# Pseudorange Measurement Method Based on AIS Signals
## 4 Accuracy Analysis of Single Timestamp Detection  
Based on the results of the previous analysis, we present two methods to detect the timestamp of the Gaussian baseband wave in the AIS system, which are the zero-crossing detection method and the differential peak detection method. Due to the interference of the channel and the thermal noise of the receiver, there is noise interference in the GMSK Gaussian baseband waveform, which is recovered by the receiver demodulator. By considering that the wireless channel usually obeys the AWGN channel model and the thermal noise of the system is also in accordance with the Gaussian characteristic [26], the noise superimposed on the baseband waveform is also consistent with the characteristics of white Gaussian noise. Therefore, it is necessary to filter out the noises from the reproduced Gaussian baseband waveform before performing the timestamp detection. As shown in Figure 7a, the SNR is equal to 10 dB, and the noise suppression was performed using a Gaussian filter whose parameter \(BT\) was set to 0.6. Figure 7b shows the relationship between the real value and the timestamp detection result, which was obtained using the zero-crossing detection method. The results obtained by the differential peak detection method for the same baseband signal are shown in Figure 7c. Since the differential detection method is more sensitive to signal jitter, there will be a large number of outliers. In addition, the amplitude of outliers related to the SNR makes the differential peak detection method much more complex than the zero-crossing detection method in actual use. Figure 7d compares the zero-crossing detection method and the differential peak detection method. It can be seen that the error jitter range of the zero-crossing detection method is smaller than that of the differential peak detection method. The detection accuracy of timestamps is affected by the SNR of the recovered baseband waveform, so we analyzed the detection accuracy under different SNR conditions. The simulation parameters were set as follows: (1) the parameter \(BT\) of the pre-Gaussian lowpass filter was set to 0.6; (2) the length of one message frame was 256 bits; (3) the digital message sequence was a binary random sequence that was different each time; (4) the same Gaussian baseband signal was processed by the zero-crossing detection method and the differential peak detection method to detect timestamp; (5) the process was repeated 20,000 times at a certain signal-to-noise ratio, and the mean and standard deviation of all timestamps detection error were calculated. Figure 6: Influence of inter-symbol interference on timestamp differential property. All communications systems have the noise floor caused by ambient atmospheric. The equation is as follows  
\[N=kTB \tag{17}\]  
where \(k=1.38\times 10^{-23}\) J/K is Boltzman's constant; \(T\) is system temperature, usually assumed to be 290 K; \(B\) is channel bandwidth measured in Hz. This is the lowest possible noise level for a system with a given physical temperature. Usually the noise received by the receiver contains additional noise from other sources in addition to the noise floor. A common model for the average additional noise power from other sources is  
\[F_{nm}=c-27.7\times\log_{10}f \tag{18}\]  
in which \(f\) is the frequency in MHz, \(c\) is a constant depending upon the channel scenarios. For coastal communication environments, \(c=72.5\) dB [23]. For AIS receivers, the channel bandwidth \(B=25\) kHz and the carrier frequency \(f=162\) MHz. Using the Equations (17) and (18), we can determine that the AIS receiver noise is \(-117\) dBm. Therefore, when the AIS signal strength is \(-107\) dBm which is the sensitivity required by the AIS standard [23], the corresponding baseband signal SNR is about 10 dB. A typical strong signal is \(-75\) dBm, and the corresponding baseband signal SNR is approximately 42 dB. Thus, the parameter SNR range was set from 0-50 dB in the simulation scheme.