Anthony J. Weiss

Direction finding in the presence of mutual coupling

An eigenstructure-based method for direction finding in the presence of sensor mutual coupling, gain, and phase uncertainties is presented. The method provides estimates of the directions-of-arrival (DOA) of all the radiating sources as well as calibration of the gain and phase of each sensor and the mutual coupling in the receiving array. The proposed algorithm is able to calibrate the array parameters without prior knowledge of the array manifold, using only signals of opportunity and avoiding the need for deploying auxiliary sources at known locations. The algorithm is described in detail, and its behavior is illustrated by numerical examples. >

Fundamental limitations in passive time delay estimation--Part I: Narrow-band systems

Time delay estimation of a noise-like random signal observed at two or more spatially separated receivers is a problem of considerable practical interest in passive radar/sonar applications. A new method is presented to analyze the mean-square error performance of delay estimation schemes based on a modified (improved) version of the Ziv-Zakai lower bound (ZZLB). This technique is shown to yield the tightest results on the attainable system performance for a wide range of signal-to-noise ratio (SNR) conditions. For delay estimation using narrow-band (ambiguity-prone) signals, the fundamental result of this study is illustrated in Fig. 3. The entire domain of SNR is divided into several disjoint segments indicating several distinct modes of operation. If the available SNR does not exceed SNR 1 , signal observations from the receiver outputs are completely dominated by noise thus essentially useless for the delay estimation. As a result, the attainable mean-square error \bar{\epsilon}^{2} is bounded only by the a priori parameter domain. If SNR 1 2 , the modified ZZLB coincides with the Barankin bound. In this regime differential delay observations are subject to ambiguities. If SNR > SNR 3 the modified ZZLB coincides with the Cramer-Rao lower bound indicating that the ambiguity in the differential delay estimation can essentially be resolved. The transition from the ambiguity-dominated mode of operation to the ambiguity-free mode of operation starts at SNR 2 and ends at SNR 3 . This is the threshold phenomenon in time delay estimation. The various deflection points SNR i and the various segments of the bound (Fig. 3) are given as functions of such important system parameters as time-bandwidth product (WT), signal bandwidth to center frequency ratio (W/ω 0 ) and the number of half wavelengths of the signal center frequency contained in the spacing between receivers. With this information the composite bound illustrated in Fig. 3 provides the most complete characterization of the attainable system performance under any prespecified SNR conditions.

Performance analysis of bearing-only target location algorithms

The performance of two well-known bearing-only location techniques, the maximum likelihood (ML) and the Stansfield estimators, is examined. Analytical expressions are obtained for the bias and the covariance matrix of the estimation error, which permit performance comparison for any case of interest. It is shown that the Stansfield algorithm provides biased estimates even for large numbers of measurements, in contrast with the ML method. The RMS error of the Stansfield technique is not necessarily larger than the RMS of the ML technique. However, it is shown that the ML technique is superior to the Stansfield method when the number of measurements is large enough. Simulation results verify the predicted theoretical performance. >

Direct position determination of narrowband radio frequency transmitters

The most common methods for location of communications or radar transmitters are based on measuring a specified parameter such as signal angle of arrival (AOA) or time of arrival (TOA). The measured parameters are then used to estimate the transmitter location. Since the AOA/TOA measurements are done at each base station separately, without using the constraint that all measurements must correspond to the same transmitter, they are suboptimal. We propose a technique that uses exactly the same data as the common methods, except that the estimation of location is based on exact maximum likelihood, and the location determination is direct. Although there are many stray parameters, including the attenuation coefficients and the signal waveform, the method requires only a two-dimensional search. Monte Carlo simulations indicate that the accuracy is equivalent to AOA, TOA, and their combination for high SNR, while for low SNR, the accuracy of the proposed method is superior.

Direction finding using spatial smoothing with interpolated arrays

The problem of estimating the directions of arrival (DOAs) of signals, some of which may be perfectly correlated, is considered. A computationally efficient estimation algorithm which combines the ideas of spatial smoothing and array interpolation is derived. In one of its forms the proposed algorithm uses the root-MUSIC (root multiple signal classification) technique to compute the DOA estimates, thus avoiding the search procedure associated with the conventional MUSIC algorithm. The proposed technique can be applied to arbitrary array geometries and a general signal covariance matrix. The performance of the algorithm was evaluated by extensive simulations, and compared with the Cramer-Rao lower bound for the DOA estimates. >

On the accuracy of a cellular location system based on RSS measurements

We discuss the performance of a cellular location system based on received signal strength (RSS) measurements. Each mobile station (MS) collects RSS measurements of the downlink control channels transmitted by the surrounding base stations. It is assumed that there is one-to-one mapping between the RSS and the MS location. Hence, these measurements can be used to obtain the MS location. We examine the accuracy of this method by deriving the Cramer-Rao bound, the concentration ellipse, and the circular error probability (CEP) of this method. In addition, we obtain an analytic expression that predicts the point at which accuracy deviates significantly from the bound (the threshold point). The accuracy of the method does not meet the FCC E911 requirement, but it is an attractive solution for less-demanding location-based services.

A general class of lower bounds in parameter estimation

A general class of Bayesian lower bounds on moments of the error in parameter estimation is formulated, and it is shown that the Cramer-Rao, the Bhattacharyya, the Bobrovsky-Zakai, and the Weiss-Weinstein lower bounds are special cases in the class. The bounds can be applied to the estimation of vector parameters and any given function of the parameters. The extension of these bounds to multiple parameter is discussed. >

Direction finding for wide-band signals using an interpolated array

The authors derive a new direction-finding algorithm for multiple wideband signals received by an arbitrary array and analyze its performance. Using an interpolation technique, they generate a set of virtual arrays, each for a different frequency band, having the same array manifold. The convergence matrices of these arrays are added to produce a composite covariance matrix. Direction-of-arrival (DOA) estimates are obtained by eigendecomposition of this composite covariance matrix using the narrowband MUSIC algorithm or its variants. Closed-form expressions for the asymptotic covariance matrix of the DOA estimation errors are derived using a perturbation analysis, evaluated for specific cases, and compared with the Cramer-Rao lower bound. Special attention is given to correlated and coherent signals. The formulas for the error covariance are quite general and can be modified to provide results for other wideband DOA estimation algorithms. >

Localization of Narrowband Radio Emitters Based on Doppler Frequency Shifts

Several techniques for emitter localization based on the Doppler effect have been described in the literature. One example is the differential Doppler (DD) method in which the signal of a stationary emitter is intercepted by at least two moving receivers. The frequency difference between the receivers is measured at several locations along their trajectories and the emitters position is then estimated based on these measurements. This two-step approach is suboptimal since each frequency difference measurement is performed independently, although all measurements correspond to a common emitter position. Instead, a single-step approach based on the maximum likelihood criterion is proposed here for both known and unknown waveforms. The position is determined directly from all the observations by a search in the position space. The method can only be used for narrowband signals, that is, under the assumption that the signal bandwidth must be small compared to the inverse of the propagation time between the receivers. Simulations show that the proposed method outperforms the DD method for weak signals while both methods converge to the Cramer-Rao bound for strong known signals. Finally, it is shown that in some cases of interest the proposed method inherently selects reliable observations while ignoring unreliable data.

On focusing matrices for wide-band array processing

A general class of transformation matrices for coherent signal-subspace processing is presented. These signal-subspace transformation (SST) matrices are shown to generate a sufficient statistic for maximum-likelihood bearing estimation. Two general forms for calculating SST matrices are presented, and the rotational signal-subspace (RSS) focusing matrices proposed by H. Hung and M. Kaveh (1988) are shown to be a special case of the SST matrices. An efficient procedure for computing a subset of the SST matrices, utilizing Householder transformations, is presented. The procedure reduces the computational load by a factor of 10, compared with that for the RSS matrices. The application of MUSIC to the coherently combined covariance matrix is also discussed, and Monte Carlo simulations comparing the performance of Householder SST matrices and RSS matrices are performed. >