# Practical Use of Starlink Downlink Tones for Positioning
## 2 Signal Detection and Tracking
### Tones Detection and Tracking
Indeed, in order to avoid a false frequency lock at the beginning of the tracking process, a wide pull-in range of the FLL is required, which is achievable with a short integration time, T.  
Given these considerations, we set the integration time of the FPLL to T = 2 ms over the first 1-s of the tracking, then, we extend it to T = 10 ms until the signal loss of lock. We have found that an equivalent noise bandwidth of \(B_{0p}=B_{0f}\) = 10 Hz is an acceptable compromise between noise and dynamic stress errors for a typical value of the expected C/No (30 dB-Hz). In this condition, we note that the dynamic stress error for the PLL is \(\sim\)0.034 cycles, and that of the FLL is \(\sim\)0.197 Hz. Many FPLL channels are instantiated to deal with receiving multiple tones. Tones from the same satellite are therefore tracked simultaneously on multiple channels. Figure 5 shows the resulting baseband signal and the estimated carrier-to-noise ratio (C/No) tracked by channel 1 for satellites that are received in succession during recording. Zooming in on the baseband signal (Figure 5b) shows that the signal envelope follows a bell shape, i.e., low amplitude toward low satellite elevation angles (i.e., when the satellite appears or disappears) and maximum power toward higher elevation angles where the satellite is closest to the observer. The oscillation in the signal amplitude has a period of \(\sim\)10 s. This can be explained by the fact that the signal is received from different satellite sidelobes as the satellite moves. The C/No of the tones is almost between 24 and 36 dB-Hz. This low signal level is due to the use of an LNB without a parabolic reflector. A parabolic reflector focuses the downlink beam to an open waveguide that feeds the LNB and thus adds a significant gain. It is interesting to evaluate tone tracking without the use of a parabolic reflector, because as mentioned above, the parabolic reflector is cumbersome for vehicles such as drones, and has a selective aperture that limits the number of satellites captured simultaneously. Phase array antennas can potentially track several satellites, but a large number of antenna elements are required to achieve parabolic reflector performances, so their cost and complexity are largely increased. Interestingly, measuring the tone frequency for localization does not require as much power as decoding useful data. The probability density function of the phase detector error and that of the frequency detector error computed with the measurements of the tracked satellites are shown in Figure 6. The phase error has a standard deviation of 0.1157 cycles (3.1 mm), and is centered around 0.0384 cycles (1 mm). The standard deviation of the frequency detector error is 10.85 Hz (0.287 m/s) and is centered around \(-\)0.2337 Hz (\(-\)6 mm/s). For both detectors, the error distribution is not symmetrical, suggesting that the incoming signal does not satisfy the hypothesis of being formed by perfect tones. The non-zero average error can be explained by the dynamic stress error and by any distortion of the incoming signal. Figure 5: (**a**) Baseband signal (Phase arm (I) and Quadrature arm (Q)) and estimated C/No of the successively received satellite tones; (**b**) Zoom in showing a low signal level at the start and end times of satellite tracking, a high signal envelope at high satellite elevations, and a signal amplitude oscillation at low frequency (\(-\)0.1 Hz). Figure 6: (**a**) Probability density function of the phase detector error, (**b**) Probability density function of the frequency detector error.