148 research outputs found
Parametric high resolution techniques for radio astronomical imaging
The increased sensitivity of future radio telescopes will result in
requirements for higher dynamic range within the image as well as better
resolution and immunity to interference. In this paper we propose a new matrix
formulation of the imaging equation in the cases of non co-planar arrays and
polarimetric measurements. Then we improve our parametric imaging techniques in
terms of resolution and estimation accuracy. This is done by enhancing both the
MVDR parametric imaging, introducing alternative dirty images and by
introducing better power estimates based on least squares, with positive
semi-definite constraints. We also discuss the use of robust Capon beamforming
and semi-definite programming for solving the self-calibration problem.
Additionally we provide statistical analysis of the bias of the MVDR beamformer
for the case of moving array, which serves as a first step in analyzing
iterative approaches such as CLEAN and the techniques proposed in this paper.
Finally we demonstrate a full deconvolution process based on the parametric
imaging techniques and show its improved resolution and sensitivity compared to
the CLEAN method.Comment: To appear in IEEE Journal of Selected Topics in Signal Processing,
Special issue on Signal Processing for Astronomy and space research. 30 page
Cooperative Localisation of a GPS-Denied UAV using Direction-of-Arrival Measurements
A GPS-denied UAV (Agent B) is localised through INS alignment with the aid of a nearby GPS-equipped UAV (Agent A), which broadcasts its position at several time instants. Agent B measures the signals' direction of arrival with respect to Agent B's inertial navigation frame. Semidefinite programming and the Orthogonal Procrustes algorithm are employed, and accuracy is improved through maximum likelihood estimation. The method is validated using flight data and simulations. A three-agent extension is explored
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Structured Sub-Nyquist Sampling with Applications in Compressive Toeplitz Covariance Estimation, Super-Resolution and Phase Retrieval
Sub-Nyquist sampling has received a huge amount of interest in the past decade. In classical compressed sensing theory, if the measurement procedure satisfies a particular condition known as Restricted Isometry Property (RIP), we can achieve stable recovery of signals of low-dimensional intrinsic structures with an order-wise optimal sample size. Such low-dimensional structures include sparse and low rank for both vector and matrix cases. The main drawback of conventional compressed sensing theory is that random measurements are required to ensure the RIP property. However, in many applications such as imaging and array signal processing, applying independent random measurements may not be practical as the systems are deterministic. Moreover, random measurements based compressed sensing always exploits convex programs for signal recovery even in the noiseless case, and solving those programs is computationally intensive if the ambient dimension is large, especially in the matrix case. The main contribution of this dissertation is that we propose a deterministic sub-Nyquist sampling framework for compressing the structured signal and come up with computationally efficient algorithms. Besides widely studied sparse and low-rank structures, we particularly focus on the cases that the signals of interest are stationary or the measurements are of Fourier type. The key difference between our work from classical compressed sensing theory is that we explicitly exploit the second-order statistics of the signals, and study the equivalent quadratic measurement model in the correlation domain. The essential observation made in this dissertation is that a difference/sum coarray structure will arise from the quadratic model if the measurements are of Fourier type. With these observations, we are able to achieve a better compression rate for covariance estimation, identify more sources in array signal processing or recover the signals of larger sparsity. In this dissertation, we will first study the problem of Toeplitz covariance estimation. In particular, we will show how to achieve an order-wise optimal compression rate using the idea of sparse arrays in both general and low-rank cases. Then, an analysis framework of super-resolution with positivity constraint is established. We will present fundamental robustness guarantees, efficient algorithms and applications in practices. Next, we will study the problem of phase-retrieval for which we successfully apply the sparse array ideas by fully exploiting the quadratic measurement model. We achieve near-optimal sample complexity for both sparse and general cases with practical Fourier measurements and provide efficient and deterministic recovery algorithms. In the end, we will further elaborate on the essential role of non-negative constraint in underdetermined inverse problems. In particular, we will analyze the nonlinear co-array interpolation problem and develop a universal upper bound of the interpolation error. Bilinear problem with non-negative constraint will be considered next and the exact characterization of the ambiguous solutions will be established for the first time in literature. At last, we will show how to apply the nested array idea to solve real problems such as Kriging. Using spatial correlation information, we are able to have a stable estimate of the field of interest with fewer sensors than classic methodologies. Extensive numerical experiments are implemented to demonstrate our theoretical claims
Optimal Precoders for Tracking the AoD and AoA of a mm-Wave Path
In millimeter-wave channels, most of the received energy is carried by a few
paths. Traditional precoders sweep the angle-of-departure (AoD) and
angle-of-arrival (AoA) space with directional precoders to identify directions
with largest power. Such precoders are heuristic and lead to sub-optimal
AoD/AoA estimation. We derive optimal precoders, minimizing the Cram\'{e}r-Rao
bound (CRB) of the AoD/AoA, assuming a fully digital architecture at the
transmitter and spatial filtering of a single path. The precoders are found by
solving a suitable convex optimization problem. We demonstrate that the
accuracy can be improved by at least a factor of two over traditional
precoders, and show that there is an optimal number of distinct precoders
beyond which the CRB does not improve.Comment: Resubmission to IEEE Trans. on Signal Processing. 12 pages and 9
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