BDS/Galileo四频精密单点定位模型性能分析与比较

北斗卫星导航系统和Galileo卫星系统都可以提供4个频率信号上的服务。本文通过与双频无电离层模型（DF）比较，评估分析了4种BDS/Galileo四频PPP模型性能，即四频无电离层双组合模型（QF1）、四频无电离层组合模型（QF2）、四频非差非组合模型（QF3）和附加电离层约束四频非差非组合模型（QF4），同时通过等价性原则理论上证明了QF1、QF2、QF3模型的等价性。此外，用1个月参考站的静态数据和1组动态数据分析了四频静态，仿动态和动态PPP性能。试验结果表明，BDS-3 B1C和B2a新频点伪距噪声要略大于B1I和B3I信号，Galileo卫星4个频率上的伪距噪声相差并不明显。对于静态和仿动态PPP模型，QF1、QF2和QF3模型定位性能基本上一致。通过附加外部电离层约束，四频PPP模型性能受到影响，BDS（BDS-2+BDS-3）静态QF4模型相比于QF1、QF2和QF3模型平均收敛时间分别减少了4.4%、4.4%和5.4%，Galileo静态Q4模型平均收敛时间相比于Q3模型增加了16.8 min。对于动态PPP，四频PPP模型相比于双频PPP性能得到提升显著，相比于QF1模型，BDS和Galileo单系统QF4模型三维定位精度分别提高了11.4%和31.4%。BDS/Galileo双系统PPP性能要优于单系统PPP。

Analysis and comparisons of the BDS/Galileo quad-frequency PPP models performances

Chinese BeiDou navigation satellite system (BDS) and Galileo system can provide the services of quad-frequency observations. In this paper, we assess the BDS/Galileo quad-frequency precise point positioning (PPP) models, i.e., PPP model with two ionosphere-free combinations (QF1), PPP model with one ionosphere-free combination (QF2), undifferenced uncombined PPP model (QF3) and ionosphere-constrained undifferenced uncombined PPP model (QF4), by comparing the dual-frequency ionosphere-free PPP model (DF). The equivalence of the QF1, QF2 and QF3 models is theoretically demonstrated by the equivalence principle. The static and simulated kinematic PPP performances are evaluated and investigated with one-month period observations from the network stations and the kinematic PPP performances are verified with a kinematic experiment in the campus. The results show that the pseudorange noises of BDS-3 B1C and B2a signals are larger than the B1I and B3I signals and the pseudorange noises differences for the Galileo quad-frequency signals are not obvious. The performances of the QF1, QF2 and QF3 models are basically consistent for the static and simulated kinematic PPP. By adding the external ionospheric constraint, the quad-frequency PPP performances are affected. Compared to the QF1, QF2 and QF3 models, the mean convergence time of the static BDS (BDS-2+BDS-3) model are reduced by 4.4%, 4.4% and 5.4%, respectively. The mean convergence time of static Q4 model increases 16.8 minutes when compared to the QF3 model. Compared to the dual-frequency PPP, the quad-frequency kinematic PPP performances are obviously improved. The three-dimensional positioning accuracy of BDS and Galileo QF4 models are improved by 11.4% and 31.4%, respectively, when compared to the QF1 models. Furthermore, the BDS/Galileo kinematic PPP models perform better than the single-system solutions.