# Carrier Phase Dual One-Way Ranging Method Based on a Frequency Hopping Signal
## 5 Simulation Results of the FH-DOWR System  
For the FH-DOWR system, the searching range for carrier phase integer ambiguity resolution is constrained by the PN code ranging accuracy. Based on (20), the relationship between the ranging accuracy and the CNR is shown in Figure 11. The results show that the code ranging accuracy is approximately 1.2\(\sim\)130 mm. In the simulation of integer ambiguity resolution, the hopping frequency is 100/3 Hz, and the frequency is \(f_{i}=(23+0.1n)\) GHz \((n=1,2,3,4,5)\). The results of the Monte Carlo simulation are shown in Figure 13.  
By analyzing the maximum and RMSE distance measurements, the simulation results at CNR = 40 dB-Hz show that if polynomial fitting is applied to the measured phase, then the accuracy probability of ambiguity resolution in the measurement results is greater than 58%. The maximum error in the carrier phase range under FH-DOWR is better than 0.6 mm  
Figure 12: Doppler frequency tracking error at CNR = 40 dB-Hz. Figure 13: Performance analysis of the carrier phase ranging of the FH-DOWR system: (**a**) measurement accuracy with carrier phase measurement value fitting; (**b**) measurement accuracy without measurement value fitting; and (**c**) probability of a successful calculation with and without fitting. (2.23 ps), and the RMSE is better than 0.247 mm (time synchronization accuracy is 0.824 ps). As the CNR increases, exceeding 60 dB-Hz, the probability of ambiguity resolution is 95.1%. Under these conditions, the maximum error in the carrier phase range is better than 0.0597 mm (the time synchronization accuracy is 0.199 ps), and the RMSE is better than 0.0217 mm (the time synchronization accuracy is 0.0728 ps). In this situation, with the increase in the CNR, the accuracy of the FH-DOWR system will remain at the level of 0.02 mm. If the time division measurement values are not fitted, then the probability of correct ambiguity resolution will decrease, as shown in Figure 13c. For a 40 dB Hz carrier wave, the probability of successful calculation is only 0.147, and the accuracy of the carrier phase measurement also decreases. The maximum distance measurement error is better than 6 mm (the time synchronization accuracy is 0.02 ns), and the RMSE is better than 2.37 mm (the time synchronization accuracy is 7.91 ps). As the carrier-to-noise ratio increases, the probability of accuracy in ambiguity resolution increases; however, even under high carrier-to-noise ratio conditions such as 80 dB Hz, the probability of accuracy does not exceed 0.458. The maximum measurement accuracy error decreases to 1.1 mm and increases to 1.1 mm (the time synchronization accuracy is 3.67 ps) and 0.337 mm (the time synchronization accuracy is 1.13 ps). If the transmitter and receiver can simultaneously transmit and receive signals from two frequency points, then more accurate carrier phase measurement results can be obtained. The frequencies are \(f_{1}=23\) GHz and \(f_{2}=23.1\) GHz. The Monte Carlo simulation results are shown in Figure 14.  
By analyzing the maximum and RMSE distance measurements, the simulation results under a CNR of 40 dB-Hz show that if polynomial fitting is applied to the carrier phase,  
Figure 14: Analysis of the carrier phase ranging performance in the case of dual-frequency continuous signals: (**a**) measurement accuracy with carrier phase measurement fitting; (**b**) measurement accuracy without measurement value fitting; and (**c**) probability of a successful calculation with and without fitting. then the accuracy probability of ambiguity resolution is 100% and the maximum error in the carrier phase range is 25.9 \(\upmu\)m. The RMSE is superior to 9.54 \(\upmu\)m. As the CNR increases, the measurement accuracy further improves. At a CNR of 80 dB-Hz, the maximum ranging is 5.99 \(\upmu\)m and the RMSE is 3.35 \(\upmu\)m.  
If the carrier phase measurement results are not fitted, then the probability of correct ambiguity resolution decreases, as shown in Figure 14c.