By connecting the output of the noise source to the SWR-bridge input, and the antenna to the DUT port the return loss or SWR of the antenna can be measured with the Airspy. To get a wider than 10 MHz view of the spectrum Anders uses the SpectrumSpy software for the Airspy which is a spectrum analyzer application that allows you to view any bandwidth that you like. With the Airspy, noise source and antenna all connected correct to the SWR-Bridge significantly notches in the spectrum show up in SpectrumSpy. These notches are the resonant points of the antenna. Visually seeing these notches allows you to fine tune the length of the antenna elements for best SWR.
Most low cost sellers of RTL-SDR dongles bundle them with a cheap fixed length whip antenna. Over on YouTube Adam 9A4QV has measured the return loss of these whip antennas with his vector network analyzer to determine at what frequencies you can expect decent performance. The return loss indicates at what frequencies you can expect a good impedance match, and thus a good standing wave ratio (SWR). The lower the return loss the better the impedance match and thus less power is wasted in the antenna meaning better receive performance.
Adams results found that without a ground plane the antenna has a return loss of less than -10dB at around 625 MHz and about 1.40 GHz. With a ground plane (placed on a metal surface) the antenna has good performance at around 535 MHz, 1.4 GHz and 2.4 GHz. This is not surprising as the antenna is designed for DVB-T TV, of which most signals are transmit near 535 MHz. Adam also remarks that the performance at the ADS-B frequency of 1090 MHz with or without ground plane is quite bad.