  One approach to extracting the global 21-cm signal from total-power
measurements at low radio frequencies is to parametrize the different
contributions to the data and then fit for these parameters. We examine
parametrizations of the 21-cm signal itself, and propose one based on modelling
the Lyman-alpha background, IGM temperature and hydrogen ionized fraction using
tanh functions. This captures the shape of the signal from a physical modelling
code better than an earlier parametrization based on interpolating between
maxima and minima of the signal, and imposes a greater level of physical
plausibility. This allows less biased constraints on the turning points of the
signal, even though these are not explicitly fit for. Biases can also be
alleviated by discarding information which is less robustly described by the
parametrization, for example by ignoring detailed shape information coming from
the covariances between turning points or from the high-frequency parts of the
signal, or by marginalizing over the high-frequency parts of the signal by
fitting a more complex foreground model. The fits are sufficiently accurate to
be usable for experiments gathering 1000 h of data, though in this case it may
be important to choose observing windows which do not include the brightest
areas of the foregrounds. Our assumption of pointed, single-antenna
observations and very broad-band fitting makes these results particularly
applicable to experiments such as the Dark Ages Radio Explorer, which would
study the global 21-cm signal from the clean environment of a low lunar orbit,
taking data from the far side.
