Abstract

Broadband radio frequency interferometric technique is being rapidly advanced in recent years and is being increasingly widely used in the lightning community for detailed discharge physics studies. Los Alamos National Laboratory is in the process of deploying two spatially separated interferometers that consist of four, dual-polarization antennas for each interferometer. For a 4-antenna array, or any array that consists of more than three antennas, the antennas cannot be assumed situated in the same plane, and a generic interferometric process is needed to take the full advantage of the additional antennas. In this paper we present and numerically verify an analytic solution for a general noncoplanar array that directly relates the source direction to the array geometry and the time delay measurement. This general and analytic solution can be used in any array configurations with three or more antennas. We then derive the analytic formulas for the associated interferometric uncertainties based on the general analytic solution. Uncertainty analysis is critically important for correct and credible interpretation of the observations, but only very limited and incomplete uncertainty analyses have been reported in the lightning community. In this paper, we first carry out the uncertainty analysis for a pair of baselines and then extend the analysis to a combination of multiple pairs of baselines. We verify the analytic uncertainty analyses with numerical experiments and discuss the behavior of the uncertainties. These analyses will hopefully help to lay the foundation for future uncertainty estimate, and for more statistically trustworthy interpretation of the interferometric observations.