# A NavCom Signal Authentication Scheme Based on Twice Two-Way Satellite Time Transfer
## 2 A Twice TWSTT NavCom Signal Authentication Scheme  
### Fundamental Theory  
One of the most accurate remote time synchronization methods is TWSTT [15; 16; 17; 18]. In this mode, the transmission path symmetry enables the propagation delay on the link to be nearly fully offset, which can make the time synchronization reach a high accuracy. Figure 1 illustrates the principle of satellite-earth TWSTT. As depicted in Figure 1, the computational model of TWSTT can be written as follows:  
\[\text{TIC}(\text{A}) =\text{A}-\text{S}+d_{ZS}+d_{SA}+d_{ZA}+S_{A} \tag{1}\] \[\text{TIC}(\text{S}) =\text{S}-\text{A}+d_{TA}+d_{AS}+d_{ZS}+S_{S} \tag{2}\]  
where \(\text{TIC}(\text{A})\) and \(\text{TIC}(\text{S})\) represent the transmission pseudo-distance values, i.e., the readings of the time interval counter. \(\text{TIC}(\text{S})\) is measured by the satellite and its information is added to the downlink communication signal for transmission to the ground terminal, A and S represent the paper time at the respective stations, \(d_{xx}\) represents the propagation delay, and \(S_{A}\) and \(S_{S}\) are the correction terms for the Sagnac effect. By taking the difference  
Figure 1: The principle of TWSTT. between Equations (1) and (2), we can derive the expression for the clock difference between the ground terminal A and the satellite S as follows:  
\[\text{A}-\text{S}=\frac{\text{TIC}(\text{A})-\text{TIC}(\text{S})}{2}+\frac{d_{ TA}-d_{RA}}{2}-\frac{d_{TS}-d_{RS}}{2}+\frac{S_{A}-S_{S}}{2}+\frac{d_{AS}-d_{SA}}{2} \tag{3}\]  
In Equation (3), the first term to the right of the equal sign is the difference between the counter readings of the ground terminal and the satellite, which is the difference between the clock difference measured by the ground terminal and the satellite. The second term corresponds to the difference between the transmission and reception delays of the ground terminal, while the third term denotes the difference between the transmission and reception delays at the satellite end. The fourth term represents the correction for the relativistic effect caused by the rotation of the Earth, i.e., the Sagnac effect, and the fifth term accounts for the difference in the spatial propagation delays for the uplink signal and the downlink signal, including ionospheric delays, tropospheric delays, geometrical path delays, and so on. The second to fourth terms can be measured or calculated in advance, and the fifth term can be well canceled due to the delay of the upper and lower paths in the very short TWSTT being equal. Thus, Equation (3) can be reduced to Equation (4). \[\text{A}-\text{S}=\frac{\text{TIC}(\text{A})-\text{TIC}(\text{S})}{2}+\frac{d_ {TA}-d_{RA}}{2}-\frac{d_{TS}-d_{RS}}{2}+\frac{S_{A}-S_{S}}{2} \tag{4}\]  
Therefore, it is only necessary to accurately calibrate and deduct the arrival times of the signals measured by the ground terminals and satellites so that the clock difference measurement can be realized by two-way time comparison. Due to the non-mutated nature of the clock difference, this paper proposes a novel NavCom signal authentication scheme based on twice TWSTT, which involves the user terminal conducting twice separate TWSTT with the same satellite. The scheme can achieve signal security authentication through a comparison of clock difference measurement values. The specific operation procedures are as follows: the user terminal initiates twice two-way authentications at two different moments, \(t_{1}\) and \(t_{2}\), during the satellite's visibility period. The clock difference measurements obtained from these two authentications are recorded as \(\Delta T_{1}\) and \(\Delta T_{2}\), respectively. Figure 2 illustrates a schematic of twice TWSTT. In Figure 2, it can be observed that only the paths of the uplink and downlink signals change during the twice TWSTT processes. Fortunately, the paths of the uplink and downlink signals are equal for the same time transfer process, which can be canceled out.