## 3 Results  
### Algorithm Verification  
To verify the performance of the proposed method, theory analysis and numerical simulation were carried out. In the remainder of this paper, the searching space included 1/2 of code CHIP step and 16 frequency shift bins, so the overall number of the whole searching space \(N\) was 32,736. Since the data rate of GPS L1 C/A signal is 50 bps, the coherent integration was limited to 10 ms due to bit transition. In the first dwell, 10 ms coherent integration and five times non-coherent integration were combined, which means a half-bit integration method was used in coherent integration [19]. In the second dwell, coherent integration time was still 10 ms and non-coherent time was extended from 5 to 10 times. In Equation (6), \(B_{pd}\) is 4.092 MHz, \(F_{s}\) is 16.368 MHz, and \(L_{sq}\) and \(L_{d}\) are both regarded as 2 dB.  
Based on Equations (3)-(10), the theoretical performance of the proposed method is derived and shown in Figure 2. Apparently, the detection probability increased with the ascending number of M. The detection probability was above 90% when M equaled 160 with signal CN0 (carrier-to-noise density) equal to 24 dB/Hz, while it did not increase notably when \(M\) was over 160. Thus, it provides a reasonable balance between detection probability and acquisition single computation overhead when M = 160.  
For further study, the proposed acquisition method was established with MATLAB and Monte-Carlo simulations were carried out whose data were collected from the Spinert GPS Constellation Simulator. In the Monte-Carlo simulation, the acquisition simulation parameters were the same as the theoretical analysis. For comparison of performance between different acquisition methods, the DD/MAX method was simulated in the same simulation environment and all \(N\) feasible cells were divided into 16 sections to obtain a low false alarm probability.  
Figure 3a shows the detection probability of MP/DD and DD/MAX methods by Monte-Carlo simulation. When detecting weak signals (CN0 equal to 23 dB/Hz), our method obviously had a detection probability of about 67%, being higher than that of DD/MAX which was only 18%. Besides, the false alarm probability of MP/DD was also acceptable because it was the complementary set of its high detection probability. Overall, these simulation results are consistent with the above theoretical analysis.  
Not only did MP/DD have remarkably high sensitivity (verified above), but it had lower AMCO compared to DD/MAX. According to Equations (3) and (10), the AMCO of MP/DD and DD/MAX were derived and normalized. As shown in Figure 3, the AMCO of MP/DD was only 26% of DD/MAX when CN0 was 23 dB/Hz. When CN0 exceeded 23 dB/Hz, the AMCO of MP/DD and DD/MAX were significantly decreased, where the difference between them was small enough to be ignored.  
Figure 3: (**a**) Monte-Carlo simulation and theoretical value of detection probability with MP/DD (proposed) and double-dwell/maximum (DD/MAX) (conventional) methods; (**b**) Monte-Carlo simulation of acquisition mean computation overhead in MP/DD and DD/MAX methods.  
Figure 2: Theoretical detection probability of multi-peak double-dwell (MP/DD) with different M values.