7,313 research outputs found
PUMA criterion = MODE criterion
We show that the recently proposed (enhanced) PUMA estimator for array
processing minimizes the same criterion function as the well-established MODE
estimator. (PUMA = principal-singular-vector utilization for modal analysis,
MODE = method of direction estimation.
Space Time MUSIC: Consistent Signal Subspace Estimation for Wide-band Sensor Arrays
Wide-band Direction of Arrival (DOA) estimation with sensor arrays is an
essential task in sonar, radar, acoustics, biomedical and multimedia
applications. Many state of the art wide-band DOA estimators coherently process
frequency binned array outputs by approximate Maximum Likelihood, Weighted
Subspace Fitting or focusing techniques. This paper shows that bin signals
obtained by filter-bank approaches do not obey the finite rank narrow-band
array model, because spectral leakage and the change of the array response with
frequency within the bin create \emph{ghost sources} dependent on the
particular realization of the source process. Therefore, existing DOA
estimators based on binning cannot claim consistency even with the perfect
knowledge of the array response. In this work, a more realistic array model
with a finite length of the sensor impulse responses is assumed, which still
has finite rank under a space-time formulation. It is shown that signal
subspaces at arbitrary frequencies can be consistently recovered under mild
conditions by applying MUSIC-type (ST-MUSIC) estimators to the dominant
eigenvectors of the wide-band space-time sensor cross-correlation matrix. A
novel Maximum Likelihood based ST-MUSIC subspace estimate is developed in order
to recover consistency. The number of sources active at each frequency are
estimated by Information Theoretic Criteria. The sample ST-MUSIC subspaces can
be fed to any subspace fitting DOA estimator at single or multiple frequencies.
Simulations confirm that the new technique clearly outperforms binning
approaches at sufficiently high signal to noise ratio, when model mismatches
exceed the noise floor.Comment: 15 pages, 10 figures. Accepted in a revised form by the IEEE Trans.
on Signal Processing on 12 February 1918. @IEEE201
Partial Relaxation Approach: An Eigenvalue-Based DOA Estimator Framework
In this paper, the partial relaxation approach is introduced and applied to
DOA estimation using spectral search. Unlike existing methods like Capon or
MUSIC which can be considered as single source approximations of multi-source
estimation criteria, the proposed approach accounts for the existence of
multiple sources. At each considered direction, the manifold structure of the
remaining interfering signals impinging on the sensor array is relaxed, which
results in closed form estimates for the interference parameters. The
conventional multidimensional optimization problem reduces, thanks to this
relaxation, to a simple spectral search. Following this principle, we propose
estimators based on the Deterministic Maximum Likelihood, Weighted Subspace
Fitting and covariance fitting methods. To calculate the pseudo-spectra
efficiently, an iterative rooting scheme based on the rational function
approximation is applied to the partial relaxation methods. Simulation results
show that the performance of the proposed estimators is superior to the
conventional methods especially in the case of low Signal-to-Noise-Ratio and
low number of snapshots, irrespectively of any specific structure of the sensor
array while maintaining a comparable computational cost as MUSIC.Comment: This work has been submitted to IEEE for possible publication.
Copyright may be transferred without notice, after which this version may no
longer be accessibl
Multisource Self-calibration for Sensor Arrays
Calibration of a sensor array is more involved if the antennas have direction
dependent gains and multiple calibrator sources are simultaneously present. We
study this case for a sensor array with arbitrary geometry but identical
elements, i.e. elements with the same direction dependent gain pattern. A
weighted alternating least squares (WALS) algorithm is derived that iteratively
solves for the direction independent complex gains of the array elements, their
noise powers and their gains in the direction of the calibrator sources. An
extension of the problem is the case where the apparent calibrator source
locations are unknown, e.g., due to refractive propagation paths. For this
case, the WALS method is supplemented with weighted subspace fitting (WSF)
direction finding techniques. Using Monte Carlo simulations we demonstrate that
both methods are asymptotically statistically efficient and converge within two
iterations even in cases of low SNR.Comment: 11 pages, 8 figure
Sparsity-Cognizant Total Least-Squares for Perturbed Compressive Sampling
Solving linear regression problems based on the total least-squares (TLS)
criterion has well-documented merits in various applications, where
perturbations appear both in the data vector as well as in the regression
matrix. However, existing TLS approaches do not account for sparsity possibly
present in the unknown vector of regression coefficients. On the other hand,
sparsity is the key attribute exploited by modern compressive sampling and
variable selection approaches to linear regression, which include noise in the
data, but do not account for perturbations in the regression matrix. The
present paper fills this gap by formulating and solving TLS optimization
problems under sparsity constraints. Near-optimum and reduced-complexity
suboptimum sparse (S-) TLS algorithms are developed to address the perturbed
compressive sampling (and the related dictionary learning) challenge, when
there is a mismatch between the true and adopted bases over which the unknown
vector is sparse. The novel S-TLS schemes also allow for perturbations in the
regression matrix of the least-absolute selection and shrinkage selection
operator (Lasso), and endow TLS approaches with ability to cope with sparse,
under-determined "errors-in-variables" models. Interesting generalizations can
further exploit prior knowledge on the perturbations to obtain novel weighted
and structured S-TLS solvers. Analysis and simulations demonstrate the
practical impact of S-TLS in calibrating the mismatch effects of contemporary
grid-based approaches to cognitive radio sensing, and robust
direction-of-arrival estimation using antenna arrays.Comment: 30 pages, 10 figures, submitted to IEEE Transactions on Signal
Processin
Robust computation of linear models by convex relaxation
Consider a dataset of vector-valued observations that consists of noisy
inliers, which are explained well by a low-dimensional subspace, along with
some number of outliers. This work describes a convex optimization problem,
called REAPER, that can reliably fit a low-dimensional model to this type of
data. This approach parameterizes linear subspaces using orthogonal projectors,
and it uses a relaxation of the set of orthogonal projectors to reach the
convex formulation. The paper provides an efficient algorithm for solving the
REAPER problem, and it documents numerical experiments which confirm that
REAPER can dependably find linear structure in synthetic and natural data. In
addition, when the inliers lie near a low-dimensional subspace, there is a
rigorous theory that describes when REAPER can approximate this subspace.Comment: Formerly titled "Robust computation of linear models, or How to find
a needle in a haystack
Long-range spin-pairing order and spin defects in quantum spin-1/2 ladders
For w-legged antiferromagnetic spin-1/2 Heisenberg ladders, a long-range
spin-pairing order can be identified which enables the separation of the space
spanned by finite-range (covalent) valence-bond configurations into w+1
subspaces. Since every subspace has an equivalent counter subspace connected by
translational symmetry, twofold degeneracy, breaking traslational symmetry is
found except for the subspace where the ground state of w=even belongs to. In
terms of energy ordering, (non)degeneracy and the discontinuities introduced in
the long-range spin-pairing order by topological spin defects, the differences
between even and odd ladders are explained in a general and systematic way.Comment: 16 pages, 7 figures, 2 tables. To be publish in The European Physical
J.
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