# An Improved PSO Algorithm and Its Application in GNSS Ambiguity Resolution
## 3 Experiments and Result Analysis
### Performance Analysis of IPSO-AR  
In this study, we use one static short baseline (approximately 1.2 km) to validate the performance of IPSO-AR. The average GPS/BDS visible satellite number is 7-8. The truth values of the estimated ambiguity-fixed resolution are obtained from multiepoch process results by using the GNSS open source software RTKLIB [39; 40], which users can download from [[http://www.rtklib.com](http://www.rtklib.com)]([http://www.rtklib.com](http://www.rtklib.com)). The processing strategies and methods of RTKLIB software are shown in Table 1.  
### Performance Analysis of IPSO-AR  
In this study, we use one static short baseline (approximately 1.2 km) to validate the performance of IPSO-AR. The average GPS/BDS visible satellite number is 7-8. The truth values of the estimated ambiguity-fixed resolution are obtained from multiepoch process results by using the GNSS open source software RTKLIB [39; 40], which users can download from [[http://www.rtklib.com](http://www.rtklib.com)]([http://www.rtklib.com](http://www.rtklib.com)). The processing strategies and methods of RTKLIB software are shown in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline
**Main Options** & **Setting** \\ \hline System & GPS/BDS \\ Observation Frequencies & L1/B1 \\ Elevation Cut-Off Angle & 15\({}^{\circ}\) \\ Positioning Mode & Static \\ Parameter Estimation & EKF \\ Stochastic Model & Elevation angle \\ Satellite Ephemeris & Broadcast \\ Satellite Antenna Model & IGS08.ATX \\ Receiver Antenna Model & IGS08.ATX \\ Ambiguity Resolution & LAMBDA \\ Ambiguity Validation Threshold & 3 \\ Integer Ambiguity Resolution & Continuous \\ Troposphere Correction & Saastamoinen \\ Ionosphere Correction & Broadcast Ionosphere Model (Klobuchar Mode) \\ Earth Tides Correction & OFF \\ Code/Carrier-Phase Error Ratio & 100 \\ Carrier-Phase Error & 0.003 + 0.003/sin(el) m \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Processing strategies and methods of RTKLIB software. GPS: Global Positioning System; BDS: BeiDou Navigation Satellite System; EKF: extended Kalman filter; LAMBDA: least-squares ambiguity decorrelation. Figure 4: Example of IPSO–AR search procedure. DD: double differenced. We adopt two indices, namely, efficiency and correct rate, to evaluate the performance of IPSO-AR. Dimension and ADOP can reflect the property of any ambiguity float resolution, which is expected to be related to the performance of IPSO-AR. Meanwhile, similar to the performances of other intelligent search algorithms and as shown by our experimental results, the performance of IPSO-AR depends on parameter settings. Among the nine parameters introduced in Section 2.2.3, the performance of IPSO-AR is the most sensitive to total population size (\(n\)) and optimal population size (\(s\)). On the basis of the above analysis, we first consider the influence of ambiguity precision on the performance of IPSO-AR. Thus, we investigate three different experimental schemes that correspond to three different kinds of ambiguity precision (high, general, or low precision) under three different parameter settings (P1, P2, and P3). Only parameters \(n\) and \(s\) are considered in our experiment. Other parameters are set similarly to those introduced in Section 3.1. The specific details of the experimental schemes are shown in Table 2.  
We use various dimensions (from 3 to 12) of GPS/BDS DD ambiguity float resolution in independent experiments to analyze the relationship between ambiguity dimension and the performance of IPSO-AR in different schemes with different parameter settings (Table 2). The corresponding satellites and frequency information are provided in Table 3. All the data in our experiment are obtained by the GPS/BDS receiver, and are not simulated. We simultaneously perform experiments on SPSO-AR to compare the performances of IPSO-AR and SPSO-AR. In contrast to IPSO-AR, SPSO-AR uses fixed inertia weight (setting of 0.5). The parameter setting for SPSO-AR is similar to that for IPSO-AR, but lacks the \(s\) term.