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.     

Linear modeling of multidimensional non-gaussian processes using cumulants

Extending the notion of second-order correlations, we define thecumulants of stationary non-Gaussian random fields, and demonstrate their potential for modeling and reconstruction of multidimensional signals and systems. Cumulants and their Fourier transforms calledpolyspectra preserve complete amplitude and phase information of a multidimensional linear process, even when it is corrupted by additive colored Gaussian noise of unknown covariance function. Relying on this property, phase reconstruction algorithms are developed using polyspectra, which can be computed via a 2-D FFT-based algorithm. Additionally, consistent ARMA parameter estimators are derived for identification of linear space-invariant multidimensional models which are driven by unobservable, i.i.d., non-Gaussian random fields. Contrary to autocorrelation based multidimensional modeling approaches, when cumulants are employed, the ARMA model is allowed to be non-minimum phase, asymmetric non-causal or non-separable.This work was performed at the University of Southern California, Los Angeles, under National Science Foundation Grant ECS-8602531 and Naval Ocean Systems Center Contract N6601-85-D-0203. The second author was partly supported by Univ. of Virginia Engr. Research Initiation Grant 6-42410, and HDL Contract 5-25227. Parts of this paper were presented at ICASSP-88, New York, NY, April 1988, and at the IV IEEE ASSP Workshop on Spectrum Estimation and Modeling, Minneapolis, MN, August 1988.     

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.     

On the concentrated stochastic likelihood function in array signal processing

The stochastic likelihood function [(STO)LF] associated with the narrowband signal processing problem can be concentrated with respect to the signal covariance matrix elements and the noise power. Although this is a known fact, no clear-cut derivation of the concentrated (STO)LF appears to be available in the literature. In this short paper we provide a simple, complete proof of the concentrated (STO)LF formula.The work of A. Nehorai was supported by the Air Force Office of Scientific Research under Grant no. F49620-93-1-0096, the Office of Naval Research under Grant no. N00014-91-J-1298, and the National Science Foundation under grant no. MIP-9122753. The work of P. Stoica was supported by the Swedish Research Council for Engineering Sciences under contract no. 93-669.     

Polynomial ambiguity resistant precoders: Theory and applications in ISI/multipath cancellation

In this paper, precoding techniques are studied for combating the intersymbol interference (ISI)/multipath effects in communication systems. We introduce a new type-precoder which we term thepolynomial ambiguity resistant (PAR) precoder for its ability to resist signal distortion induced by finite impulse response (FIR) channels. In particular, the precoder allows a receiver to identify an input signal without knowing the channel characteristics at the expense of a minimum amount of bandwidth increase. A family of such precoders, which is linear (no modulo operations), channel independent, and modulation pattern preserving (except for some occasional 0 symbols), is presented. Also presented is a closed-form algorithm that can simultaneously identify the input signals and zero-forcing equalizers.Work supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant No. F49620-97-1-0253 and F49620-98-1-0352, the National Science Foundation CAREER Program under Grant MIP-9703377, and the University of Delaware Research Foundation.Work supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant No. F49620-97-1-0318, the Office of Naval Research (ONR) under Grant No. N00014-97-1-0475, and the National Science Foundation CAREER Program under Grant MIP-9703074.     

The asymptotic CRLB for the spectrum of ARMA processes

This paper addresses the issue of quantifying the frequency domain accuracy of autoregressive moving average (ARMA) spectral estimates as dictated by the Cramer-Rao lower bound (CRLB). Classical work in this area has led to expressions that are asymptotically exact as both data length and model order tend to infinity, although they are commonly used in finite model order and finite data length settings as approximations. More recent work has established quantifications that, for AR models, are exact for finite model order. By employing new analysis methods based on rational orthonormal parameterizations, together with the ideas of reproducing kernel Hilbert spaces, this paper develops quantifications that extend this previous work by being exact for finite model order in all of the AR, MA, and ARMA system cases. These quantifications, via their explicit dependence on poles and zeros of the underlying spectral factor, reveal certain fundamental aspects of the accuracy achievable by spectral estimates of ARMA processes.     

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.     

Enhanced autoregressive moving average spectral estimation appliedto the measurement of Doppler spectral width

The measurement of clear-air turbulence with a Doppler radar is investigated. An autoregressive moving average (ARMA) model is proposed to improve the Doppler spectral width estimates. An iterative algorithm that has its origin in system identification is used for the estimation of the ARMA parameters. By taking advantage of a priori knowledge of the correlation matrix, which arises in the derivation of the governing equations of the ARMA parameters, the ARMA spectral estimate can be improved. This improvement is shown in terms of bias and variance of the spectral width estimate     

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.     

Evaluation of Simple Algorithms for Spectral Parameter Analysis of the Electroencephalogram

Simple autoregressive moving-average (ARMA) and autoregressive (AR) algorithms were tested for use in spectral parameter analysis (SPA) of the background electroencephalogram (EEG). In studies on simulated EEG, both algorithms successfully extracted estimates of the spectral component parameters, and their performance was relatively independent of assumed model order. The ARMA algorithm was unbiased. The AR algorithm, though biased, was simpler and more precise and, thus, may be the most suitable for on-line use. The test results on simulated data were supported by the successful application of the algorithms to human EEG recorded during surgery.     

A new approach to spectral estimation: a tunable high-resolutionspectral estimator

Traditional maximum entropy spectral estimation determines a power spectrum from covariance estimates. Here, we present a new approach to spectral estimation, which is based on the use of filter banks as a means of obtaining spectral interpolation data. Such data replaces standard covariance estimates. A computational procedure for obtaining suitable pole-zero (ARMA) models from such data is presented. The choice of the zeros (MA-part) of the model is completely arbitrary. By suitable choices of filter bank poles and spectral zeros, the estimator can be tuned to exhibit high resolution in targeted regions of the spectrum     

ARMA Model Order Determination Using Edge Detection: A New Perspective

An edge detection-based approach to estimate the order of an autoregressive moving average (ARMA) model process is presented. The proposed method performs edge detection to select the ARMA order by extracting the outlines of a data covariance matrix derived from the observed data sequence. The method is based on the minimum eigenvalue (MEV) criterion developed by Liang et al., IEEE Trans. Signal Process., 41(10): 3003-3009, 1993. The algorithm transforms the MEV covariance matrix into an image by normalizing and resizing the original covariance matrix. Then, a search is performed to locate changes in the intensity function, i.e., pixels where the brightness changes abruptly. Examples are presented to demonstrate the performance of this algorithm.     

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.     

On the efficacy of linear system analysis of renal autoregulationin rats

To assess the linearity of the mechanisms subserving renal blood flow autoregulation, broadband arterial pressure fluctuations at three different power levels were induced experimentally and the resulting renal blood flow responses were recorded. Linear system analysis methods were applied in both the time and frequency domain. In the frequency domain, spectral estimates employing fast Fourier transform (FFT), autoregressive moving average (ARMA), and moving average (MA) methods were used. The residuals (i.e. model prediction errors) of the MA model were smaller than the ARMA, model for all levels of arterial pressure forcings. The observed low coherence values and significant model residuals in the 0.02-0.05-Hz frequency range suggest that the tubuloglomerular feedback (TGF) active in this frequency range is a nonlinear vascular control mechanism. In addition, experimental results suggest that the operation of the TGF mechanism is more evident at low/moderate pressure fluctuations and becomes overwhelmed when the arterial pressure forcing is too high     

Autocorrelation model-based identification method for ARMA systems in noise

A novel method for parameter estimation of minimum-phase autoregressive moving average (ARMA) systems in noise is presented. The ARMA parameters are estimated using a damped sinusoidal model representation of the autocorrelation function of the noise-free ARMA signal. The AR parameters are obtained directly from the estimates of the damped sinusoidal model parameters with guaranteed stability. The MA parameters are estimated using a correlation matching technique. Simulation results show that the proposed method can estimate the ARMA parameters with better accuracy as compared to other reported methods, in particular for low SNRs.     

Maximum entropy spectral analysis and ARMA processes (Corresp.)

The maximum entropy spectral analysis for discrete-time stationary processes was first proposed by J. P. Burg. He showed that if a finite number of covariance lag values of a stationary process are known, then an autoregressive (AR) process with the given autocorrelation values best fits the given constraints in the sense of maximizing thc differential entropy rate of the model. A more general type of prior knowledge of the process is considered, and it is shown that the maximum entropy method, subject to our constraints, is equivalent to fitting a mixed autoregressive moving average (ARMA) model.     

On the mechanism of transient instability of power systems

In recent studies, it has been verifiedheuristically andexperimentally (via simulations) that instability in power systems due to a fault occurs when one machine or a group of machines, called thecritical group, loses synchronism with the remaining machines. Using energy functions associated with a critical group (rather than system-wide functions), transient stability results which are less conservative than other existing results, have been obtained. The existence and identity of a critical group is ascertained in these studies byoff-line simulations.In this paper, we present results, for power systems with uniform damping, which establishanalytically theexistence and theidentity of the critical group of machines due to a given fault. We also present a result to determine estimates of the domain of attraction of asymptotically stable equilibrium points in power systems. The results presented herein can potentially be usedon-line to determine which machines belong to a critical group, and to use this information for corrective action (e.g.,shedding of the critical generators orfast valving for these generators).The applicability of the present results is demonstrated by means of a specific example (a 162-bus, 17-generator model of the power network of the State of Iowa).This research was suppored in part by the National Science Foundation under Grant Number ECS-84-19918.     

Adaptive parametric algorithms for processing coherentDoppler-lidar signal

The authors study the autoregressive and moving average (ARMA) filter for lidar signal processing. After a short presentation of the atmospheric laser Doppler instrument project (ALADIN), they introduce the objective of this paper, which is to extract the Doppler frequency and to retrieve the spectral width of a noised lidar signal. A general presentation of ARMA filters and parametric adaptive algorithms (PAAs) is provided. Then they present results about the choice of the model, the Doppler frequency estimate, and the spectral width estimate. Finally, they study the possible estimate of SNR, which is biased by the first estimates (Doppler frequency and spectral width)     

Direction finding using data-supported optimization

A novel data-supported optimization technique for maximum likelihood (ML) direction-of-arrival estimation is proposed. The essence of our approach is to optimize the likelihood function at certaindata-supported points obtained by a resampled root-MUSIC procedure. These points are shown to comprise a small but representative subset of all possible searching points and contain enough information for solving the ML problem.This work was supported in part by grants from the National Sciences and Engineering Research Council of Canada (NSERC), Ministry of Energy, Science and Technology (MEST) of Ontario, Communications and Information Technology Ontario (CITO), and by the Senior Individual Grant Program of the Swedish Foundation for Strategic Research.