In this paper, an adaptive algorithm for direction-finding of correlated sources is presented. The algorithm is low in computational complexity and it does not require determination of the effective rank of the array ...
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In this paper, an adaptive algorithm for direction-finding of correlated sources is presented. The algorithm is low in computational complexity and it does not require determination of the effective rank of the array correlation matrix. The algorithm employs a gradient technique to determine the minimum eigenvector of the correlation matrix and an orthogonalization technique to determine the second minimum eigenvector. The two noise eigenvectors are then used to compute the spatial spectra. The angle of arrivals can then be found by superimposing the two spectra. To verify further the true arrivals, additional spatial spectral can be computed using a combination of the two noise eigenvectors. Numerical results show that the proposed algorithms are effective in resolving correlated sources.
Cumulants, and their associated Fourier transforms, known as polyspectra, are very useful in situations where one or more of the preceding phenomena - non-Gaussianity, nonminimum phase, colored Gaussian noise, and non...
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Cumulants, and their associated Fourier transforms, known as polyspectra, are very useful in situations where one or more of the preceding phenomena - non-Gaussianity, nonminimum phase, colored Gaussian noise, and nonlinearities - are present. Because second-order-based techniques have not led to very useful results in the face of these phenomena, it is no exaggeration to believe that it should be possible to reexamine every application and/or method that has ever made use of second-order statistics, using higher-order statistics, to see if better results can be obtained. The purpose of this paper is to give a brief introduction to cumulants and polyspectra and to give a brief overview of some of their applications.
We develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signalprocessing applications employing the 'signal subspace' approach. The noise subspace is estimated...
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We develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signalprocessing applications employing the 'signal subspace' approach. The noise subspace is estimated using a rank-revealing QR factorization instead of the more expensive singular value or eigenvalue decompositions. Using incremental condition estimation to monitor the smallest singular values of triangular matrices, we can update the rank-revealing triangular factorization inexpensively when new rows are added and old rows are deleted. Experiments demonstrate that the new approach usually requires O(n2) work to update an n × n matrix, and accurately tracks the noise subspace.
We develop an algorithm for adaptively estimating the noise subspace of a data matrix, as is required in signalprocessing applications employing the 'signal subspace' approach. The noise subspace is estimated...
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This paper presents a new systolic array implementation of the Kalman filter that is not excessive in either hardware or computation steps. For a dynamic system with N states and M observation components, the array us...
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This paper presents a new systolic array implementation of the Kalman filter that is not excessive in either hardware or computation steps. For a dynamic system with N states and M observation components, the array uses N(N+1) processors and about 4N+6M computation steps. In some applications, it is also required that the processing system continue to function even after some of the components of the system fail. The Kalman filter systolic array is extended to one that is tolerant of faults in the processing elements of the array by using techniques of algorithm-based fault tolerance. Overhead for fault tolerance is about 47% additional hardware and 17% additional computational steps in the example of radar tracking.
A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in num...
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A new parallel Jacobi-like algorithm for computing the eigenvalues of a general complex matrix is presented. The asymptotic convergence rate of this algorithm is provably quadratic and this is also demonstrated in numerical experiments. The algorithm promises to be suitable for real-time signalprocessing applications. In particular, the algorithm can be implemented using n2/4 processors, taking O (n log2 n) time for random matrices.
Effective signal detection and feature extraction in noisy environments generally depend on exploiting some knowledge of the signal. When the signal is exactly known, the matched filter is the optimum signal processin...
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Current bilinear time-frequency representations apply a fixed kernel to smooth the Wigner distribution. However, the choice of a fixed kernel limits the class of signals that can be analyzed effectively. This paper pr...
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Current bilinear time-frequency representations apply a fixed kernel to smooth the Wigner distribution. However, the choice of a fixed kernel limits the class of signals that can be analyzed effectively. This paper presents optimality criteria for the design of signal-dependent kernels that suppress cross-components while passing as much auto-component energy as possible, irrespective of the form of the signal. A fast algorithm for the optimal kernel solution makes the procedure competitive computationally with fixed kernel methods. Examples demonstrate the superior performance of the optimal kernel for a frequency modulated signal.
Autocorrelation and spectra of linear random processes can be can be expressed in terms of cumulants and polyspectra, respectively. The insensitivity of the latter to additive Gaussian noise of unknown covariance, is ...
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Autocorrelation and spectra of linear random processes can be can be expressed in terms of cumulants and polyspectra, respectively. The insensitivity of the latter to additive Gaussian noise of unknown covariance, is exploited in this paper to develop spectral estimators of deterministic and linear non-Gaussian signals using polyspectra. In the time-domain, windowed projections of third-order cumulants are shown to yield consistent estimators of the autocorrelation sequence. Both batch and recursive algorithms are derived. In the frequency-domain, a Fourier-slice solution and a least-squares approach are described for performing spectral analysis through windowed bi-periodograms. Asymptotic variance expressions of the time- and frequency-domain estimators are also presented. Two-dimensional extensions are indicated, and potential applications are discussed. Simulations are provided to illustrate the performance of the proposed algorithms and compare them with conventional approaches.
This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hilbert space of the group states. In particular, the paper con...
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This paper addresses the problem of designing signals for general group representations subject to constraints which are formulated as convex sets in the Hilbert space of the group states. In particular, the paper considers irreducible representations in an infinite dimensional Hilbert space and derives an iterative procedure for proceeding from an arbitrary element of the Hilbert space to a state of the group subject to a priori imposed constraints with closed convex range. As examples, the paper focusses on narrowband and wideband radar ambiguity synthesis.
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