Showing papers by "Mats Viberg published in 1995"

Computationally efficient angle estimation for signals with known waveforms

Abstract: This paper presents a large sample decoupled maximum likelihood (DEML) angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially colored noise. The DEML estimator decouples the multidimensional problem of the exact ML estimator to a set of 1-D problems and, hence, is computationally efficient. We shall derive the asymptotic statistical performance of the DEML estimator and compare the performance with its Cramer-Rao bound (CRB), i.e., the best possible performance for the class of asymptotically unbiased estimators. We will show that the DEML estimator is asymptotically statistically efficient for uncorrelated signals with known waveforms. We will also show that for moderately correlated signals with known waveforms, the DEML estimator is no longer a large sample maximum likelihood (ML) estimator, but the DEML estimator may still be used for angle estimation, and the performance degradation relative to the CRB is small. We shall show that the DEML estimator can also be used to estimate the arrival angles of desired signals with known waveforms in the presence of interfering or jamming signals by modeling the interfering or jamming signals as random processes with an unknown spatial covariance matrix. Finally, several numerical examples showing the performance of the DEML estimator are presented in this paper. >

Performance analysis of direction finding with large arrays and finite data

Abstract: This paper considers analysis of methods for estimating the parameters of narrow-band signals arriving at an array of sensors. This problem has important applications in, for instance, radar direction finding and underwater source localization. The so-called deterministic and stochastic maximum likelihood (ML) methods are the main focus of this paper. A performance analysis is carried out assuming a finite number of samples and that the array is composed of a sufficiently large number of sensors. Several thousands of antennas are not uncommon in, e.g., radar applications. Strong consistency of the parameter estimates is proved, and the asymptotic covariance matrix of the estimation error is derived. Unlike the previously studied large sample case, the present analysis shows that the accuracy is the same for the two ML methods. Furthermore, the asymptotic covariance matrix of the estimation error coincides with the deterministic Cramer-Rao bound. Under a certain assumption, the ML methods can be implemented by means of conventional beamforming for a large enough number of sensors. We also include a simple simulation study, which indicates that both ML methods provide efficient estimates for very moderate array sizes, whereas the beamforming method requires a somewhat larger array aperture to overcome the inherent bias and resolution problem. >

Array processing in correlated noise fields based on instrumental variables and subspace fitting

Abstract: Accurate signal parameter estimation from sensor array data is a problem which has received much attention in the last decade. A number of parametric estimation techniques have been proposed in the literature. In general, these methods require knowledge of the sensor-to-sensor correlation of the noise, which constitutes a significant drawback. This difficulty can be overcome only by introducing alternative assumptions that enable separating the signals from the noise. In some applications, the raw sensor outputs can be preprocessed so that the emitter signals are temporally correlated with correlation length longer than that of the noise. An instrumental variable (IV) approach can then be used for estimating the signal parameters without knowledge of the spatial color of the noise. A computationally simple IV approach has recently been proposed by the authors. Herein, a refined technique that can give significantly better performance is derived. A statistical analysis of the parameter estimates is performed, enabling optimal selection of certain user-specified quantities. A lower bound on the attainable error variance is also presented. The proposed optimal IV method is shown to attain the bound if the signals have a quasideterministic character. >

Sensor array signal processing : two decades later

Abstract: The problem of estimating the parameters of superimposed signals using an array of sensors has received considerable research interest in the last two decades. Many theoretical studies have been carried out and deep insight has been gained. Traditional applications of array processing include source localization and interference suppression in radar and sonar. The proliferation of estimation algorithms has, however, recently spurred an increasing interest in new applications, such as spatial diversity in personal communications, medical applications and line detection in images. The goal of this manuscript is to provide a brief review of the recent research activities in sensor array signal processing. The focus is on estimation algorithms. These are classified into spectral-based and parametric methods respectively, depending on the way the estimates are computed. Some of the most well-known algorithms are presented, and their relative merits and shortcomings are described. References to more detailed analyses and special research topics are also given. Some applications of sensor array processing methods are also commented upon, and potential new ones are mentioned. The results of real data experiments are also presented, demonstrating the usefulness of recently proposed estimation techniques .

Optimal IV-SSF approach to array signal processing in colored noise fields

Abstract: The paper describes and analyses, in a unifying manner, the spatial and temporal IV-SSF (instrumental variable-signal subspace fitting) approaches recently proposed for array signal processing in colored noise fields. We derive a general, optimally-weighted, IV-SSF direction estimator and show that this estimator encompasses the UNCLE estimator of Wong and Wu (see IEEE Trans.SP, vol.42, Sept. 1994), which is a spatial IV-SSF method; and the temporal IV-SSF estimator of Viberg, Stoica and Ottersten (see IEEE Trans.SP, May 1995). The latter two estimators have seemingly different forms, so their asymptotic equivalence shown in this paper comes as a surprising unifying result.

On maximum-likelihood estimation of difference equation parameters

Abstract: The article is prompted by a paper written by Liang, Wilkes and Cadzow (see ibid., vol.41, p. 3003-3009, 1993) which discussed the maximum likelihood (ML) estimation of difference equation parameters in a flawed manner. The correct ML parameter estimate is derived herein by means of a high-level argument based on the invariance principle as well as by a direct calculation. Contrary to what is suggested in the aforementioned paper, all ML-based order estimation procedures (such as AIC or GAIC rules) yield results that do not depend on the normalizing constraint imposed on the parameter vector. >