Integration of unmanned aerial vehicles (UAVs) for surveillance or monitoring applications into fifth generation (5G) New Radio (NR) cellular networks is an intriguing problem that has recently tackled a lot of interest in both academia and industry. For an efficient spectrum usage, we consider a recently-proposed sky-ground nonorthogonal multiple access (NOMA) scheme, where a cellular-connected UAV acting as aerial user (AU) and a static terrestrial user (TU) are paired to simultaneously transmit their uplink signals to a base station (BS) in the same time-frequency resource blocks. In such a case, due to the highly dynamic nature of the UAV, the signal transmitted by the AU experiences both time dispersion due to multipath propagation effects and frequency dispersion caused by Doppler shifts. On the other hand, for a static ground network, frequency dispersion of the signal transmitted by the TU is negligible and only multipath effects have to be taken into account. To decode the superposed signals at the BS through successive interference cancellation, accurate estimates of both the AU and TU channels are needed. In this paper, we propose channel estimation procedures that suitably exploit the different circular/noncircular modulation formats (modulation diversity) and the different almost-cyclostationarity features (Doppler diversity) of the AU and TU by means of widely-linear time-varying processing. Our estimation approach is semi-blind since Doppler shifts and time delays of the AU are estimated based on the received data only, whereas the remaining relevant parameters of the AU and TU channels are acquired relying also on the available training symbols, which are transmitted by the AU and TU in a nonorthogonal manner.