A self-calibration approach for optical long baseline interferometry imaging

Current optical interferometers are affected by unknown turbulent phases on each telescope. In the field of radio-interferometry, the self-calibration technique is a powerful tool to process interferometric data with missing phase information. This paper intends to revisit the application of self-calibration to Optical Long Baseline Interferometry (OLBI). We cast rigorously the OLBI data processing problem into the self-calibration framework and demonstrate the efficiency of the method on real astronomical OLBI dataset

Robust approaches to remote calibration of a transmitting array

We consider the problem of estimating the gains and phases of the RF channels of a M-element transmitting array, based on a calibration procedure where M orthogonal signals are sent through M orthogonal beams and received on a single antenna. The received data vector obeys a linear model of the type y ¼ AFg þ n where A is an unknown complex scalar accounting for propagation loss and g is the vector of unknown complex gains. In order to improve the performance of the least-squares (LS) estimator at low signal to noise ratio (SNR), we propose to exploit knowledge of the nominal value of g, viz g. Towards this end, two approaches are presented. First, a Bayesian approach is advocated where A and g are considered as random variables, with a non-informative prior distribution for A and a Gaussian prior distribution for g. The posterior distributions of the unknown random variables are derived and a Gibbs sampling strategy is presented that enables one to generate samples distributed according to these posterior distributions, leading to the minimum mean-square error (MMSE) estimator. A second approach consists in solving a constrained least-squares problem in which h ¼ Ag is constrained to be close to a scaled version of g. This second approach yields a closed-form solution, which amounts to a linear combination of g and the LS estimator. Numerical simulations show that the two new estimators significantly outperform the conventional LS estimator, especially at low SNR

Signal waveform estimation in the presence of uncertainties about the steering vector

We consider the problem of signal waveform estimation using an array of sensors where there exist uncertainties about the steering vector of interest. This problem occurs in many situations, including arrays undergoing deformations, uncalibrated arrays, scattering around the source, etc. In this paper, we assume that some statistical knowledge about the variations of the steering vector is available. Within this framework, two approaches are proposed, depending on whether the signal is assumed to be deterministic or random. In the former case, the maximum likelihood (ML) estimator is derived. It is shown that it amounts to a beamforming-like processing of the observations, and an iterative algorithm is presented to obtain the ML weight vector. For random signals, a Bayesian approach is advocated, and we successively derive an (approximate) minimum mean-square error estimator and maximum a posteriori estimators. Numerical examples are provided to illustrate the performances of the estimators

Matched direction detectors and estimators for array processing with subspace steering vector uncertainties

In this paper, we consider the problem of estimating and detecting a signal whose associated spatial signature is known to lie in a given linear subspace but whose coordinates in this subspace are otherwise unknown, in the presence of subspace interference and broad-band noise. This situation arises when, on one hand, there exist uncertainties about the steering vector but, on the other hand, some knowledge about the steering vector errors is available. First, we derive the maximum-likelihood estimator (MLE) for the problem and compute the corresponding Cramer-Rao bound. Next, the maximum-likelihood estimates are used to derive a generalized likelihood ratio test (GLRT). The GLRT is compared and contrasted with the standard matched subspace detectors. The performances of the estimators and detectors are illustrated by means of numerical simulations

Auto-Calibration of Co-located Uniform Linear Array Antennas

An algorithm for auto-calibration of a group of co-located uniform linear array antennas is presented. If the number of signal sources are known and, for at least one array, the ratio of the gains between two consecutive antenna elements is known, the individual unknown antenna gains can be estimated. The method is based on determining the antenna calibration parameters such that a matrix built from the array snapshots has a given rank. A numerical example illustrates the performance of the method. The numerical results suggest that the method is consistent in SNR

Spatial Signature Estimation with an Uncalibrated Uniform Linear Array

In this paper, the problem of spatial signature estimation using a uniform linear array (ULA) with unknown sensor gain and phase errors is considered. As is well known, the directions-of-arrival (DOAs) can only be determined within an unknown rotational angle in this array model. However, the phase ambiguity has no impact on the identification of the spatial signature. Two auto-calibration methods are presented for spatial signature estimation. In our methods, the rotational DOAs and model error parameters are firstly obtained, and the spatial signature is subsequently calculated. The first method extracts two subarrays from the ULA to construct an estimator, and the elements of the array can be used several times in one subarray. The other fully exploits multiple invariances in the interior of the sensor array, and a multidimensional nonlinear problem is formulated. A Gauss–Newton iterative algorithm is applied for solving it. The first method can provide excellent initial inputs for the second one. The effectiveness of the proposed algorithms is demonstrated by several simulation results

Tratamiento óptimo de contaminantes y sistemáticos para la explotación presente y futura de datos del Fondo Cósmico de Microondas

Uno de los hitos más esperados en cosmología es la detección de las ondas gravitacionales primordiales, ya que constituirían una prueba irrefutable de la existencia de un periodo inflacionario. En principio, pueden medirse a través de la huella marcada en la señal del modo B del Fondo Cósmico de Microondas. Sin embargo, esta detección conlleva muchos retos desde el punto de vista experimental y de análisis de datos, ya que es relativamente débil en comparación con otras fuentes de modos B, como los contaminantes astrofísicos, los modos lensados de E a B, y los errores sistemáticos. Esta tesis es uno de los muchos esfuerzos en el campo del análisis de datos dedicados a la detección de esta señal de forma insesgada. Este trabajo es una tesis por compendio de artículos que incluye cuatro estudios realizados en el contexto de la separación de componentes aplicada a los datos de polarización del Fondo Cósmico de Microondas. Se presenta un nuevo método de separación de componentes (B-SeCRET) que se ha aplicado en varios contextos dentro de diferentes colaboraciones e iniciativas como: simulaciones para estudios predictivos de la futura misión del satélite LiteBIRD, simulaciones de iniciativas de experimentos en tierra como ELFS, y a los datos del instrumento QUIJOTE MFI, WMAP y Planck. Además se incluyen tres aplicaciones de esta metodología: 1) el estudio y optimización de los diseños experimentales, 2) la mitigación de los errores sistemáticos, y 3) la caracterización de contaminantes astrofísicos. En particular se probó: 1) la viabilidad de la detección de ondas gravitaciones con un telescopio terrestre operando el régimen de microondas de baja frecuencia (de 10 a 120 GHz), además de su alta complementariedad con otras misiones como LiteBIRD, 2) la posibilidad de calibrar los ángulos de polarización a partir de la señal multifrecuencia mediante dos métodos (uno basado en anular el cross espectro de potencias EB y otro parametrizando este sistemático en la parte de separación de componentes con B-SeCRET), ambas metodologías recuperan una estimación insesgada de la amplitud de las ondas gravitacionales primordiales, 3) la mejora en la caracterización de la emisión de sincrotrón cuando se añaden los datos del instrumento QUIJOTE-MFI junto con datos de WMAP y Planck, en particular se presenta el primer mapa detallado del índice espectral del sincrotrón en hemisferio norte el cual presenta variaciones espaciales más significativas que los obtenidos con solo datos de WMAP y Planck. En conclusión, esta tesis prueba que B-SeCRET es una metodología versátil para analizar los datos presentes y futuros relativos al estudio del fondo cósmico de microondas debido a su capacidad de tratar simultáneamente con contaminantes astrofísicos y errores sistemáticos.One of the most awaited milestones in cosmology is the detection of primordial gravitational waves, as they would constitute compelling evidence of the existence of an inflationary period. In principle, they can be measured through their imprint in the B-mode signal of the Cosmic Microwave Background. However, this detection carries many challenges from an experimental and data analysis point of view, as it is relatively weak compared to other sources of B-modes, such as astrophysical contaminants, E-to-B lens modes, and systematic errors. This thesis is one of many efforts in the field of data analysis devoted to the detection of this signal in an unbiased manner. This work is a compilation thesis that includes four studies performed in the context of component separation applied to Cosmic Microwave Background polarization data. A new component separation method (B-SeCRET) is presented. This method has been applied in several contexts within different collaborations and initiatives, such as simulations for predictive studies of the future LiteBIRD satellite mission, simulations of ground-based experiment initiatives such as ELFS, and QUIJOTE MFI, WMAP and Planck instrument data. In addition, three applications of this methodology are included: 1) the study and optimization of experimental designs, 2) the mitigation of systematic errors, and 3) the characterization of astrophysical contaminants. In particular, we tested: 1) the feasibility of gravitational wave detection with a ground-based telescope operating the low-frequency microwave regime (from 10 to 120 GHz), in addition to its high complementarity with other missions such as LiteBIRD, 2) the possibility of calibrating the polarization angles from the multi-frequency signal using two methods (one based on canceling the EB cross-spectrum and the other by parameterizing this systematic in the component separation part with B-SeCRET), both methodologies recover an unbiased estimate of the amplitude of the primordial gravitational waves, 3) the improvement in the characterization of the synchrotron emission when the QUIJOTE-MFI instrument data are added together with WMAP and Planck data, in particular, the first detailed map of the synchrotron spectral index in the northern hemisphere is presented, which presents more significant spatial variations than those obtained with only WMAP and Planck data. In conclusion, this thesis proves that B-SeCRET is a versatile methodology to analyze present and future data related to the study of the cosmic microwave background due to its ability to deal simultaneously with astrophysical contaminants and systematic errors