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.
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.
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.
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.
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.
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.
Focussing techniques have proven efficient in direction-of-arrival estimation of broadband signals. However, when used alone at high frequency operation, these techniques cannot accurately locate the sources, due to t...
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Focussing techniques have proven efficient in direction-of-arrival estimation of broadband signals. However, when used alone at high frequency operation, these techniques cannot accurately locate the sources, due to the numerous spurious peaks in the spectrum. Since the spurious peaks depend on the array manifold, their location varies from one focussing frequency to another. Improved jammer localization can, therefore, be achieved by focussing at different frequencies and then averaging the corresponding MUSIC spectra. The averaging smooths out the undesired peaks while boosting the common spectral peaks, allowing correct detection and location of the waveforms impinging on the array.
The scale dependent wavelet transform can be augmented by a rotation dependent version as well as other generalizations. Tomographic analysis and line segment transforms are special cases of rotation dependent wavelet...
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The scale dependent wavelet transform can be augmented by a rotation dependent version as well as other generalizations. Tomographic analysis and line segment transforms are special cases of rotation dependent wavelet analysis. Other cases suggested by biological analogy9 are a rotation dependent edge segment transform (using edge segments rather than line segments) and a binocular rotation dependent wavelet transform that introduces depth information into the reconstructed image. Applications to robot vision and synthetic aperture radar appear particularly promising.
We develop redundant CORDIC scheme where the scale factor is forced to be constant while computing angles for 2 × 1 plane rotations. Based on the scheme, we present a fixed-point implementation of matrix triangul...
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We develop redundant CORDIC scheme where the scale factor is forced to be constant while computing angles for 2 × 1 plane rotations. Based on the scheme, we present a fixed-point implementation of matrix triangularization by Luk's parallel algorithm, with the following additional features: (1) the final scaling operation is done by shifting, (2) the number of iterations in CORDIC rotation unit is reduced by about 25% by expressing the direction of the rotation in radix-2 and radix-4, and (3) the conventional number representation of rotated output is obtained on-the-fly, not from a carry-propagate adder. The number of hardware modules and the speed are evaluated and compared with the previous CORDIC schemes.
We consider the problem of detecting a known Gaussian random transient in the presence of a strong, known, random, Gaussian, narrowband interference. This can be regarded as a special case of the classical problem of ...
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