Non-linear Redundancy Calibration

For radio interferometric arrays with a sufficient number of redundant spacings the multiplicity of measurements of the same sky visibility can be used to determine both the antenna gains as well as the true visibilities. Many of the earlier approaches to this problem focused on linearized versions of the relation between the measured and the true visibilities. Here we propose to use a standard non-linear minimization algorithm to solve for both the antenna gains as well as the true visibilities. We show through simulations done in the context of the ongoing upgrade to the Ooty Radio Telescope that the non-linear minimization algorithm is fast compared to the earlier approaches. Further, unlike the most straightforward linearized approach, which works with the logarithms of the visibilities and the gains, the non-linear minimization algorithm leads to unbiased solutions. Finally we present error estimates for the estimated gains and visibilities. Monte-Carlo simulations establish that the estimator is indeed statistically efficient, achieving the Cramer-Rao bound.Comment: 9 pages, 5 figures. Accepted for publication in MNRAS. The definitive version will be available at http://mnras.oxfordjournals.or

TDIR: Time-Delay Interferometric Ranging for Space-Borne Gravitational-Wave Detectors

Space-borne interferometric gravitational-wave detectors, sensitive in the low-frequency (mHz) band, will fly in the next decade. In these detectors, the spacecraft-to-spacecraft light-travel times will necessarily be unequal and time-varying, and (because of aberration) will have different values on up- and down-links. In such unequal-armlength interferometers, laser phase noise will be canceled by taking linear combinations of the laser-phase observables measured between pairs of spacecraft, appropriately time-shifted by the light propagation times along the corresponding arms. This procedure, known as time-delay interferometry (TDI), requires an accurate knowledge of the light-time delays as functions of time. Here we propose a high-accuracy technique to estimate these time delays and study its use in the context of the Laser Interferometer Space Antenna (LISA) mission. We refer to this ranging technique, which relies on the TDI combinations themselves, as Time-Delay Interferometric Ranging (TDIR). For every TDI combination, we show that, by minimizing the rms power in that combination (averaged over integration times $\sim 10^4$ s) with respect to the time-delay parameters, we obtain estimates of the time delays accurate enough to cancel laser noise to a level well below the secondary noises. Thus TDIR allows the implementation of TDI without the use of dedicated inter-spacecraft ranging systems, with a potential simplification of the LISA design. In this paper we define the TDIR procedure formally, and we characterize its expected performance via simulations with the \textit{Synthetic LISA} software package.Comment: 5 pages, 2 figure