Chair: Allan Steinhardt, Massachusetts Institute of Technology, Lincoln Laboratory (USA)
Edward J. Baranoski, MIT Lincoln Laboratory (USA)
This paper examines an alternative multi-dimensional adaptive array processing architecture which provides a unique highly- parallelizable algorithm suitable for distributed processing. The principle is to perform interference cancellation on each element using a different sparse sampling of the remaining elements as auxiliary inputs. By doing so, special correlations in the data can be exploited to significantly reduce the degrees of freedom required in each adaptive process. This reduces both the computation count and the number of samples required for adaptivity. An example space-time adaptive nulling application for an airborne radar shows near optimal performance with a factor of four computational savings over equivalent space-time techniques.
Louis L. Scharf, University of Colorado (USA)
John K. Thomas, University of Colorado (USA)
How does one adaptively split a measurement subspace into signal and orthogonal subspaces of reduced rank so that detectors, estimators, and quantizers may be adaptively designed from experimental data? We provide some answers to this question by decomposing experimental correlations into their Wishart distributed Schur complements and showing how these distributions may be used to identify subspaces.
Keith A. Burgess, University of Wisconsin-Madison (USA)
Barry D. Van Veen, University of Wisconsin-Madison (USA)
The robustness of a subspace generalized likelihood ratio test (GLRT) detector to signal mismatch is addressed for data conforming to the generalized multivariate analysis of variance model. This model assumes a deterministic signal of known form in the presence of unknown, colored, Gaussian noise. The subspace GLRT compresses data into a lower-dimensional subspace prior to detection. It is shown in this paper that a subspace GLRT reduces the performance loss due to mismatch relative to that of a non-subspace detector.
Weige Chen, University of Virginia (USA)
Guotong Zhou, University of Virginia (USA)
Georgios B. Giannakis, University of Virginia (USA)
We are interested in estimating the Doppler shift occurred in weather radar returns, which yields precipitation velocity information. Conventional techniques including the pulse pair processor rely heavily on the assumption that the additive noise is white and hence their performance degrades when the noise color is unknown. Because the data length for a given range gate is usually small, we employ the high resolution MUSIC algorithm to estimate the Doppler shift. The challenge lies not only in proving that MUSIC is applicable to weather radar signals which are affected by multiplicative noise, but also in showing that MUSIC is robust when the additive noise is colored. The resulting algorithm can also be used to infer wind speed from a small number of lidar observations where the velocity is approximately constant. Assuming linear shear over a longer range, we employ the ambiguity function to estimate the acceleration and instantaneous wind velocity. Real weather radar and lidar data as well as simulated examples are provided to illustrate the performance of the algorithms.
Jean-Pierre Delmas, Institut National des Telecommunications (FRANCE)
In this paper, we address adaptive estimation methods of eigenspaces of covariance matrices. We are interested in methods based on several coupled maximizations or minimizations of Rayleigh ratios where the constraints are replaced by appropriate parameterizations (Givens and mixed Givens/Householder). We prove the convergence of these algorithms with the help of the associated Ordinary Differential Equation, and we propose an evaluation of the performances by computing the variances of the estimated eigenvectors for fixed gain factors. We show that these variances are very sensitive to the difference between two consecutive eigenvalues. Moreover, they also depend on whether the successive analyzed vector signals are correlated or not, and thus greatly depend on the origin of the covariance matrices of interest (spatial, temporal, spatio-temporal). Finally we show that the performances can be improved when the centro-symmetric property of some of those covariance matrices is taken into account.
Olivier Tremois, IRISA/CNRS (FRANCE)
J.P. LeCadre, IRISA/CNRS (FRANCE)
This paper deals with the analysis of performance of source trajectory estimation by using the measurements provided by multiple towed arrays (or platforms). In numerous practical situations, the maneuvering ability of the receiver (e.g. a ship towing linear arrays) is limited leading thus to consider that the observer motion is rectilinear and uniform. Even if this hypothesis appears quite limitative, practical and tactical considerations fully justify its interest. This leads to consider multiple (platform) target motion analysis (denoted MTMA) and to analyse the performance of such trajectory estimation methods. Analytic formulations of the variance of the source state vector components are obtained in terms of physical parameters (source distance, source velocity, inter-arrays distance). It is worth noting that a rather similar problem has been previously considered. The main difference is that the performance analysis is extended to long integration time MTMA which mainly constitutes the original contribution of this article.
Filiep Vanpoucke, Katholieke Universiteit Leuven (BELGIUM)
Marc Moonen, Katholieke Universiteit Leuven (BELGIUM)
We introduce a factored spherical SVD updating algorithm which can be used for subspace tracking. It is a non-iterative algorithm for approximate SVD updating. The orthogonal matrix tracking the signal subspace is parameterized as a sequence of Givens rotations. This factorization has two important advantages. On the algorithmic level it cures the error accumulation problem inherent in the algorithm. The subspace matrix is now confined to the manifold of orthogonal matrices at all time. On the architectural level the factored algorithm is more amenable to parallel - even systolic - implementation. Moreover, the SFG contains only rotation nodes. Therefore, an ideal processor for a real-time parallel ASIC architecture is a CORDIC processor.
L. Frenkel, Tel-Aviv University (ISRAEL)
M. Feder, Tel-Aviv University (ISRAEL)
We investigate the application of EM algorithm to the classical problem of multiple target tracking (MTT) for a known number of targets. Conventional algorithms, have a computational complexity that depends exponentially on the targets' number, and usually divide the problem into a localization stage and a tracking stage. The new algorithms achieve a linear dependency, and integrate those two stages. Three major optimization criteria are proposed, using deterministic and stochastic dynamic models for the targets.
Victor I. Turchin, Russian Academy of Science (RUSSIA)
Alex B. Gershman, EPFL (SWITZERLAND)
The application of sensor array processing methods for estimation and localization of wavefield sources is well known. In this paper we extend the sensor array processing approach to estimating the parameters of the fields of a nonwave nature (the so-called nonwave fields). Considering the static and diffusion fields as typical examples of nonwave field, we derive the Cramer-Rao bounds of source parameter estimation errors. These theoretical results are completed by the experimental results of localization of diffusion sources in distilled water by a chemical sensor array, showing potentially high performance of sensor array approach. A modified version of the well-known CLEAN deconvolution algorithm has been used for experimental data processing. The nonwave field sensor array processing can find various applications such as localization of pollution sources and another types of admixtures, detection of metallic masses and wandering currents, etc.
Hong Liu, Northeastern University (USA)
Hanoch Lev-Ari, Northeastern University (USA)
An analytical framework for the implementation of optimal filters in the multiresolution (i.e., subband) domain is presented. In particular, we concentrate on filter bank based on the notions of wavelets and wave- packets. We show how the notion of sparse estimation can lead to significant reduction in computational cost, with only a minor degradation in performance. The combination of a wavelet-based filter bank with a sparse estimation scheme results in a configuration with five design parameters: (i) resolution level, (ii) degree of subband channel overlap, (iii) subband utilization ratio, (iv) estimation sparsity, and (v) filter order. We demonstrate the effect of each one of these design parameters on the over-all cost-performance trade-off.