorithm with other FIR filtering approaches including the Welch (1967) and Capon (1969) methods. We also describe how to apply the FIR filtering approaches to target range signature estimation and synthetic aperture radar (SAR) imaging. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method, which is also a special case of the FIR filtering approach. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method     

Reflectivity estimation for multibaseline interferometric radar imaging of layover extended sources

In recent years, there has been great interest in exploiting the advanced multibaseline operation of synthetic aperture radar interferometry (InSAR) for solving layover effects from complex orography, which can degrade both SAR and InSAR imagery of terrain radar reflectivity and height. In this work, the problem of retrieving radar reflectivity of layover areas is addressed. It is formulated as the problem of estimating a multicomponent sinusoidal signal corrupted by multiplicative complex correlated noise and additive white Gaussian noise. Application of nonparametric [e.g., Capon, amplitude and phase estimation filter (APES)], parametric [least squares, modern parametric RELAXation spectral estimator (RELAX)], and hybrid spectral estimators for amplitude estimation is investigated for a multilook scenario. In particular, the multilook extensions of RELAX and APES are applied to the interferometric problem. Performance analysis is investigated through a Cramer-Rao lower bound calculation and Monte Carlo simulation. The method of least squares, coupled with Capon's approach to spatial frequency estimation, multilook APES, and multilook RELAX turn out to provide accurate reflectivity estimates for undistorted multibaseline image formation of layover areas.     

Performance analysis of forward-backward matched-filterbankspectral estimators

The problem of complex spectral estimation is of great interest in many applications. This paper studies the general class of the forward-backward matched-filterbank (MAFI) spectral estimators including the widely used Capon as well as the more recently introduced amplitude and phase estimation of a sinusoid (APES) methods. In particular, we show by means of a higher order expansion technique that the one-dimensional (1-D) Capon estimator underestimates the true spectrum, whereas the 1-D APES method is unbiased; we also show that the bias of the forward-backward Capon is half that of the forward-only Capon (to within a second-order approximation). Furthermore. We show that these results can be extended to the two-dimensional (2-D) Capon and APES estimators. Numerical examples are also presented to demonstrate quantitatively the properties of and the relation between these MAFI estimators     

Using APES for interferometric SAR imaging

We present an adaptive finite impulse response (FIR) filtering approach, which is referred to as the Amplitude and Phase EStimation (APES) algorithm, for interferometric synthetic aperture radar (SAR) imaging. We compare the APES algorithm with other FIR filtering approaches including the Capon and fast Fourier transform (FFT) methods. We show via both numerical and experimental examples that the adaptive FIR filtering approaches such as Capon and APES can yield more accurate spectral estimates with much lower sidelobes and narrower spectral peaks than the FFT method. We show that although the APES algorithm yields somewhat wider spectral peaks than the Capon method, the former gives more accurate overall spectral estimates and SAR images than the latter and the FFT method.     

Efficient Algorithms for Adaptive Capon and APES Spectral Estimation

In this paper fast algorithms for adaptive Capon and amplitude and phase estimation (APES) methods for spectral analysis of time varying signals, are derived. Fast, stable, nonrecursive formulae are derived, based on time shifting properties of the pertinent variables. As a consequence, efficient frequency domain recursive least squares (RLS) based, as well as fast RLS based algorithms for the adaptive estimation of the power spectra are developed. Stability issues of the frequency domain estimators are considered, and stabilization procedures are proposed. The computational complexity of the proposed algorithms is lower than relevant existing methods. The performance of the proposed algorithms is demonstrated through extensive simulations.     

Efficient time-recursive implementation of matched filterbank spectral estimators

In this paper, we present a computationally efficient sliding window time updating of the Capon and amplitude and phase estimation (APES) matched filterbank spectral estimators based on the time-variant displacement structure of the data covariance matrix. The presented algorithm forms a natural extension of the most computationally efficient algorithm to date, and offers a significant computational gain as compared to the computational complexity associated with the batch re-evaluation of the spectral estimates for each time-update. Furthermore, through simulations, the algorithm is found to be numerically superior to the time-updated spectral estimate formed from directly updating the data covariance matrix.     

APES算法在MIMO雷达参数估计中的稳健性研究

 多输入多输出(MIMO,Multiple-Input Multiple-Output)雷达用多个发射天线同时发射多个独立信号照射目标,并使用多个接收天线接收目标回波信号.本文研究了MIMO雷达中参数估计的稳健性问题.本文应用幅度相位估计(APES,Amplitude and Phase EStimation)技术,利用目标的方位角最大似然估计值,得到了衰落向量的APES估计算法.考虑到方位角估计的不准确性,借鉴稳健的Capon波束形成器的设计思想,本文推导了衰落向量的稳健的APES估计算法.仿真实验表明,衰落向量的APES算法与稳健的APES算法性能十分接近.因此,衰落向量的APES估计算法是稳健的.     

Capon estimation of covariance sequences

Estimating the covariance sequence of a wide-sense stationary process is of fundamental importance in digital signal processing (DSP). A new method, which makes use of Fourier inversion of the Capon spectral estimates and is referred to as theCapon method, is presented in this paper. It is shown that the Capon power spectral density (PSD) estimator yields an equivalent autoregressive (AR) or autoregressive moving-average (ARMA) process; hence, theexact covariance sequence corresponsing to the Capon spectrum can be computed in a rather convenient way. Also, without much accuracy loss, the computation can be significantly reduced via an approximate Capon method that utilizes the fast Fourier transform (FFT). Using a variety of ARMA signals, we show that Capon covariance estimates are generally better than standard sample covariance estimates and can be used to improve performances in DSP applications that are critically dependent on the accuracy of the covariance sequence estimates.This work was supported in part by National Science Foundation Grant MIP-9308302, Advanced Research Project Agency Grant MDA-972-93-1-0015, the Senior Individual Grant Program of the Swedish Foundation for Strategic Research and the Swedish Research Council for Engineering Sciences (TFR).     

Multi-dimensional Capon spectral estimation using discrete Zhang neural networks

The minimum variance spectral estimator, also known as the Capon spectral estimator, is a high resolution spectral estimator used extensively in practice. In this paper, we derive a novel implementation of a very computationally demanding matched filter-bank based a spectral estimator, namely the multi-dimensional Capon spectral estimator. To avoid the direct computation of the inverse covariance matrix used to estimate the Capon spectrum which can be computationally very expensive, particularly when the dimension of the matrix is large, we propose to use the discrete Zhang neural network for the online covariance matrix inversion. The computational complexity of the proposed algorithm for one-dimensional (1-D), as well as for two-dimensional (2-D) and three-dimensional (3-D) data sequences is lower when a parallel implementation is used.     

Distributed multichannel speech enhancement with minimum mean-square error short-time spectral amplitude, log-spectral amplitude, and spectral phase estimation

In this paper, the authors present optimal multichannel frequency domain estimators for minimum mean-square error (MMSE) short-time spectral amplitude (STSA), log-spectral amplitude (LSA), and spectral phase estimation in a widely distributed microphone configuration. The estimators utilize Rayleigh and Gaussian statistical models for the speech prior and noise likelihood with a diffuse noise field for the surrounding environment. Based on the Signal-to-Noise Ratio (SNR) and Segmental Signal-to-Noise Ratio (SSNR) along with the Log-Likelihood Ratio (LLR) and Perceptual Evaluation of Speech Quality (PESQ) as objective metrics, the multichannel LSA estimator decreases background noise and speech distortion and increases speech quality compared to the baseline single channel STSA and LSA estimators, where the optimal multichannel spectral phase estimator serves as a significant quantity to the improvements, and demonstrates robustness due to time alignment and attenuation factor estimation. Overall, the optimal distributed microphone spectral estimators show strong results in noisy environments with application to many consumer, industrial, and military products.     

Nonparametric spectral analysis of gapped data via an adaptive filtering approach

We present an algorithm for nonparametric complex spectral analysis of gapped data via an adaptive finite impulse response (FIR) filtering approach, referred to as the gapped-data amplitude and phase estimation (GAPES) algorithm. The incomplete data sequence may contain gaps of various sizes. The GAPES algorithm iterates the following two steps: (1) estimating the adaptive FIR filter and the corresponding complex spectrum via amplitude and phase estimation (APES), a nonparametric adaptive FIR filtering approach, and (2) filling in the gaps via a least-squares APES fitting criterion. The initial condition for the iteration is obtained from the available data segments via APES. Numerical results are presented to demonstrate the effectiveness of the proposed GAPES algorithm.This work was supported in part by the Senior Individual Grant Program of the Swedish Foundation for Strategic Research, AFRL/SNAT, Air Force Research Laboratory, Air Force Material Command, USAF, under grant number F33615-99-1-1507, and the National Science Foundation Grant MIP-9457388. The US Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright notice thereon.     

频谱分析技术在层析SAR森林垂直结构信息提取中的应用性能分析

为了分析频谱分析在不同应用场景的信号提取能力,分别应用数值模拟与真实林区的多基线InSAR数据分析五种频谱分析方法的提取效果.数值模拟实验表明,Capon方法受信噪比影响较小;在TSAR林区实验中,Capon方法提取森林垂直结构信息效果最优,NSF方法提取冠层高度及地表信息效果最优.     

A generalized capon estimator for localization of multiple spread sources

In this correspondence, we develop a generalized Capon spatial spectrum estimator for localization of multiple incoherently distributed (spread) sources in sensor arrays. The proposed generalized Capon technique estimates the source central angles and angular spreads by means of a two-dimensional (2-D) parameter search. Simulation results show that the proposed method has a substantially improved performance compared with several popular spread source localization methods.     

Complex amplitude estimation in the known steering matrix and generalized waveform case

We consider a special growth-curve (SGC) model with a known steering matrix and generalized waveform in the presence of unknown interference and noise. Several estimators of the complex amplitude based on this model are derived, including the methods of approximate maximum likelihood (AML), minimum variance distortionless response (MVDR), and amplitude and phase estimation (APES). We analyze the statistical properties of these estimators and show that in the presence of temporally white but spatially correlated noise and interference, AML is asymptotically statistically efficient for a large snapshot number while MVDR and APES are asymptotically equivalent but not statistically efficient. Via several numerical examples, we also show that when the noise and interference are both spatially and temporally correlated, the APES estimator can achieve better estimation accuracy and exhibit greater robustness than the other methods.     

Study of Capon method for array signal processing

The mean-square error (MSE) of Capon estimate of the directions-of-arrival (DOA) is established in the narrowband array processing case. An improved Capon-like DOA estimator is proposed and its MSE is studied as well. Performance comparisons between the standard and improved Capon DOA estimates, and between these two estimates and the linear prediction DOA estimate, are performed. It is concluded that the improved Capon-like method introduced in this paper provides more accurate DOA estimates in most cases.This work has been supported by the Swedish Research Council for Engineering Sciences under contract 91–676.     

Evolutionary periodogram for nonstationary signals

Presents a novel estimator for the time-dependent spectrum of a nonstationary signal. By modeling the signal, at any given frequency, as having a time-varying amplitude accurately represented by an orthonormal basis expansion, the authors are able to compute a minimum mean-squared error estimate of this time-varying amplitude. Repeating the process over all frequencies, they obtain a power distribution as a function of time and frequency that is consistent with the Wold-Cramer evolutionary spectrum. Based on the model assumptions, the authors develop the evolutionary periodogram (EP) for nonstationary signals, an estimator analogous to the periodogram used in the stationary case. They also derive the time-frequency resolution of the new estimator. The approach is free of some of the drawbacks of the bilinear distributions and of the short-time Fourier transform spectral estimates. It is guaranteed to produce nonnegative spectra without the cross-term behavior of the bilinear distributions, and it does not require windowing of data in the time domain. Examples illustrating the new estimator are given     

Frequency offset estimation in the intermediate frequency for satellite-based AIS signals

In this paper, an accurate frequency offset estimator is investigated in the intermediate frequency for the satellite-based automatic identification system (AIS) signals. Using Gaussian minimum shift keying (GMSK) modulation for transmission, the AIS signal is shown to be a plane wave with the modulated phase information and carrier frequency resulting from the Doppler effects. Hence, the phase information can be eliminated with a re-modulated signal, and the frequency offset can be estimated by the ratio of the maximum spectral amplitude and its neighbor spectral amplitude based on the fast Fourier transformation (FFT) interpolation. The estimator has low complexity, and it is easy to implement. Computer simulations are used to assess the performance of the estimator.     

Minimum variance filters and mixed spectrum estimation

This paper presents a spectral density estimator based on a normalized minimum variance (MV) estimator as the one proposed by Lagunas. With an equivalent frequency resolution, this new estimator preserves the amplitude estimation lost in Lagunas one. This proposition comes from a theoretical study of MV filters that highlights this amplitude lost. Two signal types are taken into account: periodic deterministic signals (narrow-band spectral structures) and stationary random signals (broad-band spectral structures). Without selecting a smoothing window, the proposed estimator is an alternative to Fourier-based estimator and, without modeling the signal, it is a concurrent to high-resolution estimators.     

Fast Implementation of Two-Dimensional APES and CAPON Spectral Estimators

The matched-filterbank spectral estimators APES and CAPON have recently received considerable attention in a number of applications. Unfortunately, their computational complexity tends to limit their usage in several cases – a problem that has previously been addressed by different authors. In this paper, we introduce a novel approach to the computation of the APES and CAPON spectra, which leads to a computational method that is considerably faster than all existing techniques. The new implementations of APES and CAPON are called fast APES and fast CAPON, respectively, and are developed for the two-dimensional case, with the one-dimensional case as a special case. Numerical examples are provided to demonstrate the application of APES to synthetic aperture radar (SAR) imaging, and to illustrate the reduction in computational complexity provided by our method.     

On the convergence of the multichannel maximum likelihood pointspectrum estimator

In 1948, Geronimus discovered that the inverse of the sum of the (modulus squared) orthogonal polynomials corresponding to a Toeplitz matrix converges to the point spectrum as the matrix order goes to infinity. In 1969, Capon independently generalized part of Geronimus' result to the random field setting as a fixed-order point spectrum estimator. Within signal processing, this Geronimus-Capon result is known as the maximum likelihood spectral estimator or alternatively, the minimum variance estimator. A simple proof that the Geronimus-Capon spectra estimator converges to the point spectrum in the multichannel setting is presented