The large availability of Low Earth Orbit (LEO) satellite systems makes them useful beyond their original purposes, such as in positioning, where their signals can be passively used. In order to determine their potential for this purpose, newly deployed systems need to be investigated. This is the case with the Starlink system, which has a large constellation and is advantageous for positioning. It transmits signals in the 10.7–12.7 GHz band, the same as that of geostationary satellite television. Signals in this band are typically received using a low-noise block down-converter (LNB) and a parabolic antenna reflector. Regarding opportunistic use of these signals in small vehicle navigation, the dimensions of the parabolic reflector and its directional gain are not practical for tracking many satellites simultaneously. In this paper, we investigate the feasibility of tracking Starlink downlink tones for opportunistic positioning in a practical situation, when signals are received without a parabolic reflector. For this purpose, an inexpensive universal LNB is selected, and then signal tracking is performed to determine the signal and frequency measurement quality, as well as the number of satellites that can be tracked simultaneously. Next, the tone measurements are aggregated to handle tracking interruptions and to recover the traditional Doppler shift model. After that, the use of measurements in multi-epoch positioning is defined, and its performance discussed as a function of the relevant measurement rate and the required multi-epoch interval duration. The results showed promising positioning which can be improved by selecting a better-quality LNB.