The redshifted 21cm line of neutral hydrogen (Hi), potentially observable at low radio frequencies (~50–200 MHz), should be a powerful probe of the physical conditions of the inter-galactic medium during Cosmic Dawn and the Epoch of Reionisation (EoR). The sky-averaged Hi signal is expected to be extremely weak (~100 mK) in comparison to the foreground of up to 104 K at the lowest frequencies of interest. The detection of such a weak signal requires an extremely stable, well characterised system and a good understanding of the foregrounds. Development of a nearly perfectly (~mK accuracy) calibrated total power radiometer system is essential for this type of experiment. We present the BIGHORNS (Broadband Instrument for Global HydrOgen ReioNisation Signal) experiment which was designed and built to detect the sky-averaged Hi signal from the EoR at low radio frequencies. The BIGHORNS system is a mobile total power radiometer, which can be deployed in any remote location in order to collect radio frequency interference (RFI) free data. The system was deployed in remote, radio quiet locations in Western Australia and low RFI sky data have been collected. We present a description of the system, its characteristics, details of data analysis, and calibration. We have identified multiple challenges to achieving the required measurement precision, which triggered two major improvements for the future system.