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Global 21-cm signal extraction from foreground and instrumental effects III: Utilizing drift-scan time dependence and full Stokes measurements

When using valid foreground and signal models, the uncertainties on extracted signals in global 21-cm signal experiments depend principally on the overlap between signal and foreground models. In this paper, we investigate two strategies for decreasing this overlap: (i) utilizing time dependence by fitting multiple drift-scan spectra simultaneously and (ii) measuring all four Stokes parameters instead of only the total power, Stokes I. Although measuring polarization requires different instruments than are used in most existing experiments, all existing experiments can utilize drift-scan measurements merely by averaging their data differently. In order to evaluate the increase in constraining power from using these two techniques, we define a method for connecting Root-Mean-Square (RMS) uncertainties to probabilistic confidence levels. Employing simulations, we find that fitting only one total power spectrum leads to RMS uncertainties at the few K level, while fitting multiple time-binned, drift-scan spectra yields uncertainties at the $\lesssim 10$ mK level. This significant improvement only appears if the spectra are modeled with one set of basis vectors, instead of using multiple sets of basis vectors that independently model each spectrum. Assuming that they are simulated accurately, measuring all four Stokes parameters also leads to lower uncertainties. These two strategies can be employed simultaneously and fitting multiple time bins of all four Stokes parameters yields the best precision measurements of the 21-cm signal, approaching the noise level in the data.