## 3 The False Lock  
The pulsing scheme is known as the most effective solution to avoid interference between pseudolite signals and GNSS signals or between pseudolite signals. However, the pulsing scheme causes an additional frequency in the original signal, which leads to the false lock effect during the signal acquisition and tracking processes. As shown in Figure 5 in the previous section, the signal acquisition process in the FPGA (field programmable gate array) module may be locked onto a side lobe in the frequency domain, as the BOC (binary offset carrier) signal acquisition process experiences a false lock due to multiple side lobes in the code chip domain. To resolve the false lock effect of the pulsed signal, previous research results, such as RTCM SC-104 or the RTCA special committee SC-159, suggested a randomized pulse sequence [11, 12]. In the case of the RTCM suggestion, the pulse duration is 93 code chips, corresponding to 1/11 of a code sequence. The average duty ratio is defined as 0.1, and the pulse position is altered for every code sequence, indicating that a complete code sequence (1023 chips) can be used after a coherent integration time of 10 ms to prevent a false lock. In Figure 6, we described how the randomized pulse sequence works to resolve the aliasing issue due to the additional frequency. In the case of the RTCM suggestion, a single pulse has 93 code chips, as explained in the above lines. The sum of 11 time slots creates a complete code sequence (1023 chips) in the correlation process, indicating that the signal acquisition and tracking process are independent of pulsing, because there are no periodic pulsed samples. The RTCA 2000 scheme uses a similar concept, but with more pseudo-randomly-distributed pulse positions. However, recently, this appears to be removed from the RTCA document due to the difficulties related to standard GPS sensors [11]. Figure 6: Principle of the randomized pulse sequence scheme (e.g., the RTCM SC-104 suggestion). The randomized pulse position is a very useful scheme, because it can avoid the false lock effect and reduce the possibility of pulse collisions. However, a long integration time of the randomized pulse scheme (e.g., 10 or 20 ms) is not suitable for high dynamic applications, which require a limited coherent integration time. Within the framework of the ground-based radio navigation system, a deterministic pulse position scheme is assumed for signal transmissions for a similar reason. In fact, this method enables a zero pulse collision within a specific area assuming a sophisticated system design, which is another advantage for certain applications. Due to the deterministic pulse position, it was necessary to overcome the false lock issue on the navigation sensor side instead of the signal transmission side. In the tracking process, a false lock arises despite the fact that a single code sequence is used for the accumulation-and-dump process. This is clearly explained in Figure 7, which presents both the tracking loop discriminator and the accumulation-and-dump filter output in the frequency domain. In this paper, we used a second order FLL (frequency-locked loop) and the atan2 discriminator, as defined in Equation (10) [14]. \[D_{FLL}=\frac{\alpha\tan 2(cross,dot)}{(t_{2}-t_{1})\cdot 2\pi} \tag{10}\]  
Here,  
\[dot=I(t_{1})\cdot I(t_{2})+Q(t_{1})\cdot Q(t_{2})\]  
\[cross=I(t_{1})\cdot Q(t_{2})-I(t_{2})\cdot Q(t_{1})\]  
If a coherent integration time of 1 ms is used for signal tracking, from Equation (10), we can determine that the distance between lock points is 1 kHz, as presented in Figure 7. Doppler values presented in Figure 8 show what occurs when the false lock problem arises. Figure 8a shows that the tracking loops were locked at the correct point. The same Doppler is estimated regardless of the duty ratio value. Figure 8b shows that the tracking loop was locked in the incorrect position, in this case 1 kHz away from the true point. The false lock in the frequency domain  
Figure 7: Tracking loop discriminator _vs._ correlator output.