# A High-Precision Energy-Efficient GPS Time-Sync Method for High-Density Seismic Surveys
## 3 Performance Evaluation and Field Measurement for Validation  
### Performance Evaluation  
GPS satellites are equipped with high-precision atomic clocks to achieve high-precision GPS timing. The satellite operating status parameters are continuously tracked and measured by ground monitoring stations [27]. They transmit orbit and time information to the GPS receiver through navigation messages (e.g., observation values, carrier and code phases, Doppler and carrier-to-noise values). The satellite clock error parameters are calculated in conjunction with the standard GPS time provided by the observatory and ground monitoring stations. The receiver gets GPS accurate timing  
Figure 11: The flow diagram of the GPS serial interruption and PPS interruption.  
after solving the data, and the synchronization accuracy is about 10\(\sim\)100 ns [28]. The GPS receiver NEO-M8 is a multi-constellation L1-frequency receiver. The synchronization error mainly comes from the accuracy error of the synchronization pulse from the GPS receiver in the entire network and the TCXO timing error of each sensor node. Satellite clocks age and drift. Indeed, satellite clocks are rubidium or cesium atoms with relative stable frequency drift, but each satellite has its own clock drift. Thus, the position solution is a hyperbolic problem due to the different clocks aligned in the system. Even though the clock offset and clock drift is relatively low compared to the external clock drift of the sensor node. Each sensor node uses an independent TCXO in its data acquisition unit, so there is a random phase difference in the master clock of different sensor nodes, which will cause ADC synchronization errors. If the phase difference between the main clocks of the two sensor nodes is 180\({}^{\circ}\) according to Figure 6, assuming that there is no error in the synchronization signal SYNC, which is derived from the PPS signal of GPS receiver, the maximum synchronization error is one master clock cycle after the two sensor nodes are synchronized with the signal. Obviously, the GPS timing error adding the master clock phase error produces the overall synchronization error. Therefore, the synchronization accuracy of the proposed time synchronization method in the whole sensor network can be expressed as follows:  
\[\Delta t_{error}=\pm\,1/f_{clk}+t_{GPS} \tag{6}\]  
where the \(f_{clk}\) represents the main clock cycle of the ADC, \(t_{GPS}\) represents the synchronization error of the GPS The main clock frequency of the ADC is 4.096 MHz and the maximum of \(t_{GPS}\) is 60 ns according to the NEO-M8N specification. Therefore, the synchronization accuracy of the proposed time synchronization method is \(\pm\) 0.3 \(\upmu\)s, i.e., 0.6 \(\upmu\)s. Further, the synchronization error does not change with time and the number of sensor nodes.  
In order to verify the performance of the proposed time synchronization method, we conducted an in-situ test and field measurement. In the in-situ test, we designed a verification method to test the stability of time synchronization of multiple nodes and the stability of time synchronization with time. Further, we have actually verified the time synchronization method in the field. The instrument parameters used are shown in Table 2.