CN115755115A - PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology - Google Patents
PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology Download PDFInfo
- Publication number
- CN115755115A CN115755115A CN202211570241.0A CN202211570241A CN115755115A CN 115755115 A CN115755115 A CN 115755115A CN 202211570241 A CN202211570241 A CN 202211570241A CN 115755115 A CN115755115 A CN 115755115A
- Authority
- CN
- China
- Prior art keywords
- gnss
- std
- ppp
- delay
- tropospheric
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Withdrawn
Links
- 238000005516 engineering process Methods 0.000 title claims abstract description 62
- 238000000034 method Methods 0.000 title claims abstract description 41
- 230000006872 improvement Effects 0.000 title claims abstract description 9
- 239000005436 troposphere Substances 0.000 title claims description 20
- 238000004587 chromatography analysis Methods 0.000 title claims description 8
- 238000003325 tomography Methods 0.000 claims abstract description 43
- 239000011159 matrix material Substances 0.000 claims description 35
- 238000013507 mapping Methods 0.000 claims description 18
- 238000012937 correction Methods 0.000 claims description 13
- 238000010276 construction Methods 0.000 claims description 9
- 239000013598 vector Substances 0.000 claims description 7
- 238000004364 calculation method Methods 0.000 claims description 6
- 238000000354 decomposition reaction Methods 0.000 claims description 4
- 230000008569 process Effects 0.000 claims description 3
- 238000012950 reanalysis Methods 0.000 claims description 3
- 238000011084 recovery Methods 0.000 claims description 3
- 150000001875 compounds Chemical class 0.000 claims 3
- 238000001914 filtration Methods 0.000 claims 2
- 238000011835 investigation Methods 0.000 claims 2
- 238000009825 accumulation Methods 0.000 claims 1
- 230000001902 propagating effect Effects 0.000 claims 1
- 230000007423 decrease Effects 0.000 description 2
- 230000001934 delay Effects 0.000 description 2
- 230000007935 neutral effect Effects 0.000 description 2
- 238000007619 statistical method Methods 0.000 description 2
- 230000008859 change Effects 0.000 description 1
- 238000013461 design Methods 0.000 description 1
- 230000000694 effects Effects 0.000 description 1
- 230000002706 hydrostatic effect Effects 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000011160 research Methods 0.000 description 1
Images
Landscapes
- Position Fixing By Use Of Radio Waves (AREA)
Abstract
本发明公开了基于GNSS对流层层析技术的PPP改善方法,涉及GNSS精密单点定位技术领域,针对目前PPP技术中观测方程包含的对流层延迟作为未知参数难以精确估计,观测方程中的未知参数较多,PPP技术的定位精度和收敛速度不够精准的问题,现提出如下方案,包括以下步骤:S1:基于PPP技术的斜路径对流层延迟STD估算;S2:层析区域网格内折射率反演;S3:利用GNSS对流层层析技术的斜路径对流层延迟STD反演;S4:GNSS对流层层析技术改善PPP定位方法。本发明引入GNSS对流层层析技术,对卫星信号路径上的STD值进行反演,并将反演的STD改正到PPP技术的观测方程中,以减少观测方程中的未知参数,进一步提升PPP技术的定位精度和收敛速度。
The invention discloses a PPP improvement method based on GNSS tropospheric tomography technology, and relates to the technical field of GNSS precise single point positioning. It is difficult to accurately estimate the tropospheric delay contained in the observation equation in the current PPP technology as an unknown parameter, and there are many unknown parameters in the observation equation. , the positioning accuracy and convergence speed of PPP technology are not accurate enough, the following scheme is proposed, including the following steps: S1: Estimation of oblique path tropospheric delay STD based on PPP technology; S2: Refractive index inversion in the tomographic area grid; S3 : Oblique path tropospheric delay STD inversion using GNSS tropospheric tomography; S4: GNSS tropospheric tomography improves PPP positioning method. The present invention introduces GNSS tropospheric tomography technology, inverts the STD value on the satellite signal path, and corrects the inverted STD into the observation equation of the PPP technology, so as to reduce the unknown parameters in the observation equation and further improve the PPP technology. Positioning accuracy and convergence speed.
Description
技术领域technical field
本发明涉及GNSS精密单点定位技术领域,尤其涉及基于GNSS对流层层析技术的PPP改善方法。The invention relates to the technical field of GNSS precise single point positioning, in particular to a PPP improvement method based on GNSS tropospheric tomography technology.
背景技术Background technique
全球卫星定位导航系统最核心和基础的功能与服务是授时和定位,其中定位可分为相对定位和绝对定位。相对定位的代表性技术为实时载波相位差分定位技术,而绝对定位的代表技术是精密单点定位(Precise Point Positioning,PPP)技术。PPP技术是指利用卫星实时或事后的精密轨道和钟差产品,对观测方程中的各项误差进行精确改正,同时采取合适的参数估计策略,在仅需一台GNSS接收机的情况下,便可实现全球范围内精密绝对定位。但GNSS信号也会受到各类误差的干扰,当信号穿过50km以下的中性大气层时,会被其中的中性大气干扰产生折射,这种折射影响被称为对流层延迟。根据卫星高度角不同,对流层延迟会对定位结果产生数米甚至数十米的误差影响。因此,对流层延迟是PPP定位中最主要的误差源之一。The core and basic functions and services of the global satellite positioning and navigation system are timing and positioning, of which positioning can be divided into relative positioning and absolute positioning. A representative technology of relative positioning is a real-time carrier phase differential positioning technology, and a representative technology of absolute positioning is a precise point positioning (Precise Point Positioning, PPP) technology. PPP technology refers to the use of satellite real-time or post-event precision orbit and clock error products to accurately correct various errors in the observation equation, and at the same time adopt an appropriate parameter estimation strategy. In the case of only one GNSS receiver, it is convenient. Accurate absolute positioning can be achieved worldwide. However, GNSS signals will also be interfered by various errors. When the signal passes through the neutral atmosphere below 50km, it will be refracted by the neutral atmospheric interference. This refraction effect is called tropospheric delay. Depending on the altitude angle of the satellite, the tropospheric delay will have an error of several meters or even tens of meters in the positioning result. Therefore, tropospheric delay is one of the most important sources of error in PPP positioning.
传统PPP定位中,斜路径对流层延迟(Slant Tropospheric Delay,STD)可表示为天顶方向对流层延迟(Zenith Tropospheric Delay,ZTD)与映射函数(MappingFunctions,MF)的乘积加上大气水平梯度改正项与其映射函数乘积。ZTD可分为天顶干延迟(Zenith Hydrostatic Delay,ZHD)和天顶湿延迟(Zenith Wet Delay,ZWD)。在处理中,由于ZHD较稳定且易于模型化,故常采用经验模型进行改正,如Saastamoinen模型、Hopfiled模型等;而ZWD不确定性较强,难以建立精确模型改正,因此利用参数估计方法确定其大小;梯度改正项为水平梯度映射函数乘以水平梯度改正北方向与东方向的分量。但经验模型和未知参数估计往往存在一定的偏差,为了减少这种估计误差,本发明提出一种利用GNSS层析技术改善PPP定位精度及收敛速度的方法。In traditional PPP positioning, the Slant Tropospheric Delay (STD) can be expressed as the product of the Zenith Tropospheric Delay (ZTD) and the mapping function (MappingFunctions, MF) plus the atmospheric horizontal gradient correction term and its mapping function product. ZTD can be divided into Zenith Dry Delay (Zenith Hydrostatic Delay, ZHD) and Zenith Wet Delay (Zenith Wet Delay, ZWD). In processing, because ZHD is relatively stable and easy to model, empirical models are often used for correction, such as Saastamoinen model, Hopfield model, etc.; while ZWD has strong uncertainty, it is difficult to establish an accurate model correction, so the parameter estimation method is used to determine its size ; The gradient correction item is the horizontal gradient mapping function multiplied by the horizontal gradient to correct the north and east components. However, there is often a certain deviation between the empirical model and the unknown parameter estimation. In order to reduce this estimation error, the present invention proposes a method for improving the PPP positioning accuracy and convergence speed by using GNSS tomographic technology.
地基GNSS对流层层析技术是指利用大量卫星信号射线上的信息重构区域三维对流层延迟结构的方法。该技术首先将研究区域离散成若干个网格,并假设卫星信号在每个网格内的折射率在一定时间内为一常数且分布均匀;每条信号路径上的观测值包含了该路径上的对流层延迟信息,因此,将每条射线在不同网格内折射率与该卫星信号在该网格内截距相乘并进一步积分得到该路径上的斜路径总延迟,多个测站对多个卫星形成的所有倾斜路径观测方程即构成了GNSS对流层层析观测方程,再结合建立的层析约束方程,得到GNSS对流层层析模型,然后通过迭代算法或非迭代算法解算GNSS对流层层析模型,从而获得各网格的折射率信息。Ground-based GNSS tropospheric tomography refers to the method of reconstructing the regional three-dimensional tropospheric delay structure by using the information on a large number of satellite signal rays. This technique first discretizes the research area into several grids, and assumes that the refractive index of the satellite signal in each grid is a constant and uniformly distributed within a certain period of time; the observations on each signal path include the The tropospheric delay information, therefore, the refraction index of each ray in different grids is multiplied by the intercept of the satellite signal in the grid and further integrated to obtain the total delay of the oblique path on the path. All oblique path observation equations formed by satellites constitute the GNSS tropospheric tomographic observation equation, combined with the established tomographic constraint equations, the GNSS tropospheric tomographic model is obtained, and then the GNSS tropospheric tomographic model is solved by iterative or non-iterative algorithms , so as to obtain the refractive index information of each grid.
但是,目前PPP技术中观测方程包含的对流层延迟作为未知参数难以精确估计,观测方程中的未知参数较多,PPP技术的定位精度和收敛速度不够精准。However, the tropospheric delay contained in the observation equation in the current PPP technology is difficult to accurately estimate as an unknown parameter. There are many unknown parameters in the observation equation, and the positioning accuracy and convergence speed of the PPP technology are not accurate enough.
发明内容Contents of the invention
本发明的目的是为了解决目前PPP技术中观测方程包含的对流层延迟作为未知参数难以精确估计,观测方程中的未知参数较多,PPP技术收敛速度较慢的缺点,提出GNSS对流层层析技术改善精密单点定位精度及加快收敛速度方法。The purpose of the present invention is to solve the disadvantages that the tropospheric delay included in the observation equation in the current PPP technology is difficult to accurately estimate as an unknown parameter, there are many unknown parameters in the observation equation, and the PPP technology has a slow convergence speed. Single-point positioning accuracy and a method to speed up the convergence speed.
为了实现上述目的,本发明采用了如下技术方案:In order to achieve the above object, the present invention adopts the following technical solutions:
基于GNSS对流层层析技术的PPP改善方法,包括以下步骤:The PPP improvement method based on GNSS tropospheric tomography technology comprises the following steps:
S1:基于PPP技术的斜路径对流层延迟STD估算:S1: STD estimation of oblique path tropospheric delay based on PPP technology:
利用PPP技术估计STD时,需综合考虑观测方程的各项误差,确保得到的STD具有较可靠的初始精度,STD计算具体过程如下:When using PPP technology to estimate STD, it is necessary to comprehensively consider the errors of the observation equation to ensure that the obtained STD has a relatively reliable initial accuracy. The specific process of STD calculation is as follows:
S1.1:PPP观测方程建立:S1.1: PPP observation equation establishment:
GNSS信号在从卫星到接收机的传播中会受到各项误差的干扰,这些误差会不同程度的影响定位精度,由于GNSS伪距观测值其本身精度为米级,因此,选择改正精度更高的载波相位观测方程,在充分顾及各项误差的情况下,GNSSPPP技术中载波相位观测方程具体表达如下:The GNSS signal will be interfered by various errors in the propagation from the satellite to the receiver, and these errors will affect the positioning accuracy to varying degrees. Since the GNSS pseudo-range observation value itself has a meter-level accuracy, it is better to choose the one with higher correction accuracy. The carrier phase observation equation, in the case of taking full account of various errors, the carrier phase observation equation in GNSSPPP technology is specifically expressed as follows:
式中,表示载波相位观测值,i为卫星信号频率,r和s分别代表接收机和卫星系统,表示星地几何距离,tr,i为接收机钟差,表示卫星钟差,为电离层延迟,为对流层延迟,Br,i和则分别为接收机端和卫星端的相位硬件延迟,λi为信号频率的波长,表示整周模糊度,为载波相位的残差项;In the formula, Indicates the carrier phase observation value, i is the satellite signal frequency, r and s represent the receiver and satellite system respectively, Indicates the geometric distance between the satellite and the earth, t r,i is the clock error of the receiver, Indicates the satellite clock error, is the ionospheric delay, is the tropospheric delay, B r,i and are the phase hardware delays of the receiver and the satellite respectively, λi is the wavelength of the signal frequency, represents the ambiguity of the whole week, is the residual term of the carrier phase;
S1.2:天顶对流层延迟ZTD估计:S1.2: Zenith Tropospheric Delay ZTD Estimation:
在传统PPP解算中,将基准站坐标作为常数处理,在已知其精确坐标的情况下,通过可联合地表实测气压的Saastamoinen等经验模型计算先验ZHD,将已知坐标与计算出的先验ZHD一同带入观测方程作为起算数据,随后对观测方程线性化,进一步联合多测站多卫星观测信号构建观测方程矩阵,并利用整体最小二乘或卡尔曼滤波方法进行解算,即可得到估计的天顶对流层总延迟ZTD和梯度项;In the traditional PPP solution, the coordinates of the reference station are treated as constants. When the precise coordinates are known, the prior ZHD is calculated through the empirical model such as Saastamoinen, which can be combined with the surface measured air pressure. The known coordinates and the calculated prior The experimental ZHD is brought into the observation equation as the initial calculation data, and then the observation equation is linearized, and the observation equation matrix is further combined with multi-station and multi-satellite observation signals, and the overall least squares or Kalman filter method is used to solve it, and then we can get Estimated zenith tropospheric total delay ZTD and gradient terms;
S1.3:斜路径总延迟STD计算:S1.3: Calculate the total delay STD of the oblique path:
斜路径对流层延迟可表示为天顶方向对流层延迟与映射函数的乘积加上大气水平梯度改正项与其映射函数乘积;The oblique path tropospheric delay can be expressed as the product of the tropospheric delay in the zenith direction and the mapping function plus the product of the atmospheric horizontal gradient correction term and its mapping function;
天顶对流层总延迟ZTD主要包括天顶干延迟ZHD和天顶湿延迟ZWD两部分,通过地表气象参数精确计算ZHD,随后由PPP估计出的ZTD减去ZHD可得天顶湿延迟ZWD,表示如下:The total zenith tropospheric delay ZTD mainly includes two parts: the zenith dry delay ZHD and the zenith wet delay ZWD. The ZHD is accurately calculated through the surface meteorological parameters, and then the zenith wet delay ZWD can be obtained by subtracting the ZHD from the ZTD estimated by the PPP, which is expressed as follows :
ZWD=ZTD-ZHD(2)ZWD=ZTD-ZHD(2)
因此,斜路径对流层延迟STD可表示如下:Therefore, the oblique path tropospheric delay STD can be expressed as follows:
式中,MFh表示ZHD对应的斜路径干映射函数,MFw表示ZWD对应的斜路径湿映射函数,MFg表示水平梯度映射函数,Gn和Ge分别表示水平梯度改正的北方向分量与东方向分量,为测站到卫星的方位角,εt表示对流层延迟残差;In the formula, MF h represents the oblique path dry mapping function corresponding to ZHD, MF w represents the oblique path wet mapping function corresponding to ZWD, MF g represents the horizontal gradient mapping function, G n and Ge represent the north direction component and the horizontal gradient correction respectively east component, is the azimuth angle from the station to the satellite, ε t is the tropospheric delay residual;
S2:层析区域网格内折射率反演:S2: Refractive index inversion in the grid of the tomographic region:
将利用PPP技术估算的斜路径对流层延迟STD用于GNSS对流层层析模型的构建中,具体步骤如下:The oblique path tropospheric delay STD estimated by PPP technology is used in the construction of the GNSS tropospheric tomography model. The specific steps are as follows:
S2.1:层析模型观测方程构建:S2.1: Construction of tomographic model observation equation:
通过将层析区域在三维方向上划分为多个离散的网格,并对穿过各网格的卫星信号射线上的折射率进行积分,可构建STD与折射率的积分方程:By dividing the tomographic area into multiple discrete grids in the three-dimensional direction, and integrating the refractive index on the satellite signal rays passing through each grid, the integral equation of STD and refractive index can be constructed:
STD=10-6·∫sNds (4)STD=10 -6 ∫ s Nds (4)
式中,N为大气折射率,包括干折射率和湿折射率,s表示由卫星传播到接收机的信号的路径长度。In the formula, N is the atmospheric refractivity, including dry refractivity and wet refractivity, and s represents the path length of the signal transmitted from the satellite to the receiver.
将上式离散化,则GNSS信号斜路径上对流层总延迟STD表示卫星信号穿过每个网格的截距与该网格内大气折射率乘积之和:Discretizing the above formula, the total tropospheric delay STD on the oblique path of the GNSS signal represents the sum of the intercept of the satellite signal passing through each grid and the product of the atmospheric refractive index in the grid:
STD=∑ijk(aijk·xijk) (5)STD=∑ ijk (a ijk x ijk ) (5)
式中,xijk表示(i,j,k)网格内的待估折射率,aijk表示射线在(i,j,k)网格内的截距,STD表示由PPP技术估算的GNSS卫星信号斜路径上的对流层总延迟估计值。In the formula, x ijk represents the refraction index to be estimated in the (i, j, k) grid, a ijk represents the intercept of the ray in the (i, j, k) grid, and STD represents the GNSS satellite estimated by the PPP technique Estimated total tropospheric delay on signal slant paths.
将研究区域内所有从顶部穿出的信号射线上的STD均用式(5)表示,则构成如下层析观测方程:The STD on all the signal rays passing through the top in the study area are expressed by formula (5), then the following tomographic observation equation is formed:
y=A·x (6)y=A x (6)
式中,y为从研究区域顶部穿出的信号射线上的STD组成的列向量,A为观测方程的系数矩阵,x为未知折射率参数组成的列向量。In the formula, y is a column vector composed of STD on the signal ray passing through the top of the study area, A is the coefficient matrix of the observation equation, and x is a column vector composed of unknown refractive index parameters.
S2.2:层析约束方程构建:S2.2: Construction of tomographic constraint equation:
由于层析区域上空GNSS卫星分布不均以及站点数目不足,使得层析区域很多网格没有射线穿过,导致观测方程的系数矩阵病态,在对层析方程求解时会出现不适定问题,因此,需构建一定的约束方程建立网格在水平和垂直方向上的函数关系,可根据高斯加权函数方法或水平平滑约束的方法构建水平约束方程,依据折射率随高度增加呈指数递减的特性,建立垂直网格内的垂直函数关系。此外,可根据层析区域内无线电探空资料、数值预报再分析资料等建立层析模型的先验信息;Due to the uneven distribution of GNSS satellites over the tomography area and the insufficient number of stations, many grids in the tomography area do not have rays passing through, resulting in ill-conditioned coefficient matrix of the observation equation, and ill-posed problems will occur when solving the tomography equation. Therefore, It is necessary to construct a certain constraint equation to establish the functional relationship between the grid in the horizontal and vertical directions. The horizontal constraint equation can be constructed according to the Gaussian weighted function method or the horizontal smooth constraint method. According to the characteristic that the refractive index decreases exponentially with the increase of height, the vertical Vertical functional relationships within the grid. In addition, the prior information of the tomographic model can be established according to the radiosonde data in the tomographic area, the numerical forecast reanalysis data, etc.;
S2.3:GNSS对流层层析模型构建:S2.3: GNSS tropospheric tomography model construction:
根据上述构建的GNSS层析观测方程、水平约束方程、垂直约束方程以及先验约束方程,建立GNSS对流层层析模型:According to the GNSS tomographic observation equation, horizontal constraint equation, vertical constraint equation and prior constraint equation constructed above, a GNSS tropospheric tomographic model is established:
式中,H、V和I分别指水平、垂直和先验约束方程的系数矩阵,C表示先验约束信息或通过探空数据等方法统计得到的层析区域内的折射率值。In the formula, H, V, and I refer to the coefficient matrix of the horizontal, vertical, and prior constraint equations, respectively, and C represents the prior constraint information or the refractive index value in the tomographic region obtained by statistical methods such as sounding data.
S2.4:GNSS对流层层析模型解算:S2.4: GNSS tropospheric tomography model solution:
本发明通过奇异值分解法(SingularValueDecomposition,SVD)对GNSS对流层层析模型(7)进行解算,将层析模型系数矩阵分解为:The present invention solves the GNSS troposphere tomography model (7) by singular value decomposition (SingularValueDecomposition, SVD), and the tomography model coefficient matrix Decomposed into:
B=UΛVT (8)B=UΛV T (8)
式中,B∈Rm×n,U∈Rm×m,V∈Rn×n,∑=diag(σ1,σ2,…,σr),σ1≥σ2≥…≥σr,σi(i=1,2,…,r)为矩阵ATA的特征值的平方根,r为矩阵B的秩(r≤min(m,n)),U是由矩阵AAT的特征向量组成的正交矩阵,V是由矩阵ATA的特征向量组成的正交矩阵。如果矩阵B的广义逆定义为:In the formula, B∈R m×n , U∈R m×m , V∈R n×n , ∑=diag(σ 1 ,σ 2 ,…,σ r ), σ 1 ≥σ 2 ≥…≥σ r , σ i (i=1,2,…,r) is the square root of the eigenvalues of the matrix A T A , r is the rank of matrix B (r≤min(m,n)), U is an orthogonal matrix composed of eigenvectors of matrix A T , and V is an orthogonal matrix composed of eigenvectors of matrix A T A. If the generalized inverse of matrix B is defined as:
B-1=VΛ-1UΤ(9)B -1 = VΛ -1 U Τ (9)
那么,线性方程组Bx=L的解,即层析区域内的折射率可表示为:Then, the solution of the linear equation system Bx=L, that is, the refractive index in the tomographic region can be expressed as:
x=B-1L=VΛ-1UΤL(10)x=B -1 L=VΛ -1 U Τ L(10)
S3:利用GNSS对流层层析技术的斜路径对流层延迟STD反演:S3: Oblique-path Tropospheric Delay STD Retrieval Using GNSS Tropospheric Tomography:
GNSS信号斜路径上的对流层总延迟STD可表示为射线穿过层析网格内的折射率与信号在该网格截距的乘积之和,因此,基于GNSS对流层层析技术获取的层析区域每个网格内的折射率,根据卫星信号在每个网格内的截距即可计算卫星信号在该网格内的STD,最后通过累计方式得到卫星信号路径上的STD,具体公式如下:The total tropospheric delay STD on the oblique path of the GNSS signal can be expressed as the sum of the product of the refractive index of the ray passing through the tomographic grid and the signal intercept in the grid. Therefore, the tomographic area obtained based on GNSS tropospheric tomography The refractive index in each grid can calculate the STD of the satellite signal in the grid according to the intercept of the satellite signal in each grid, and finally obtain the STD on the satellite signal path by accumulating, the specific formula is as follows:
式中,xijk表示由层析技术反演得到的(i,j,k)网格内的折射率,aijk表示射线在(i,j,k)网格内的截距,表示利用GNSS对流层层析技术反演的斜路径对流层总延迟恢复值;In the formula, x ijk represents the refractive index in the (i, j, k) grid obtained by tomographic inversion, a ijk represents the intercept of the ray in the (i, j, k) grid, Indicates the tropospheric total delay recovery value of the oblique path retrieved by GNSS tropospheric tomography technology;
通过上述方法,即可计算出层析区域内不同高度角和方位角的GNSS信号斜路径上的对流层总延迟STD;Through the above method, the total tropospheric delay STD on the oblique path of the GNSS signal at different elevation angles and azimuth angles in the tomographic area can be calculated;
S4:GNSS对流层层析技术改善PPP定位方法:S4: GNSS tropospheric tomography technology improves PPP positioning method:
将GNSS对流层层析技术反演的卫星信号传播路径上的STD加入到PPP观测方程中,对传统PPP观测方程进行改进,则公式(1)可表达成如下形式:The STD on the satellite signal propagation path retrieved by GNSS tropospheric tomography technology is added to the PPP observation equation, and the traditional PPP observation equation is improved. The formula (1) can be expressed as follows:
式中,表示利用GNSS层析技术反演得到的卫星s到接收机r的斜路径对流层总延迟。In the formula, Indicates the total tropospheric delay of the oblique path from satellite s to receiver r retrieved by GNSS tomographic technology.
因此,顾及GNSS层析技术改善后的PPP观测方程可表达如下:Therefore, taking into account the improved PPP observation equation of GNSS tomographic technology, it can be expressed as follows:
式中,表示消除了STD项的载波相位观测值,为经过改正后的载波相位残差,其余各项不变;In the formula, Indicates the carrier phase observations with the STD term removed, is the corrected carrier phase residual, and the rest remain unchanged;
最后,进一步对上式线性化,并联合多测站多卫星载波相位观测值构建PPP技术的函数模型和误差模型,利用整体最小二乘或卡尔曼滤波方法对PPP函数模型进行解算,得到高精度的PPP定位结果,并加快PPP收敛速度。Finally, the above formula is further linearized, and the function model and error model of the PPP technology are constructed by combining the carrier phase observations of multiple stations and multiple satellites. Accurate PPP positioning results and speed up PPP convergence.
本发明中,所述的基于GNSS对流层层析技术的PPP改善方法,利用GNSS对流层层析技术精确估计PPP观测方程中所需的斜路径对流层延迟STD,首先需要利用PPP技术估计出不同测站对应多个卫星信号路径上的STD;然后,利用PPP技术获取的STD构建GNSS对流层层析观测方程,并联合层析约束方程构建GNSS对流层层析模型,通过迭代或非迭代方法对层析模型解算得到层析区域每个网格内的折射率;再次,根据GNSS卫星信号斜路径上的对流层延迟可表示为射线穿过层析区域内网格的折射率与相应截距的乘积之和,计算每条卫星信号路径上的STD;最后,将估算的STD反带入到PPP的观测方程中,减少观测方程中的未知参数,达到提高精度和收敛速度的目的;In the present invention, the PPP improvement method based on GNSS tropospheric tomography technology uses GNSS tropospheric tomography technology to accurately estimate the oblique path tropospheric delay STD required in the PPP observation equation. First, it is necessary to use PPP technology to estimate the corresponding STD on multiple satellite signal paths; then, use the STD obtained by PPP technology to construct the GNSS tropospheric tomographic observation equation, and combine the tomographic constraint equations to construct the GNSS tropospheric tomographic model, and solve the tomographic model by iterative or non-iterative methods Obtain the refractive index in each grid in the tomographic area; again, according to the tropospheric delay on the oblique path of the GNSS satellite signal, it can be expressed as the sum of the products of the refractive index of the ray passing through the grid in the tomographic area and the corresponding intercept, and calculate STD on each satellite signal path; finally, bring the estimated STD back into the PPP observation equation, reduce the unknown parameters in the observation equation, and achieve the purpose of improving accuracy and convergence speed;
本发明设计合理,针对PPP技术中观测方程包含的对流层延迟作为未知参数难以精确估计的现状,引入GNSS对流层层析技术,对卫星信号路径上的STD值进行反演,并将反演的STD改正到PPP技术的观测方程中,以减少观测方程中的未知参数,通过引入GNSS对流层层析技术计算的STD去弥补PPP技术参数估计的缺陷,进一步提升PPP技术的定位精度和收敛速度。The present invention is reasonable in design, aiming at the fact that the tropospheric delay contained in the observation equation in the PPP technology is difficult to accurately estimate as an unknown parameter, the GNSS tropospheric tomography technology is introduced to invert the STD value on the satellite signal path, and correct the inverted STD Into the observation equation of PPP technology, in order to reduce the unknown parameters in the observation equation, the STD calculated by GNSS tropospheric tomography technology is introduced to make up for the shortcomings of PPP technology parameter estimation, and further improve the positioning accuracy and convergence speed of PPP technology.
附图说明Description of drawings
图1为本发明提出的基于GNSS对流层层析技术的PPP改善方法的步骤流程图。Fig. 1 is a flow chart of the steps of the PPP improvement method based on GNSS tropospheric chromatography technology proposed by the present invention.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图,对本发明实施例中的技术方案进行清楚、完整地描述。显然,所描述的实施例仅仅是本发明一部分实施例,而不是全部的实施例。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Apparently, the described embodiments are only some of the embodiments of the present invention, but not all of them.
参照图1,本方案提供的一种实施例:基于GNSS对流层层析技术的PPP改善方法,包括以下步骤:With reference to Fig. 1, a kind of embodiment that this scheme provides: the PPP improvement method based on GNSS tropospheric tomography technology, comprises the following steps:
S1:基于PPP技术的斜路径对流层延迟STD估算:S1: STD estimation of oblique path tropospheric delay based on PPP technology:
利用PPP技术估计STD时,需综合考虑观测方程的各项误差,确保得到的STD具有较可靠的初始精度,STD计算具体过程如下:When using PPP technology to estimate STD, it is necessary to comprehensively consider the errors of the observation equation to ensure that the obtained STD has a relatively reliable initial accuracy. The specific process of STD calculation is as follows:
S1.1:PPP观测方程建立:S1.1: PPP observation equation establishment:
GNSS信号在从卫星到接收机的传播中会受到各项误差的干扰,这些误差会不同程度的影响定位精度,由于GNSS伪距观测值其本身精度为米级,因此,选择改正精度更高的载波相位观测方程,在充分顾及各项误差的情况下,GNSSPPP技术中载波相位观测方程具体表达如下:The GNSS signal will be interfered by various errors in the propagation from the satellite to the receiver, and these errors will affect the positioning accuracy to varying degrees. Since the GNSS pseudo-range observation value itself has a meter-level accuracy, it is better to choose the one with higher correction accuracy. The carrier phase observation equation, in the case of taking full account of various errors, the carrier phase observation equation in GNSSPPP technology is specifically expressed as follows:
式中,表示载波相位观测值,i为卫星信号频率,r和s分别代表接收机和卫星系统,表示星地几何距离,tr,i为接收机钟差,表示卫星钟差,为电离层延迟,为对流层延迟,Br,i和则分别为接收机端和卫星端的相位硬件延迟,λi为信号频率的波长,表示整周模糊度,为载波相位的残差项;In the formula, Indicates the carrier phase observation value, i is the satellite signal frequency, r and s represent the receiver and satellite system respectively, Indicates the geometric distance between the satellite and the earth, t r,i is the clock error of the receiver, Indicates the satellite clock error, is the ionospheric delay, is the tropospheric delay, B r,i and are the phase hardware delays of the receiver and the satellite respectively, λi is the wavelength of the signal frequency, represents the ambiguity of the whole week, is the residual term of the carrier phase;
S1.2:天顶对流层延迟ZTD估计:S1.2: Zenith Tropospheric Delay ZTD Estimation:
在传统PPP解算中,将基准站坐标作为常数处理,在已知其精确坐标的情况下,通过可联合地表实测气压的Saastamoinen等经验模型计算先验ZHD,将已知坐标与计算出的先验ZHD一同带入观测方程作为起算数据,随后对观测方程线性化,进一步联合多测站多卫星观测信号构建观测方程矩阵,并利用整体最小二乘或卡尔曼滤波方法进行解算,即可得到估计的天顶对流层总延迟ZTD和梯度项;In the traditional PPP solution, the coordinates of the reference station are treated as constants. When the precise coordinates are known, the prior ZHD is calculated through the empirical model such as Saastamoinen, which can be combined with the surface measured air pressure. The known coordinates and the calculated prior The experimental ZHD is brought into the observation equation as the initial calculation data, and then the observation equation is linearized, and the observation equation matrix is further combined with multi-station and multi-satellite observation signals, and the overall least squares or Kalman filter method is used to solve it, and then we can get Estimated zenith tropospheric total delay ZTD and gradient terms;
S1.3:斜路径总延迟STD计算:S1.3: Calculate the total delay STD of the oblique path:
斜路径对流层延迟可表示为天顶方向对流层延迟与映射函数的乘积加上大气水平梯度改正项与其映射函数乘积;The oblique path tropospheric delay can be expressed as the product of the tropospheric delay in the zenith direction and the mapping function plus the product of the atmospheric horizontal gradient correction term and its mapping function;
天顶对流层总延迟ZTD主要包括天顶干延迟ZHD和天顶湿延迟ZWD两部分,通过地表气象参数精确计算ZHD,随后由PPP估计出的ZTD减去ZHD可得天顶湿延迟ZWD,表示如下:The total zenith tropospheric delay ZTD mainly includes two parts: the zenith dry delay ZHD and the zenith wet delay ZWD. The ZHD is accurately calculated through the surface meteorological parameters, and then the zenith wet delay ZWD can be obtained by subtracting the ZHD from the ZTD estimated by the PPP, which is expressed as follows :
ZWD=ZTD-ZHD(2)ZWD=ZTD-ZHD(2)
因此,斜路径对流层延迟STD可表示如下:Therefore, the oblique path tropospheric delay STD can be expressed as follows:
式中,MFh表示ZHD对应的斜路径干映射函数,MFw表示ZWD对应的斜路径湿映射函数,MFg表示水平梯度映射函数,Gn和Ge分别表示水平梯度改正的北方向分量与东方向分量,为测站到卫星的方位角,εt表示对流层延迟残差;In the formula, MF h represents the oblique path dry mapping function corresponding to ZHD, MF w represents the oblique path wet mapping function corresponding to ZWD, MF g represents the horizontal gradient mapping function, G n and Ge represent the north direction component and the horizontal gradient correction respectively east component, is the azimuth angle from the station to the satellite, ε t is the tropospheric delay residual;
S2:层析区域网格内折射率反演:S2: Refractive index inversion in the grid of the tomographic region:
将利用PPP技术估算的斜路径对流层延迟STD用于GNSS对流层层析模型的构建中,具体步骤如下:The oblique path tropospheric delay STD estimated by PPP technology is used in the construction of the GNSS tropospheric tomography model. The specific steps are as follows:
S2.1:层析模型观测方程构建:S2.1: Construction of tomographic model observation equation:
通过将层析区域在三维方向上划分为多个离散的网格,并对穿过各网格的卫星信号射线上的折射率进行积分,可构建STD与折射率的积分方程:By dividing the tomographic area into multiple discrete grids in the three-dimensional direction, and integrating the refractive index on the satellite signal rays passing through each grid, the integral equation of STD and refractive index can be constructed:
STD=10-6·∫sNds (4)STD=10 -6 ∫ s Nds (4)
式中,N为大气折射率,包括干折射率和湿折射率,s表示由卫星传播到接收机的信号的路径长度。In the formula, N is the atmospheric refractivity, including dry refractivity and wet refractivity, and s represents the path length of the signal transmitted from the satellite to the receiver.
将上式离散化,则GNSS信号斜路径上对流层总延迟STD表示卫星信号穿过每个网格的截距与该网格内大气折射率乘积之和:Discretizing the above formula, the total tropospheric delay STD on the oblique path of the GNSS signal represents the sum of the intercept of the satellite signal passing through each grid and the product of the atmospheric refractive index in the grid:
STD=∑ijk(aijk·xijk) (5)STD=∑ ijk (a ijk x ijk ) (5)
式中,xijk表示(i,j,k)网格内的待估折射率,aijk表示射线在(i,j,k)网格内的截距,STD表示由PPP技术估算的GNSS卫星信号斜路径上的对流层总延迟估计值。In the formula, x ijk represents the refraction index to be estimated in the (i, j, k) grid, a ijk represents the intercept of the ray in the (i, j, k) grid, and STD represents the GNSS satellite estimated by the PPP technique Estimated total tropospheric delay on signal slant paths.
将研究区域内所有从顶部穿出的信号射线上的STD均用式(5)表示,则构成如下层析观测方程:The STD on all the signal rays passing through the top in the study area are expressed by formula (5), then the following tomographic observation equation is formed:
y=A·x (6)y=A x (6)
式中,y为从研究区域顶部穿出的信号射线上的STD组成的列向量,A为观测方程的系数矩阵,x为未知折射率参数组成的列向量。In the formula, y is a column vector composed of STD on the signal ray passing through the top of the study area, A is the coefficient matrix of the observation equation, and x is a column vector composed of unknown refractive index parameters.
S2.2:层析约束方程构建:S2.2: Construction of tomographic constraint equation:
由于层析区域上空GNSS卫星分布不均以及站点数目不足,使得层析区域很多网格没有射线穿过,导致观测方程的系数矩阵病态,在对层析方程求解时会出现不适定问题,因此,需构建一定的约束方程建立网格在水平和垂直方向上的函数关系,可根据高斯加权函数方法或水平平滑约束的方法构建水平约束方程,依据折射率随高度增加呈指数递减的特性,建立垂直网格内的垂直函数关系。此外,可根据层析区域内无线电探空资料、数值预报再分析资料等建立层析模型的先验信息;Due to the uneven distribution of GNSS satellites over the tomography area and the insufficient number of stations, many grids in the tomography area do not have rays passing through, resulting in ill-conditioned coefficient matrix of the observation equation, and ill-posed problems will occur when solving the tomography equation. Therefore, It is necessary to construct a certain constraint equation to establish the functional relationship between the grid in the horizontal and vertical directions. The horizontal constraint equation can be constructed according to the Gaussian weighted function method or the horizontal smooth constraint method. According to the characteristic that the refractive index decreases exponentially with the increase of height, the vertical Vertical functional relationships within the grid. In addition, the prior information of the tomographic model can be established according to the radiosonde data in the tomographic area, the numerical forecast reanalysis data, etc.;
S2.3:GNSS对流层层析模型构建:S2.3: GNSS tropospheric tomography model construction:
根据上述构建的GNSS层析观测方程、水平约束方程、垂直约束方程以及先验约束方程,建立GNSS对流层层析模型:According to the GNSS tomographic observation equation, horizontal constraint equation, vertical constraint equation and prior constraint equation constructed above, a GNSS tropospheric tomographic model is established:
式中,H、V和I分别指水平、垂直和先验约束方程的系数矩阵,C表示先验约束信息或通过探空数据等方法统计得到的层析区域内的折射率值。In the formula, H, V, and I refer to the coefficient matrix of the horizontal, vertical, and prior constraint equations, respectively, and C represents the prior constraint information or the refractive index value in the tomographic region obtained by statistical methods such as sounding data.
S2.4:GNSS对流层层析模型解算:S2.4: GNSS tropospheric tomography model solution:
本发明通过奇异值分解法(SingularValueDecomposition,SVD)对GNSS对流层层析模型(7)进行解算,将层析模型系数矩阵分解为:The present invention solves the GNSS troposphere tomography model (7) by singular value decomposition (SingularValueDecomposition, SVD), and the tomography model coefficient matrix Decomposed into:
B=UΛVT(8)B=UΛV T (8)
式中,B∈Rm×n,U∈Rm×m,V∈Rn×n,∑=diag(σ1,σ2,…,σr),σ1≥σ2≥…≥σr,σi(i=1,2,…,r)为矩阵ATA的特征值的平方根,r为矩阵B的秩(r≤min(m,n)),U是由矩阵AAT的特征向量组成的正交矩阵,V是由矩阵ATA的特征向量组成的正交矩阵。如果矩阵B的广义逆定义为:In the formula, B∈R m×n , U∈R m×m , V∈R n×n , ∑=diag(σ 1 ,σ 2 ,…,σ r ), σ 1 ≥σ 2 ≥…≥σ r , σ i (i=1,2,…,r) is the square root of the eigenvalues of the matrix A T A , r is the rank of matrix B (r≤min(m,n)), U is an orthogonal matrix composed of eigenvectors of matrix A T , and V is an orthogonal matrix composed of eigenvectors of matrix A T A. If the generalized inverse of matrix B is defined as:
B-1=VΛ-1UΤ(9)B -1 = VΛ -1 U Τ (9)
那么,线性方程组Bx=L的解,即层析区域内的折射率可表示为:Then, the solution of the linear equation system Bx=L, that is, the refractive index in the tomographic region can be expressed as:
x=B-1L=VΛ-1UΤL(10)x=B -1 L=VΛ -1 U Τ L(10)
S3:利用GNSS对流层层析技术的斜路径对流层延迟STD反演:S3: Oblique-path Tropospheric Delay STD Retrieval Using GNSS Tropospheric Tomography:
GNSS信号斜路径上的对流层总延迟STD可表示为射线穿过层析网格内的折射率与信号在该网格截距的乘积之和,因此,基于GNSS对流层层析技术获取的层析区域每个网格内的折射率,根据卫星信号在每个网格内的截距即可计算卫星信号在该网格内的STD,最后通过累计方式得到卫星信号路径上的STD,具体公式如下:The total tropospheric delay STD on the oblique path of the GNSS signal can be expressed as the sum of the product of the refractive index of the ray passing through the tomographic grid and the signal intercept in the grid. Therefore, the tomographic area obtained based on GNSS tropospheric tomography The refractive index in each grid can calculate the STD of the satellite signal in the grid according to the intercept of the satellite signal in each grid, and finally obtain the STD on the satellite signal path by accumulating, the specific formula is as follows:
式中,xijk表示由层析技术反演得到的(i,j,k)网格内的折射率,aijk表示射线在(i,j,k)网格内的截距,表示利用GNSS对流层层析技术反演的斜路径对流层总延迟恢复值;In the formula, x ijk represents the refractive index in the (i, j, k) grid obtained by tomographic inversion, a ijk represents the intercept of the ray in the (i, j, k) grid, Indicates the tropospheric total delay recovery value of the oblique path retrieved by GNSS tropospheric tomography technology;
通过上述方法,即可计算出层析区域内不同高度角和方位角的GNSS信号斜路径上的对流层总延迟STD;Through the above method, the total tropospheric delay STD on the oblique path of the GNSS signal at different elevation angles and azimuth angles in the tomographic area can be calculated;
S4:GNSS对流层层析技术改善PPP定位方法:S4: GNSS tropospheric tomography technology improves PPP positioning method:
将GNSS对流层层析技术反演的卫星信号传播路径上的STD加入到PPP观测方程中,对传统PPP观测方程进行改进,则公式(1)可表达成如下形式:The STD on the satellite signal propagation path retrieved by GNSS tropospheric tomography technology is added to the PPP observation equation, and the traditional PPP observation equation is improved. The formula (1) can be expressed as follows:
式中,表示利用GNSS层析技术反演得到的卫星s到接收机r的斜路径对流层总延迟。In the formula, Indicates the total tropospheric delay of the oblique path from satellite s to receiver r retrieved by GNSS tomographic technology.
因此,顾及GNSS层析技术改善后的PPP观测方程可表达如下:Therefore, taking into account the improved PPP observation equation of GNSS tomographic technology, it can be expressed as follows:
式中,表示消除了STD项的载波相位观测值,为经过改正后的载波相位残差,其余各项不变;In the formula, Indicates the carrier phase observations with the STD term removed, is the corrected carrier phase residual, and the rest remain unchanged;
最后,进一步对上式线性化,并联合多测站多卫星载波相位观测值构建PPP技术的函数模型和误差模型,利用整体最小二乘或卡尔曼滤波方法对PPP函数模型进行解算,得到高精度的PPP定位结果,并加快PPP收敛速度。Finally, the above formula is further linearized, and the function model and error model of the PPP technology are constructed by combining the carrier phase observations of multiple stations and multiple satellites. Accurate PPP positioning results and speed up PPP convergence.
以上所述,仅为本发明较佳的具体实施方式,但本发明的保护范围并不局限于此,任何熟悉本技术领域的技术人员在本发明揭露的技术范围内,根据本发明的技术方案及其发明构思加以等同替换或改变,都应涵盖在本发明的保护范围之内。The above is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto, any person familiar with the technical field within the technical scope disclosed in the present invention, according to the technical solution of the present invention Any equivalent replacement or change of the inventive concepts thereof shall fall within the protection scope of the present invention.
以上公开的本发明优选实施例只是用于帮助阐述本发明。优选实施例并没有详尽叙述所有的细节,也不限制该发明仅为所述的具体实施方式。显然,根据本说明书的内容,可作很多的修改和变化。本说明书选取并具体描述这些实施例,是为了更好地解释本发明的原理和实际应用,从而使所属技术领域技术人员能很好地理解和利用本发明。本发明仅受权利要求书及其全部范围和等效物的限制。The preferred embodiments of the invention disclosed above are only to help illustrate the invention. The preferred embodiments are not exhaustive in all detail, nor are the inventions limited to specific embodiments described. Obviously, many modifications and variations can be made based on the contents of this specification. This description selects and specifically describes these embodiments in order to better explain the principle and practical application of the present invention, so that those skilled in the art can well understand and utilize the present invention. The invention is to be limited only by the claims, along with their full scope and equivalents.
Claims (1)
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211570241.0A CN115755115A (en) | 2022-12-08 | 2022-12-08 | PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211570241.0A CN115755115A (en) | 2022-12-08 | 2022-12-08 | PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology |
Publications (1)
Publication Number | Publication Date |
---|---|
CN115755115A true CN115755115A (en) | 2023-03-07 |
Family
ID=85344638
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202211570241.0A Withdrawn CN115755115A (en) | 2022-12-08 | 2022-12-08 | PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN115755115A (en) |
Cited By (2)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN116340710A (en) * | 2023-05-30 | 2023-06-27 | 中国科学院精密测量科学与技术创新研究院 | Neutral atmospheric skew delay calculation method based on layered rapid three-dimensional ray tracing |
CN117970382A (en) * | 2024-03-29 | 2024-05-03 | 中国科学院国家空间科学中心 | A GNSS simulation test method and system |
-
2022
- 2022-12-08 CN CN202211570241.0A patent/CN115755115A/en not_active Withdrawn
Cited By (3)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN116340710A (en) * | 2023-05-30 | 2023-06-27 | 中国科学院精密测量科学与技术创新研究院 | Neutral atmospheric skew delay calculation method based on layered rapid three-dimensional ray tracing |
CN116340710B (en) * | 2023-05-30 | 2023-09-12 | 中国科学院精密测量科学与技术创新研究院 | Neutral atmospheric skew delay calculation method based on layered rapid three-dimensional ray tracing |
CN117970382A (en) * | 2024-03-29 | 2024-05-03 | 中国科学院国家空间科学中心 | A GNSS simulation test method and system |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Chen et al. | Voxel-optimized regional water vapor tomography and comparison with radiosonde and numerical weather model | |
CA3036928C (en) | Localization and tracking using location, signal strength, and pseudorange data | |
Xia et al. | GNSS troposphere tomography based on two-step reconstructions using GPS observations and COSMIC profiles | |
CN103760572B (en) | A kind of single-frequency PPP ionosphere based on region CORS method of weighting | |
CN107422351A (en) | A kind of GNSS decimeter grade Differential positioning methods based on virtual grid | |
CN107797126A (en) | BDS/GPS broadcast type network RTK algorithms based on Star Network | |
CN105629263A (en) | Troposphere atmosphere delay error correction method and correction system | |
CN108549095B (en) | Non-differential parallel enhancement method and system for regional CORS network | |
Zhao et al. | An improved GNSS tropospheric tomography method with the GPT2w model | |
CN115755115A (en) | PPP (Point-to-Point protocol) improvement method based on GNSS troposphere chromatography technology | |
CN108196284B (en) | GNSS network data processing method for fixing single-difference ambiguity between satellites | |
JP2010528320A (en) | Reduction of distance-dependent error in real-time kinematic (RTK) positioning | |
CN109541647B (en) | GNSS Multipath Effect Correction Method Based on Half-Celestial Spherical Grid Point Model | |
CN104656108A (en) | Sparse reference station network zenith troposphere delay modeling method considering elevation difference | |
CN106646564A (en) | Navigation enhancing method based on low track satellite | |
CN104375157A (en) | Inertial navigation assisted Big Dipper single-frequency whole-cycle ambiguity calculation method under short baseline condition | |
CN115616643B (en) | City area modeling auxiliary positioning method | |
CN115982564A (en) | Method and device for calculating electron density of regional ionized layer and computer equipment | |
CN104007479A (en) | Ionized layer chromatography technology and ionized layer delay correction method based on multi-scale subdivision | |
CN105510945A (en) | PPP positioning method applied to satellite navigation landing outfield detection | |
CN103543454B (en) | A kind of Satellite Orbit Determination system being embedded in wireless network | |
CN111983650A (en) | GNSS-based high-precision time transfer method | |
Zhao et al. | An optimal tropospheric tomography approach with the support of an auxiliary area | |
Zhao et al. | A troposphere tomography method considering the weighting of input information | |
Zhang et al. | AN IMPROVED TROPOSPHERIC TOMOGRAPHY METHOD BASED ON THE DYNAMIC NODE PARAMETERIZED ALGORITHM. |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
WW01 | Invention patent application withdrawn after publication |
Application publication date: 20230307 |
|
WW01 | Invention patent application withdrawn after publication |