## 2 Novel LEO Augmented GNSS Receiver System Structure
### Tracking Method in the LEO-Augmented GNSS Receiver  
Signal acquisition can be considered as a coarse estimation of GNSS signal parameters, which is unable to meet positioning requirements. On the other hand, the relative motion between the satellite and the receiver causes the signal parameters to change over time. Carrier and code tracking loops with feedback functions are often used as estimates of fine GNSS signal parameters in the tracking stage. The rate of the PRN code is much lower than the carrier frequency. Thus, the carrier-tracking loop is so fragile to be the most important part of a GNSS receiver. Under weak signal conditions, the loop bandwidth is often reduced to improve the accuracy of the carrier tracking loop. However, as a result of the oscillator noise and dynamics on the carrier tracking loop, the bandwidth cannot be reduced arbitrarily. Otherwise, it will cause the phenomena of lock-lose. To improve the tracking ability of the receiver in weak signal environments, such as strong wideband jamming in the military, this paper proposes a carrier tracking loop structure that is LEO satellite-assisted. It is noteworthy that the receiver does not need to extract the navigation bit from the signal processing, for it can get the GNSS ephemeris from LEO. On the other hand, the receiver is supposed to work well when it starts to encounter the jamming stress. At this time, the local PNR code is still aligned to the received signal  
Figure 2: LEO-assisted GNSS signal acquisition. and can be used to assist the loop with ephemeris. The navigation bit is used to remove the bit reversal and extend the coherent integration time. Therefore, only FLL is considered to track the ultra-low SNR signals. As shown in Figure 3, the receiver uses the obtained satellite navigation ephemeris to remove the bit reverse in the coherent integration of the GNSS signal after receiving and demodulating the signal sent by the LEO satellite. It can effectively extend the time of coherent integration and improve the input SNR of the loop. Furthermore, the receiver obtains the local initial position by Doppler positioning from the LEO signal. The receiver uses the position information and GNSS ephemeris information to calculate the Doppler of the GNSS signal, which can eliminate the dynamic effects and further compress the loop bandwidth. As a result, the tracking sensitivity can be enhanced. To track GNSS signals with ultra-low SNR, we use a frequency-locked loop (FLL) to improve the loop's tracking ability. The commonly used Costas discriminator has a pull-in range between \(-1/(2T_{coh})\) and \(1/(2T_{coh})\). When the integration time is long enough, the oscillator frequency drift and the Doppler rate-of-change could cause the frequency error to exceed the pull-in range. In high dynamics, a Differential Amplitude-based frequency discriminator [9] with a wider frequency pull-in range is adopted in this paper. As shown in Figure 4, the local carrier is divided into three channels (fast frequency, slow frequency, and estimated frequency) which correlate with the signal removed by pseudocode. The results of the three-channel correlators are accumulated after coherent integration and non-coherent integration. Then, these results enter the Differential Amplitude discriminator for frequency discrimination. The frequency error \(f_{e}\) processed by the loop filter is used with the Doppler shift from LEO satellite to adjust the carrier NCO. In Figure 4, we assume that the signal in Equation (1) removed the PRN code correctly. Thus, an obtained complex signal satisfies the following expression:  
\[r(t)=AD(t)[cos(2\pi f_{e}t+\phi_{e})+isin(2\pi f_{e}t+\phi_{e})]+n(t). \tag{2}\]  
Figure 4: Frequency-locked loop (FLL) structure based on a DA frequency discriminator. Figure 3: LEO-assisted carrier tracking loop structure.