# Variance-Triggered Two-Step GPS Acquisition
## 6 Related Works  
Time-domain algorithms seek to improve detection requirements like success rate and acquisition time mainly by increasing the length of the observed signal and then folding or sub-sampling it [19; 20]. The longer signal length improves accuracy at lower C/N0 ratios because the averaging process reduces noise influence. These strategies, however, iterate over the phase and frequency cells differently than the proposed VTTS strategy. Since the correlation peaks raise incrementally in the VTTS acquisition, the detection of peaks may happen while they are still forming. This is the main difference between the existing time-domain acquisition techniques and the VTTS acquisition. Increasing integration time is recurrently part of the most effective approaches to increase the success rate. In practice, the existing strategies may always present a trade-off between success rate and acquisition time. We have chosen to not exploit this trade-off in this work, leaving this for a forthcoming investigation. Instead, we have shown that even with only 1 millisecond of the signal, \begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & \multicolumn{8}{c}{**C/N0 (dB-Hz)**} \\ \cline{2-10}  & **34** & **36** & **38** & **40** & **42** & **44** & **46** & **48** & **50** \\ \hline \multicolumn{10}{c}{**Acquisition Time (s)**} \\ \hline SA-FTD & 22.80 & 23.16 & 22.83 & 23.18 & 19.05 & 16.07 & 14.79 & 13.57 & 13.43 \\ SA-VTD & 17.49 & 19.10 & 22.78 & 21.31 & 14.35 & 14.36 & 16.30 & 13.98 & 12.86 \\ SA-RD & 21.57 & 21.02 & 23.33 & 21.67 & 20.37 & 14.70 & 15.87 & 13.97 & 13.25 \\ VTTS 1 round & 0.73 & 0.73 & 0.73 & 0.72 & 0.72 & 0.74 & 0.72 & 0.74 & 0.79 \\ VTTS 5 rounds & 4.39 & 4.38 & 4.38 & 4.38 & 4.40 & 4.28 & 3.70 & 2.70 & 2.20 \\ VTTS 10 rounds & 8.10 & 8.06 & 8.05 & 8.08 & 8.11 & 6.87 & 5.49 & 3.19 & 2.68 \\ VTTS 16 rounds & 11.70 & 11.76 & 11.78 & 11.74 & 11.53 & 8.70 & 6.60 & 3.30 & 2.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: This table represents the time to acquisition vs C/N0 for the three SA versions and VTTS acquisition with four different rounds (1, 5, 10, 16). The performance of the algorithm was superior in all cases. For round = 1 the VTTS was up to 21 times faster. However, the success rate for this round = 1 is worse than the SA. A better comparison scenario is from round = 5. In this scenario the VTTS was 5.8 times better than the SA in the best C/N0 and 3.7 times better in the worst C/N0 analyzed. When we used round = 16, the gains were 1.85 and 5.05 in the worst and best C/N0 respectively. Figure 10: Time to detection for the three SA versions and VTTS acquisition with the maximum number of detection rounds equal to 1, 5, 10 and 16.  
equivalent to a single complete integration over the 1023 chips, the VTTS approach can be quite effective. Longer integration periods would certainly improve VTTS accuracy, as it is the case for the other time domain methods. This work is considerably different from a preliminary version of the proposed strategy, as presented in [12]. In this work we introduce the mathematical support, an unprecedented memory usage analysis, and a more thorough analysis of success rate, false positive rates, and time to acquisition that involved several levels of C/N0 ratio. The proposed variance-triggered detection differs from another existing method that does not use a fixed correlation-value threshold to detect the presence of a signal. While the proposed technique uses the variance of normalized peaks, the Ratio Detection (RD) [14] detects signal power based on the ratio of the largest and the second largest correlation value of an incoming signal. In the RD, when the ratio between the peak values exceeds a selected threshold, the signal is considered acquired. In both methods, if more than one peak is selected inside the same chip, the detection algorithm complicates slightly because they have almost the same energy. To solve that, our technique uses the normalized variance of the highest and the lowest peaks from a list of the highest peaks.