Array Processing: Direction Finding

Multiple Invariance Spatio-Temporal Spectral Estimation

Authors:

John W.C. Robinson, Defense Research Establishment, S-172 90 Stockholm, Sweden (Sweden)

Page (NA) Paper number 1532

Abstract:

Simultaneous frequency and direction-of-arrival (DOA) estimation can be formulated as a 2D processing problem or as a set of coupled 1D problems. In narrow-band cases the 2D approach can be used to remove the need for frequency-DOA pairing procedures but the price can be a considerably higher computational cost. Therefore, the 1D approach a viable alternative in many applications. This paper presents an ESPRIT based technique using the multiple 1D approach. It requires few sensors, guarantees identifiability of the parameters and admits several sources on the same frequency or DOA.

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Analysis of Forward-Only and Forward-Backward Sample Covariances

Authors:

Magnus Jansson, Dept. of Signals, Sensors and Systems, Royal Inst. of Technology (KTH), Sweden (Sweden)
Petre Stoica, Systems and Control group, Uppsala University, Sweden (Sweden)

Page (NA) Paper number 1182

Abstract:

In some applications the covariance matrix of the observations is not only symmetric with respect to its main diagonal but also with respect to the anti-diagonal. The standard forward-only sample covariance estimate does not impose this extra symmetry. In such cases one often uses the so-called forward-backward sample covariance estimate. In this paper, a direct comparative study of the relative accuracy of the two sample estimates is performed. An explicit expression for the difference between the estimation error covariance matrices of the two sample estimates is given. The presented results are also useful in the analysis of estimators based on either of the two sample covariances. As an example, spatial power estimation by means of the Capon method is considered. It is shown that Capon based on the forward-only sample covariance (F-Capon) underestimates the power spectrum, and also that the bias for Capon based on the forward-backward sample covariance is half that of F-Capon.

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Rectification of Cross Spectral Matrices for Arrays of Arbitrary Geometry

Authors:

Philippe Forster,
Thierry Asté,

Page (NA) Paper number 1311

Abstract:

In high resolution methods applied to Uniform Linear Arrays (ULA), the pre-processing that consists in forcing the estimated Cross Spectral Matrix (CSM) to be Toeplitz by averaging its elements along its diagonals is known to increase drastically the resolving power: that is why it is always done in practise. However, this approach is limited to linear arrays because of the required Toeplitz structure for the CSM. This paper generalizes this technique to arrays of arbitrary geometry: the developed method is referred to as rectification. It proceeds by searching first for a vector subspace of hermitian matrices that contains the manifold generated by the CSM's when the Angle Of Arrival varies: this preliminary step is performed only one time for a given array geometry. Next, rectification of estimated CSM's is achieved by projecting them onto this subspace, resulting in denoising and increased resolving power of source localization methods at a very low computational cost. As a by product, the storage requirements for the CSM's are greatly reduced.

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MODE With Extra-Roots (MODEX): a New DOA Estimation Algorithm With An Improved Threshold Performance

Authors:

Alex B. Gershman, Signal Theory Group, Ruhr University, Bochum, Germany (Germany)
Petre Stoica, Systems and Control Group, Uppsala University, Uppsala, Sweden (Sweden)

Page (NA) Paper number 1060

Abstract:

We propose a new MODE-based direction of arrival (DOA) estimation algorithm with an improved SNR threshold as compared to the conventional MODE technique. Our algorithm preserves all good properties of MODE, such as asymptotic efficiency, excellent performance in scenarios with coherent sources, as well as a reasonable computational cost. Similarly to root-MODE, the proposed method does not require any global multidimensional optimization since it is based on a combination of polynomial rooting and a simple combinatorial search. Our technique is referred to as MODEX (MODE with EXtra roots) because it makes use of a certain polynomial with a larger degree than that of the conventional MODE-polynomial. The source DOA's are estimated via checking a certain (enlarged) number of candidate DOA's using either the stochastic or the deterministic Maximum Likelihood (ML) function. To reduce the computational cost of MODEX, a priori information about source localization sectors can be exploited.

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A New Unitary ESPRIT-Based Technique for Direction Finding

Authors:

Martin Haardt, Siemens AG, OEN MN P 36, Munich, Germany (Germany)
Alex B. Gershman, Signal Theory Group, Ruhr University, Bochum, Germany (Germany)

Page (NA) Paper number 1152

Abstract:

A new pseudo-noise resampling technique is proposed to mitigate the effect of outliers in Unitary ESPRIT. This scheme improves the performance of Unitary ESPRIT in unreliable situations, where the so-called reliability test has a failure. For this purpose, we exploit a pseudo-noise resampling of a failed Unitary ESPRIT estimator with a censored selection of ``successful'' resamplings recovering the non-failed outputs of the reliability test.

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Derivative DFT Beamspace ESPRIT: A High Performance Closed-Form 2-D Arrival Angle Estimation Algorithm

Authors:

Cherian P Mathews, Department of Electrical and Computer Engineering, University of West Florida, Pensacola, FL 32514, USA (USA)

Page (NA) Paper number 1997

Abstract:

This paper presents Derivative DFT Beamspace ESPRIT, a new closed-form algorithm for direction-of-arrival (DOA) estimation with uniform linear arrays or uniform rectangular arrays. The algorithm uses a novel virtual derivative DFT beamforming procedure to improve upon the performance of the recently developed DFT Beamspace ESPRIT algorithm. This beamforming procedure yields an additional invariance relationship which the algorithm exploits to obtain higher estimation accuracy (the algorithm is shown to outperform both DFT Beamspace ESPRIT and Unitary ESPRIT). Further, Derivative DFT Beamspace ESPRIT possesses all the attractive features (such as low computational complexity, and the ability to provide automatically paired source azimuth and elevation angle estimates) of the two aforementioned algorithms.

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Identifiability and Manifold Ambiguity in DOA Estimation for Nonuniform Linear Antenna Arrays

Authors:

Yuri I Abramovich, CRC for Sensor Signal & Information Processing (CSSIP), Adelaide, Australia (Australia)
Nicholas K Spencer, CRC for Sensor Signal & Information Processing (CSSIP), Adelaide, Australia (Australia)
Alexei Y Gorokhov, L2S, Ecole Superieure d'Electricite, Gif-sur-Yvette, France (France)

Page (NA) Paper number 1407

Abstract:

This paper considers the direction-of-arrival (DOA) estimation identifiability problem for uncorrelated Gaussian sources and nonuniform antenna arrays. It is now known that sparse arrays always suffer from "manifold ambiguity", which arises due to linear dependence amongst the columns of the array manifold matrix (the "steering vectors"). While the standard subspace DOA estimation algorithms such as MUSIC fail to provide proper unambiguous estimates under these conditions, we demonstrate that in most cases involving uncorrelated Gaussian sources, manifold ambiguity does not necessarily imply nonidentifiability. An effective manifold ambiguity resolution algorithm is introduced. A "superior" number of uncorrelated Gaussian sources (more than sensors) may also be unambiguously localised by sparse arrays under specified identifiability conditions. While manifold ambiguity does not apply to superior scenarios, a similar "co-array manifold ambiguity" phenomenon may compromise DOA estimation. The proposed algorithm can also resolve such ambiguity in all identifiable cases.

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Beam-Augmented Space-Time Adaptive Processing

Authors:

Yaron Seliktar,
Douglas B Williams,
E. Jeff Holder,

Page (NA) Paper number 1581

Abstract:

Combined monostatic clutter (MSC) and terrain scattered interference (TSI) pose a difficult challenge for adaptive radar processing. Mitigation techniques exist for each interference alone but are insufficient for their combined effects. Current approaches separate the problem into two stages where TSI is suppressed first and then MSC. The problem with this cascade approach is that during the initial TSI suppression stage, the MSC becomes corrupted. In this paper an innovative technique is introduced for achieving a significant improvement in cancellation performance for both MSC and TSI, even when the jammer appears in the mainbeam. The majority of the interference rejection, both TSI and MSC, is accomplished with an MSC filter, with further TSI suppression accomplished via an additional tapped reference beam. Simultaneous optimization of the MSC filter weights and reference beam weights yields the desired processor. Performance results using Mountaintop data demonstrate the superiority of the proposed processor over existing processors.

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