PPP algorithm for multi-frequency GPS/Galileo/BDS-3 with IFCB time-varying characteristic constraints

doi:10.11947/j.AGCS.2025.20240183

Abstract

Abstract:

The influence of the third frequency on the positioning model needs to be considered in multi-frequency high-precision positioning. The current traditional inter frequency clock bias (IFCB) estimation method is not well adapted to real-time applications, and the reliability and accuracy are limited by the number of stations in the reference network, so the study of IFCB parameters is crucial. In this paper, we focus on studying and analyzing the impact of IFCB on multi-frequency PPP of multi-GNSS, propose a multi-frequency PPP algorithm considering the constraints of time-varying characteristics of IFCB parameters, proposed an algorithm for extracting power spectral density based on station IFCB observations, and comprehensively analyze the time-varying characteristics of IFCB and the impacts of different IFCB models on the performance of un-differential and un-combined PPP. The experimental results show that it is feasible and efficient to extract the IFCB power spectral density using station IFCB observations. Compared with the ignoring IFCB method, the PPP has the largest improvement in convergence time by 46.51% using the random walk process estimation IFCB considering the constraints of PSD, and the average improvement by 43.54% and 34.50% using the iGMAS product and CNES product, and the 3D positioning accuracy by 41.68%, 32.24% and 24.64%, respectively. The adoption of power spectral density constrained IFCB parameters with IFCB time characteristics can truly reflect the IFCB changes. Therefore, in multi-GNSS multi-frequency PPP processing, a random model process that takes the IFCB parameters to be constrained by time-varying properties can speed up convergence and improve the positioning accuracy, which is better than the product correction method and more conducive to the application of real-time multi-frequency PPP.

Key words: tri-frequency, PPP, multi-GNSS, random-walk, IFCB, time-varying

CLC Number:

P228

Yangyang LU, Huizhong ZHU, Bo LI, Jun LI, Aigong XU. PPP algorithm for multi-frequency GPS/Galileo/BDS-3 with IFCB time-varying characteristic constraints[J]. Acta Geodaetica et Cartographica Sinica, 2025, 54(2): 233-247.

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选项	处理策略
观测值	非组合观测值
频率	BDS-3：B1、B3、B2a；GPS：L1、L2、L5；GA L：E1、E5a、E5b
参数估计	EKF
采样率/s	30
权重方案	高度角定权模型
截止高度角/（°）	7
卫星轨道	WH U精密星历
卫星钟差	WH U精密钟差
PCO	IGS14.atx
PCV	GPS/Galileo
相位缠绕	模型改正
地球固体潮
海洋潮汐
极移
相对论效应
对流层延迟	干延迟（Saastamoinen模型改正）+湿延迟（随机游走估计）
电离层延迟	随机游走
ISB	白噪声
IFB	白噪声
测站坐标	动态，白噪声估计
接收机钟差	白噪声
模糊度	弧段内常数估计

PRN	IFCB_CNT/m	IFCB_iGMAS/m
G01	0.10	0.13
G03	0.13	0.17
G06	0.11	0.12
G08	0.18	0.22
G09	0.14	0.12
G10	0.13	0.14
G24	0.09	0.05
G25	0.11	0.11
G26	0.12	0.10
G27	0.15	0.19
G30	0.08	0.06
G32	0.09	0.10

PRN	PSD均值	PSD振幅
G01	0.07	0.13
G03	0.19	1.24
G06	0.09	0.61
G08	0.16	0.88
G09	0.08	0.25
G10	0.05	0.20
G24	0.04	0.17
G25	0.16	0.37
G26	0.13	0.39
G27	0.06	0.09
G30	0.03	0.12
G32	0.13	0.28

参数	IFCB方案	E	N	U	3D
RMS/m	NO	0.025 2	0.018 6	0.037 3	0.048 7
	CNT	0.016 0	0.014 0	0.029 8	0.036 7
	iGMAS	0.014 6	0.012 3	0.026 9	0.033 0
	RW	0.012 0	0.009 3	0.024 0	0.028 4
	WN	0.012 6	0.009 5	0.024 6	0.029 2
提升率/（%）	CNT	36.51	24.73	20.11	24.64
	iGMAS	42.06	33.87	27.88	32.24
	RW	52.38	50.00	35.66	41.68
	WN	50.00	48.92	34.05	40.04

IFCB方案	收敛时间平均数/min	收敛时间中位数/min
NO	30.64	22.26
CNT	20.07	17.94
iGMAS	17.30	14.82
RW	16.39	14.64
WN	16.42	14.92