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.     

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.     

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     

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.     

Combining Capon and APES for estimation of spectral lines

We propose combining the Capon and the APES spectral estimators for estimation of both the amplitude and the frequency of spectral lines. The so-obtained estimator does not suffer from Capon's biased amplitude estimates nor from APES' biased frequency estimates or resolution problem. Furthermore, the combined estimator is computationally simpler than APES and has about the same complexity as Capon. Numerical simulations are presented illustrating the increased performance.This work was supported in part by the Swedish Foundation for Strategic Research.     

SAR stereo imaging algorithm based on Capon spectrum estimation

This letter presents a novel approach for the Synthetic Aperture Radar （SAR） stereo imaging based on the Capon spectrum estimation technique. In order to deal with nonuniform sampling space and lead to super resolution in the elevation direction, Capon approach is used to focus the SAR data on a certain height. Results obtained on simulated data demonstrate the feasibility of the Capon based algorithm. Compared with the classical Fast Fourier Transform （FFT）, the Capon based algorithm shows better resolution quality.     

Complex ISAR imaging of maneuvering targets via the Capon estimator

An inverse synthetic aperture radar (ISAR) can be used to produce high-resolution images of moving targets of interest by utilizing the relative motion between the target and the radar and by transmitting signals with large bandwidth. Most ISAR imaging algorithms are based on the range-Doppler processing, which implies that the Doppler shifts remain constant during the coherent integration time. For maneuvering targets, the Doppler shifts are time varying. In this case, the algorithms will produce blurred images. We present herein an adaptive Capon (1969) spectral estimation algorithm for the complex ISAR image formation of maneuvering targets. It is an efficient recursive implementation of the well-known Capon complex spectral estimation algorithm by using FFT and simple matrix operations     

Amplitude spectrum estimation for two-dimensional gapped data

The amplitude and phase estimation (APES) approach to nonparametric spectrum estimation of uniformly sampled data has received considerable interest. We consider the extension of APES to gapped data, i.e., uniformly sampled data with missing samples. It has been shown that the APES estimate of the spectrum is the minimizer of a certain least-squares (LS) criterion, and our extension of APES is based on minimizing this LS criterion with respect to the missing data as well. A computationally efficient method for doing this based on cyclic minimization and the conjugate gradient algorithm is proposed. The new algorithm is called gapped-data APES (GAPES) and is developed for the two-dimensional (2-D) case, with the one-dimensional (1-D) case as a special instance. Numerical examples are provided to demonstrate the performance of the algorithm and to show the advantages of 2-D data processing over 1-D (row or column-wise) data processing, as well as to show the applicability of the algorithm to synthetic aperture radar (SAR) imaging     

Estimation-based synthesis of H∞-optimal adaptive FIR filtersfor filtered-LMS problems

This paper presents a systematic synthesis procedure for H∞-optimal adaptive FIR filters in the context of an active noise cancellation (ANC) problem. An estimation interpretation of the adaptive control problem is introduced first. Based on this interpretation, an H∞ estimation problem is formulated, and its finite horizon prediction (filtering) solution is discussed. The solution minimizes the maximum energy gain from the disturbances to the predicted (filtered) estimation error and serves as the adaptation criterion for the weight vector in the adaptive FIR filter. We refer to this adaptation scheme as estimation-based adaptive filtering (EBAF). We show that the steady-state gain vector in the EBAF algorithm approaches that of the classical (normalized) filtered-X LMS algorithm. The error terms, however, are shown to be different. Thus, these classical algorithms can be considered to be approximations of our algorithm. We examine the performance of the proposed EBAF algorithm (both experimentally and in simulation) in an active noise cancellation problem of a one-dimensional (1-D) acoustic duct for both narrowband and broadband cases. Comparisons to the results from a conventional filtered-LMS (FxLMS) algorithm show faster convergence without compromising steady-state performance and/or robustness of the algorithm to feedback contamination of the reference signal     

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.     

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).     

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.     

从混合有色噪声背景中提取正弦随相调频信号的方法

提出了从混合有色背景噪声中提取正弦随机调频信号方法－－基于高阶累积量FIR自适应滤波方法。其主要特点是：FIR自适应滤波系数是用输入信号的四阶以上累积量进行更新的；FIR自适应滤波器是收敛于与有用信号类型匹配的滤波器。因此，它既能有效地提取有用信号（匹配信号），又能有效地抑制混合有色噪声（非匹配信号）。仿真结果表明，与短时相关方法相比，该方法是很有效的。     

Iterative Adaptive Approaches to MIMO Radar Imaging

Multiple-input multiple-output (MIMO) radar can achieve superior performance through waveform diversity over conventional phased-array radar systems. When a MIMO radar transmits orthogonal waveforms, the reflected signals from scatterers are linearly independent of each other. Therefore, adaptive receive filters, such as Capon and amplitude and phase estimation (APES) filters, can be directly employed in MIMO radar applications. High levels of noise and strong clutter, however, significantly worsen detection performance of the data-dependent beamformers due to a shortage of snapshots. The iterative adaptive approach (IAA), a nonparametric and user parameter-free weighted least-squares algorithm, was recently shown to offer improved resolution and interference rejection performance in several passive and active sensing applications. In this paper, we show how IAA can be extended to MIMO radar imaging, in both the negligible and nonnegligible intrapulse Doppler cases, and we also establish some theoretical convergence properties of IAA. In addition, we propose a regularized IAA algorithm, referred to as IAA-R, which can perform better than IAA by accounting for unrepresented additive noise terms in the signal model. Numerical examples are presented to demonstrate the superior performance of MIMO radar over single-input multiple-output (SIMO) radar, and further highlight the improved performance achieved with the proposed IAA-R method for target imaging.      

一种改善单脉冲雷达测角精度的新方法

提出了一种基于最大平均改善因子的自适应动目标显示（AMTI）和APES算法提高测角精度的新方法。在单脉,中雷达系统中,雨杂波降低了多普勒频率检测精度,从而降低了雷达的跟踪能力。传统的动目标显示（MTI）和快速傅里叶变换（FFT）不能满足精密跟踪的要求。为了抑制雨杂波,选择了基于最大平均改善因子的自适应MTI方法。此外,还选用了APES方法来提高频率估计精度。相对于传统的MTI和FFT方法,新的方法具有更好的多普勒频率估计精度,从而可提高比幅法测角精度。最后通过仿真证明了该方法的有效性。     

单音干扰下OFDM系统中频域迭代干扰消除算法

针对正交频分复用（OFDM,Orthogonal Frequency Division Multiplexing）系统受单音干扰问题,提出了一种有效的频域迭代干扰消除算法。所提算法首先在频域对干扰进行准确估计和重构,然后进行干扰消除。为实现更准确的干扰频率粗估计,提出了新的结合补零内插的频谱波峰搜索方法,有效地避免了干扰位于两子载波之间时频谱泄露导致的谱峰错判。干扰频率精确估计综合采用频率转化、低通滤波、加权相位平均算法迭代实现,估计误差在每一次迭代中减小。仿真结果表明:对于-20dB以上的干信比,所提算法能保证干扰参数的精确估计,使系统达到没有干扰时的误码率性能。      

自适应阵列天线中DOA估计算法研究

波达方向(DOA)估计是自适应阵列天线系统中的一个关键技术之一,通过对波达方向估计算法中的延迟-相加算法、Capon最小方差算法和多重信号分类算法分别进行讨论,并建立均匀直线阵对这3种算法分别进行仿真,仿真结果证明多重信号分类算法相对于前两种算法有最尖锐的谱峰和最高的分辨率。     

Sidelobe reduction via adaptive FIR filtering in SAR imagery.

The paper describes a class of adaptive weighting functions that greatly reduce sidelobes, interference, and noise in Fourier transform data. By restricting the class of adaptive weighting functions, the adaptively weighted Fourier transform data can be represented as the convolution of the unweighted Fourier transform with a data adaptive FIR filter where one selects the FIR filter coefficients to maximize signal-to-interference ratio. This adaptive sidelobe reduction (ASR) procedure is analogous to Capon's (1969) minimum variance method (MVM) of adaptive spectral estimation. Unlike MVM, which provides a statistical estimate of the real-valued power spectral density, thereby estimating noise level and improving resolution, ASR provides a single-realization complex-valued estimate of the Fourier transform that suppresses sidelobes and noise. Further, the computational complexity of ASR is dramatically lower than that of MVM, which is critical for large multidimensional problems such as synthetic aperture radar (SAR) image formation. ASR performance characteristics can be varied through the choice of filter order, l(1)- or l(2)-norm filter vector constraints and a separable or nonseparable multidimensional implementation. The author compares simulated point scattering SAR imagery produced by the ASR, MVM, and MUSIC algorithms and illustrates ASR performance on three sets of collected SAR imagery.     

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.