BDS/GPS差分系统间偏差估计算法及性能分析
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摘要
基于BDS/GPS单频紧组合相对定位模型,提出联合卡尔曼滤波与粒子滤波估计差分系统间偏差(DISB)的算法,并利用实测短基线数据对比分析卡尔曼滤波算法与本文算法估计DISB的效果。实验表明,载波DISB的整数部分会影响参考卫星站间单差模糊度的估计,从而影响载波DISB小数部分的估计结果;利用本文算法估计并改正DISB后得到的模糊度解算的可靠性和固定解精度均优于卡尔曼滤波,固定解精度最大可提高10%～20%。
In this paper,based on the relative positioning model of BDS/GPS single-frequency tight combination,we propose a combination algorithm of Kalman filter and particle filter to estimate the differential inter-system bias(DISB)of BDS/GPS tightly combined,and then analyze the algorithm performance by contrast with Kalman filter algorithm using short baseline data.The results show that the integer part of the phase DISB can affect the estimation of the DISB fractional part by changing the single-differenced ambiguity of pivot satellite.Further,the DISB of the proposed algorithm estimation corrects the tight combination and can improve the reliability of ambiguity resolution and fixed solution precision.Fixed solution precision can be increased by 10%～20%.
In this paper,based on the relative positioning model of BDS/GPS single-frequency tight combination,we propose a combination algorithm of Kalman filter and particle filter to estimate the differential inter-system bias(DISB)of BDS/GPS tightly combined,and then analyze the algorithm performance by contrast with Kalman filter algorithm using short baseline data.The results show that the integer part of the phase DISB can affect the estimation of the DISB fractional part by changing the single-differenced ambiguity of pivot satellite.Further,the DISB of the proposed algorithm estimation corrects the tight combination and can improve the reliability of ambiguity resolution and fixed solution precision.Fixed solution precision can be increased by 10%～20%.
引文
[1]张小红,吴明魁,刘万科.Beidou B2/Galileo E5b短基线紧组合相对定位模型及性能评估[J].测绘学报,2016,45(增2):1-11(Zhang Xiaohong,Wu Mingkui,Liu Wanke.Model and Performance Analysis of Tight Combined Beidou B2and Galileo E5bRelative Positioning for Short Baseline[J].Acta Geodaetica et Cartographica Sinica,2016,45(S2):1-11)
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[4] Odijk D,Teunissen P J G.Characterization of between-Receiver GPS-Galileo Inter-System Biases and Their Effect on Mixed Ambiguity Resolution[J].GPS Solutions,2013,17(4):521-533
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[6]周英东,柴洪洲,王敏,等.BDS/Galileo紧组合系统间偏差估计与模糊度固定效果分析[J].测绘科学技术学报,2017,34(2):141-146(Zhou Yingdong,Chai Hongzhou,Wang Min,et al.Assessment of BDS/Galileo Inter-System Biases and Their Effect on Ambiguity Resolution[J].Journal of Geomatics Science and Technology,2017,34(2):141-146)
[7] Odolinski R,Teunissen P J G,Odijk D.Combined BDS,Galileo,QZSS and GPS Single-Frequency RTK[J].GPS Solutions,2014,19(1):151-163
[8]楼益栋,龚晓鹏,辜声峰,等.BDS/GPS混合双差分RTK定位方法及结果分析[J].大地测量与地球动力学,2016,36(1):1-5(Lou Yidong,Gong Xiaopeng,Gu Shengfeng,et al.An Algorithm and Results Analysis for GPS+BDS Inter-System Mix Double-Difference RTK[J].Journal of Geodesy and Geodynamic,2016,36(1):1-5)
[9]隋心,邹鑫慈,徐爱功,等.BDS/GPS接收机端系统偏差实时估计方法[J].测绘科学,2016,41(12):106-109(Sui Xin,Zou Xinci,Xu Aigong,et al.A Real-Time Estimation Algorithm for the BDS/GPS Inter-System Biases at the Receiver End[J].Science of Surveying and Mapping,2016,41(12):106-109)
[10]Tian Y M,Ge M R,Neitzel F,et al.Particle Filter-Based Estimation of Inter-System Phase Bias for Real-Time Integer Ambiguity Resolution[J].GPS Solutions,2017,21(3):949-961
[11]Nadarajah N,Teunissen P J G,Raziq N.Beidou Inter-Satellite-Type Bias Evaluation and Calibration for Mixed Receiver Attitude Determination[J].Sensors,2013,13(7):9 435-9 463
[12]Nadarajah N,Teunissen P J G,Sleewaegen J M,et al.The Mixed-Receiver Beidou Inter-Satellite-Type Bias and Its Impact on RTK Positioning[J].GPS Solutions,2015,19(3):357-368
[13]Takasu T,Yasuda A.Development of the Low-Cost RTKGPS Receiver with an Open Source Program Package RTK LIB[C].International Symposium on GPS/GNSS,Jeju,2009
[14]Teunissen P J G.The Least-Squares Ambiguity Decorrelation Adjustment:A Method for Fast GPS Integer Ambiguity Estimation[J].Journal of Geodesy,1995,70(1-2):65-82
[15]Tian Y M,Ge M R,Neitzel F.Particle Filter-Based Estimation of Inter-Frequency Phase Bias for Real-Time GLONASS Integer Ambiguity Resolution[J].Journal of Geodesy,2015,89(11):1 145-1 158
[2] Paziewski J,Wielgosz P.Accounting for Galileo-GPS Inter-System Biases in Precise Satellite Positioning[J].Journal of Geodesy,2015,89(1):81-93
[3] Odijk D,Teunissen P J G,Huisman L.First Results of Mixed GPS+GIOVE Single-Frequency RTK in Australia[J].Journal of Spatial Science,2012,57(1):3-18
[4] Odijk D,Teunissen P J G.Characterization of between-Receiver GPS-Galileo Inter-System Biases and Their Effect on Mixed Ambiguity Resolution[J].GPS Solutions,2013,17(4):521-533
[5] Wu M K,Zhang X H,Liu W K,et al.Tightly Combined Beidou B2and Galileo E5bSignals for Precise Relative Positioning[J].Journal of Navigation,2017,70(6):1-14
[6]周英东,柴洪洲,王敏,等.BDS/Galileo紧组合系统间偏差估计与模糊度固定效果分析[J].测绘科学技术学报,2017,34(2):141-146(Zhou Yingdong,Chai Hongzhou,Wang Min,et al.Assessment of BDS/Galileo Inter-System Biases and Their Effect on Ambiguity Resolution[J].Journal of Geomatics Science and Technology,2017,34(2):141-146)
[7] Odolinski R,Teunissen P J G,Odijk D.Combined BDS,Galileo,QZSS and GPS Single-Frequency RTK[J].GPS Solutions,2014,19(1):151-163
[8]楼益栋,龚晓鹏,辜声峰,等.BDS/GPS混合双差分RTK定位方法及结果分析[J].大地测量与地球动力学,2016,36(1):1-5(Lou Yidong,Gong Xiaopeng,Gu Shengfeng,et al.An Algorithm and Results Analysis for GPS+BDS Inter-System Mix Double-Difference RTK[J].Journal of Geodesy and Geodynamic,2016,36(1):1-5)
[9]隋心,邹鑫慈,徐爱功,等.BDS/GPS接收机端系统偏差实时估计方法[J].测绘科学,2016,41(12):106-109(Sui Xin,Zou Xinci,Xu Aigong,et al.A Real-Time Estimation Algorithm for the BDS/GPS Inter-System Biases at the Receiver End[J].Science of Surveying and Mapping,2016,41(12):106-109)
[10]Tian Y M,Ge M R,Neitzel F,et al.Particle Filter-Based Estimation of Inter-System Phase Bias for Real-Time Integer Ambiguity Resolution[J].GPS Solutions,2017,21(3):949-961
[11]Nadarajah N,Teunissen P J G,Raziq N.Beidou Inter-Satellite-Type Bias Evaluation and Calibration for Mixed Receiver Attitude Determination[J].Sensors,2013,13(7):9 435-9 463
[12]Nadarajah N,Teunissen P J G,Sleewaegen J M,et al.The Mixed-Receiver Beidou Inter-Satellite-Type Bias and Its Impact on RTK Positioning[J].GPS Solutions,2015,19(3):357-368
[13]Takasu T,Yasuda A.Development of the Low-Cost RTKGPS Receiver with an Open Source Program Package RTK LIB[C].International Symposium on GPS/GNSS,Jeju,2009
[14]Teunissen P J G.The Least-Squares Ambiguity Decorrelation Adjustment:A Method for Fast GPS Integer Ambiguity Estimation[J].Journal of Geodesy,1995,70(1-2):65-82
[15]Tian Y M,Ge M R,Neitzel F.Particle Filter-Based Estimation of Inter-Frequency Phase Bias for Real-Time GLONASS Integer Ambiguity Resolution[J].Journal of Geodesy,2015,89(11):1 145-1 158