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Register a new userCalibration of Radio Interferometers Using a Sparse DoA Estimation Framework
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The calibration of modern radio interferometers is a significant challenge, specifically at low frequencies. In this perspective, we propose a novel iterative calibration algorithm, which employs the popular sparse representation framework, in the regime where the propagation conditions shift dissimilarly the directions of the sources. More precisely, our algorithm is designed to estimate the apparent directions of the calibration sources, their powers, the directional and undirectional complex gains of the array elements and their noise powers, with a reasonable computational complexity. Numerical simulations reveal that the proposed scheme is statistically efficient at low SNR and even with additional non-calibration sources at unknown directions.
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Having an accurate calibration method is crucial for any scientific research done by a radio telescope. The next generation radio telescopes such as the Square Kilometre Array (SKA) will have a large number of receivers which will produce exabytes of data per day. In this paper we propose new direction-dependent and independent calibration algorithms that, while requiring much less storage during calibration, converge very fast. The calibration problem can be formulated as a non-linear least square optimization problem. We show that combining a block-LDU decomposition with Gauss-Newton iterations produces systems of equations with convergent matrices. This allows significant reduction in complexity per iteration and very fast converging algorithms. We also discuss extensions to direction-dependent calibration. The proposed algorithms are evaluated using simulations.
In order to meet the theoretically achievable imaging performance, calibration of modern radio interferometers is a mandatory challenge, especially at low frequencies. In this perspective, we propose a novel parallel iterative multi-wavelength calibration algorithm. The proposed algorithm estimates the apparent directions of the calibration sources, the directional and undirectional complex gains of the array elements and their noise powers, with a reasonable computational complexity. Furthermore, the algorithm takes into account the specific variation of the aforementioned parameter values across wavelength. Realistic numerical simulations reveal that the proposed scheme outperforms the mono-wavelength calibration scheme and approaches the derived constrained Cramer-Rao bound even with the presence of non-calibration sources at unknown directions, in a computationally efficient manner.
Accurate photometric redshifts are a lynchpin for many future experiments to pin down the cosmological model and for studies of galaxy evolution. In this study, a novel sparse regression framework for photometric redshift estimation is presented. Simulated and real data from SDSS DR12 were used to train and test the proposed models. We show that approaches which include careful data preparation and model design offer a significant improvement in comparison with several competing machine learning algorithms. Standard implementations of most regression algorithms have as the objective the minimization of the sum of squared errors. For redshift inference, however, this induces a bias in the posterior mean of the output distribution, which can be problematic. In this paper we directly target minimizing $Delta z = (z_textrm{s} - z_textrm{p})/(1+z_textrm{s})$ and address the bias problem via a distribution-based weighting scheme, incorporated as part of the optimization objective. The results are compared with other machine learning algorithms in the field such as Artificial Neural Networks (ANN), Gaussian Processes (GPs) and sparse GPs. The proposed framework reaches a mean absolute $Delta z = 0.0026(1+z_textrm{s})$, over the redshift range of $0 le z_textrm{s} le 2$ on the simulated data, and $Delta z = 0.0178(1+z_textrm{s})$ over the entire redshift range on the SDSS DR12 survey, outperforming the standard ANNz used in the literature. We also investigate how the relative size of the training set affects the photometric redshift accuracy. We find that a training set of textgreater 30 per cent of total sample size, provides little additional constraint on the photometric redshifts, and note that our GP formalism strongly outperforms ANNz in the sparse data regime for the simulated data set.
We consider the problem of direction-of-arrival (DOA) estimation in unknown partially correlated noise environments where the noise covariance matrix is sparse. A sparse noise covariance matrix is a common model for a sparse array of sensors consisted of several widely separated subarrays. Since interelement spacing among sensors in a subarray is small, the noise in the subarray is in general spatially correlated, while, due to large distances between subarrays, the noise between them is uncorrelated. Consequently, the noise covariance matrix of such an array has a block diagonal structure which is indeed sparse. Moreover, in an ordinary nonsparse array, because of small distance between adjacent sensors, there is noise coupling between neighboring sensors, whereas one can assume that nonadjacent sensors have spatially uncorrelated noise which makes again the array noise covariance matrix sparse. Utilizing some recently available tools in low-rank/sparse matrix decomposition, matrix completion, and sparse representation, we propose a novel method which can resolve possibly correlated or even coherent sources in the aforementioned partly correlated noise. In particular, when the sources are uncorrelated, our approach involves solving a second-order cone programming (SOCP), and if they are correlated or coherent, one needs to solve a computationally harder convex program. We demonstrate the effectiveness of the proposed algorithm by numerical simulations and comparison to the Cramer-Rao bound (CRB).
The performance of the existing sparse Bayesian learning (SBL) methods for off-gird DOA estimation is dependent on the trade off between the accuracy and the computational workload. To speed up the off-grid SBL method while remain a reasonable accuracy, this letter describes a computationally efficient root SBL method for off-grid DOA estimation, where a coarse refinable grid, whose sampled locations are viewed as the adjustable parameters, is adopted. We utilize an expectation-maximization (EM) algorithm to iteratively refine this coarse grid, and illustrate that each updated grid point can be simply achieved by the root of a certain polynomial. Simulation results demonstrate that the computational complexity is significantly reduced and the modeling error can be almost eliminated.
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