152 research outputs found
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
Fundamental Imaging Limits of Radio Telescope Arrays
The fidelity of radio astronomical images is generally assessed by practical
experience, i.e. using rules of thumb, although some aspects and cases have
been treated rigorously. In this paper we present a mathematical framework
capable of describing the fundamental limits of radio astronomical imaging
problems. Although the data model assumes a single snapshot observation, i.e.
variations in time and frequency are not considered, this framework is
sufficiently general to allow extension to synthesis observations. Using tools
from statistical signal processing and linear algebra, we discuss the
tractability of the imaging and deconvolution problem, the redistribution of
noise in the map by the imaging and deconvolution process, the covariance of
the image values due to propagation of calibration errors and thermal noise and
the upper limit on the number of sources tractable by self calibration. The
combination of covariance of the image values and the number of tractable
sources determines the effective noise floor achievable in the imaging process.
The effective noise provides a better figure of merit than dynamic range since
it includes the spatial variations of the noise. Our results provide handles
for improving the imaging performance by design of the array.Comment: 12 pages, 8 figure
Radio Astronomical Image Formation using Constrained Least Squares and Krylov Subspaces
Image formation for radio astronomy can be defined as estimating the spatial
power distribution of celestial sources over the sky, given an array of
antennas. One of the challenges with image formation is that the problem
becomes ill-posed as the number of pixels becomes large. The introduction of
constraints that incorporate a-priori knowledge is crucial. In this paper we
show that in addition to non-negativity, the magnitude of each pixel in an
image is also bounded from above. Indeed, the classical "dirty image" is an
upper bound, but a much tighter upper bound can be formed from the data using
array processing techniques. This formulates image formation as a least squares
optimization problem with inequality constraints. We propose to solve this
constrained least squares problem using active set techniques, and the steps
needed to implement it are described. It is shown that the least squares part
of the problem can be efficiently implemented with Krylov subspace based
techniques, where the structure of the problem allows massive parallelism and
reduced storage needs. The performance of the algorithm is evaluated using
simulations
Position and Orientation Estimation of a Rigid Body: Rigid Body Localization
Rigid body localization refers to a problem of estimating the position of a
rigid body along with its orientation using anchors. We consider a setup in
which a few sensors are mounted on a rigid body. The absolute position of the
rigid body is not known, but, the relative position of the sensors or the
topology of the sensors on the rigid body is known. We express the absolute
position of the sensors as an affine function of the Stiefel manifold and
propose a simple least-squares (LS) estimator as well as a constrained total
least-squares (CTLS) estimator to jointly estimate the orientation and the
position of the rigid body. To account for the perturbations of the sensors, we
also propose a constrained total least-squares (CTLS) estimator. Analytical
closed-form solutions for the proposed estimators are provided. Simulations are
used to corroborate and analyze the performance of the proposed estimators.Comment: 4 pages and 1 reference page; 3 Figures; In Proc. of ICASSP 201
Radio astronomical imaging in the presence of strong radio interference
Radio-astronomical observations are increasingly contaminated by
interference, and suppression techniques become essential. A powerful candidate
for interference mitigation is adaptive spatial filtering. We study the effect
of spatial filtering techniques on radio astronomical imaging. Current
deconvolution procedures such as CLEAN are shown to be unsuitable to spatially
filtered data, and the necessary corrections are derived. To that end, we
reformulate the imaging (deconvolution/calibration) process as a sequential
estimation of the locations of astronomical sources. This not only leads to an
extended CLEAN algorithm, the formulation also allows to insert other array
signal processing techniques for direction finding, and gives estimates of the
expected image quality and the amount of interference suppression that can be
achieved. Finally, a maximum likelihood procedure for the imaging is derived,
and an approximate ML image formation technique is proposed to overcome the
computational burden involved. Some of the effects of the new algorithms are
shown in simulated images. Keywords: Radio astronomy, synthesis imaging,
parametric imaging, interference mitigation, spatial filtering, maximum
likelihood, minimum variance, CLEAN.Comment: 27 pages, 7 figures. Paper with higher resolution color figures at
http://cobalt.et.tudelft.nl/~leshem/postscripts/leshem/imaging.ps.g
Calibration Challenges for Future Radio Telescopes
Instruments for radio astronomical observations have come a long way. While
the first telescopes were based on very large dishes and 2-antenna
interferometers, current instruments consist of dozens of steerable dishes,
whereas future instruments will be even larger distributed sensor arrays with a
hierarchy of phased array elements. For such arrays to provide meaningful
output (images), accurate calibration is of critical importance. Calibration
must solve for the unknown antenna gains and phases, as well as the unknown
atmospheric and ionospheric disturbances. Future telescopes will have a large
number of elements and a large field of view. In this case the parameters are
strongly direction dependent, resulting in a large number of unknown parameters
even if appropriately constrained physical or phenomenological descriptions are
used. This makes calibration a daunting parameter estimation task, that is
reviewed from a signal processing perspective in this article.Comment: 12 pages, 7 figures, 20 subfigures The title quoted in the meta-data
is the title after release / final editing
- …