CN102288978B

CN102288978B - Continuous operational reference system (CORS) base station cycle slip detection and recovering method

Info

Publication number: CN102288978B
Application number: CN 201110202670
Authority: CN
Inventors: 潘树国; 王庆; 王胜利
Original assignee: Southeast University
Current assignee: Southeast University
Priority date: 2011-07-20
Filing date: 2011-07-20
Publication date: 2013-09-18
Anticipated expiration: 2031-07-20
Also published as: CN102288978A

Abstract

The invention discloses a CORS base station cycle slip detection and repair method. First, the ionospheric residual method is used to detect cycle slips, determine the satellites with cycle slips and the corresponding observation values, and then establish a single calendar based on the cycle slip detection results. The single-epoch double-difference observation equation is divided into two types, the first type is observation equation without cycle slip, and the second type is observation equation with cycle slip, and the cycle slip generated by non-reference satellite is used as rough difference, the cycle slip generated by the reference satellite is used as the system error, and the first type of observation equation is used for parameter estimation to determine the cycle slip of the reference satellite, and the estimated parameters are brought into the second type of observation equation, and the correction number is calculated to obtain the non-reference satellite Finally, according to the relationship between the baselines in the CORS triangulation network, the observation data of the base station where the cycle slip occurs is repaired. Due to the direct use of the precise coordinates of the CORS network and the strong time correlation of errors such as double-difference troposphere and ionosphere, it can accurately detect and repair cycle slips.

Description

A CORS base station cycle slip detection and repair method

技术领域 technical field

本发明涉及GNSS网络差分定位技术，尤其涉及一种CORS基站(连续运行参考站)周跳探测与修复方法，是CORS系统完备性监测的重要组成部分。The invention relates to GNSS network differential positioning technology, in particular to a CORS base station (continuous operation reference station) cycle slip detection and repair method, which is an important part of CORS system integrity monitoring.

背景技术 Background technique

GNSS网络差分定位技术是目前卫星定位领域的热门技术，广泛应用于测绘及国土资源调查等行业，以虚拟参考站(VRS)技术为代表的网络差分技术兴起，使得建立基准站网络式GPS服务体系成为当前GPS技术应用发展的最新趋势。VRS技术作为多基准站环境下的GPS实时动态定位技术，是集Internet技术、无线通讯技术、计算机网络技术以及GPS技术为一体的网络RTK定位技术，也是当前应用最广、最成功的代表性高新技术成果，VRS技术体系代表了常规RTK之后新一代定位技术的发展方向。GNSS network differential positioning technology is currently a popular technology in the field of satellite positioning. It is widely used in surveying and mapping, land and resources survey and other industries. The rise of network differential technology represented by virtual reference station (VRS) technology has enabled the establishment of a base station network GPS service system Become the latest trend in the development of current GPS technology applications. As a GPS real-time dynamic positioning technology in a multi-reference station environment, VRS technology is a network RTK positioning technology integrating Internet technology, wireless communication technology, computer network technology and GPS technology. It is also the most widely used and most successful representative high-tech technology. Technical achievements, the VRS technology system represents the development direction of a new generation of positioning technology after conventional RTK.

VRS技术定位的基本方法为：各个参考站连续采集观测数据，实时传输到数据处理与控制中心的数据库，进行网络计算；控制中心在线解算GPS参考站网内各独立基线的载波相位整周模糊度值；数据处理中心利用参考站网载波相位观测值计算每条基线上的双差综合误差，并据此建立距离相关误差的空间参数模型；移动站用户将通过单点定位得到的NMEA格式的概略坐标发送给控制中心，控制中心在该坐标位置创建一个虚拟参考站(VRS)；控制中心根据参考站、用户及GPS卫星的相对几何关系，通过内插计算模型得到移动站与参考站间的空间相关误差，再根据虚拟观测值计算模型生成VRS处的虚拟观测值；控制中心把虚拟观测值作为网络差分改正信息发送给移动站用户；用户移动站接收网络差分信息与VRS构成短基线，通过常规RTK计算模型进行差分解算，确定用户位置，见图1所示。The basic method of VRS technology positioning is: each reference station continuously collects observation data, transmits it to the database of the data processing and control center in real time, and performs network calculation; degree value; the data processing center calculates the double-difference comprehensive error on each baseline by using the carrier phase observation value of the reference station network, and establishes the spatial parameter model of the distance-related error accordingly; The rough coordinates are sent to the control center, and the control center creates a virtual reference station (VRS) at the coordinate position; the control center obtains the distance between the mobile station and the reference station through an interpolation calculation model according to the relative geometric relationship between the reference station, the user, and the GPS satellite. space correlation error, and then generate the virtual observation value at the VRS according to the virtual observation value calculation model; the control center sends the virtual observation value as network difference correction information to the mobile station user; the user mobile station receives the network difference information and VRS to form a short baseline, through The conventional RTK calculation model performs differential calculation to determine the user's position, as shown in Figure 1.

在VRS中，对流层和电离层双差改正数的正确预报是用户精确定位的基础，而在实时数据处理中，周跳的存在，将使对流层和电离层双差改正数的预报值产生系统性误差。对于周跳探测和修复的研究，方法很多，典型的周跳探测方法有两类，一类是通过检查观测数据及其线性组合的连续性来探测周跳，因为周跳破坏了数据的连续性。这类方法中比较经典的有高次差法、多项式拟合法、小波分析法。检验量包括电离层组合、双差组合等。另一类是利用粗差探测技术探测周跳，有卡尔曼滤波法、拟准检定法。以上方法都是集中在使用单站、单颗卫星的数据进行周跳的探测，在探测出周跳之后，再使用周跳修复方法进行修复。In VRS, the correct forecast of tropospheric and ionospheric double-difference corrections is the basis for precise positioning of the user, while in real-time data processing, the existence of cycle slips will make the forecast value of tropospheric and ionospheric double-difference corrections systematically error. For the research on cycle slip detection and repair, there are many methods, and there are two types of typical cycle slip detection methods, one is to detect cycle slip by checking the continuity of observed data and its linear combination, because cycle slip destroys the continuity of data . Among the more classic methods of this kind are high-order difference method, polynomial fitting method, and wavelet analysis method. The inspection quantities include ionospheric combination, double-difference combination, etc. The other is to use gross error detection technology to detect cycle slips, including Kalman filter method and quasi-quasi test method. The above methods are all focused on using the data of a single station and a single satellite to detect the cycle slip, and after the cycle slip is detected, the cycle slip repair method is used to repair it.

发明内容 Contents of the invention

本发明公开了一种CORS基站周跳探测与修复方法，采用如下技术方案：The invention discloses a CORS base station cycle slip detection and repair method, which adopts the following technical scheme:

一种CORS基站周跳探测与修复方法，其特征在于：根据CORS网中已知的精确坐标以及对流层、电离层误差的时间相关性及初始化后已知的整周模糊度，依据非参考卫星引起单个双差观测方程出现粗差、而参考卫星引起所有双差观测方程中出现系统性误差的性质，使用电离层残差法进行周跳探测，根据周跳探测结果，建立单历元双差观测方程，最后进行周跳修复，包括以下步骤：A CORS base station cycle slip detection and repair method is characterized in that: according to the known precise coordinates in the CORS network and the time correlation of troposphere and ionosphere errors and the known integer ambiguity after initialization, based on non-reference satellites Gross errors appear in a single double-difference observation equation, while the reference satellite causes systematic errors in all double-difference observation equations. The ionospheric residual method is used for cycle slip detection. Based on the cycle slip detection results, a single-epoch double-difference observation is established. Equations, and finally perform cycle slip repair, including the following steps:

1)根据电离层残差法进行周跳的探测，确定存在周跳的卫星及所对应的观测值，建立单历元双差观测方程；1) According to the ionospheric residual method, detect the cycle slip, determine the satellites with cycle slip and the corresponding observation values, and establish the single-epoch double-difference observation equation;

2)将双差观测方程分为两类，第一类为无周跳双差观测方程，第二类为存在周跳的双差观测方程，将非参考卫星产生的周跳作为粗差，参考卫星的周跳作为系统误差；2) Divide the double-difference observation equation into two types, the first type is the double-difference observation equation without cycle slip, and the second type is the double-difference observation equation with cycle slip. The cycle slip of the satellite is used as the systematic error;

3)使用第一类双差观测方程进行参数估计，确定参考卫星的周跳；3) Use the first type of double-difference observation equation to estimate the parameters and determine the cycle slip of the reference satellite;

4)将第一类双差观测方程估计出的参数带入第二类双差观测方程，计算改正数，得到非参考卫星的周跳值；4) Bring the estimated parameters of the first type of double-difference observation equation into the second type of double-difference observation equation, calculate the correction number, and obtain the cycle slip value of the non-reference satellite;

5)根据CORS三角网中基线间的关系修复发生周跳的基站观测数据。5) According to the relationship between the baselines in the CORS triangulation network, the observation data of the base station where the cycle slip occurs is repaired.

具体方法是：The specific method is:

1)电离层残差法进行周跳探测1) Ionospheric residual method for cycle slip detection

GPS载波相位非差观测的基本观测方程为：The basic observation equation of GPS carrier phase non-difference observation is:

其中，t为观测历元；i表示对应L1和L2载波；

表示载波相位观测值；R表示卫星与接收机之间的几何距离；λ表示波长；N表示载波相位观测值的整周模糊度；T表示对流层误差；I表示电离层误差；ε表示非模型误差；Among them, t is the observation epoch; i represents the corresponding L1 and L2 carriers;

R is the geometric distance between the satellite and the receiver; λ is the wavelength; N is the integer ambiguity of the carrier phase observation; T is the tropospheric error; I is the ionospheric error; ε is the non-model error ;

将L1和L2载波相位观测值求差可得：The difference between the L1 and L2 carrier phase observations can be obtained:

其中I为L1和L2载波观测电离层误差之差；ε为L1和L2载波观测单差非模型误差；Where I is the difference between the ionospheric errors of L1 and L2 carrier observations; ε is the single-difference non-model error of L1 and L2 carrier observations;

将上述电离层误差之差进行历元间求差，可得：Calculate the difference between the above ionospheric errors between epochs, we can get:

根据电离层的性质，对于采样率为1秒的CORS系统来说，在短时间内，电离层变化为微小量，在观测值不发生周跳时，电离层残差不会超过0.1周，如果超过0.1周，则认为观测值中存在周跳，从而探测出周跳，根据此周跳探测结果，将双差观测值进行分类；According to the nature of the ionosphere, for a CORS system with a sampling rate of 1 second, the ionosphere changes in a small amount in a short period of time, and the ionosphere residual error will not exceed 0.1 cycle when no cycle slip occurs in the observed value. If If it exceeds 0.1 cycle, it is considered that there is a cycle slip in the observation value, so that the cycle slip is detected, and the double-difference observation value is classified according to the detection result of the cycle slip;

2)双差观测方程分类2) Classification of double-difference observation equations

使用载波相位观测的双差观测方程，该双差观测方程为：Using the double-difference observation equation for carrier phase observations, the double-difference observation equation is:

${δ δ}_{A A,, B B}^{i i,, j j} (({t t}_{i i})) = = - - &dtri; &dtri; {ΔI ΔI}_{A A,, B B}^{i i,, j j} (({t t}_{i i})) + + Δ Δ {&dtri; &dtri; T T}_{A A,, B B}^{i i,, j j} (({t t}_{i i})) + + Δ Δ &dtri; &dtri; {δm δm}_{A A,, B B}^{i i,, j j} (({t t}_{i i})) + + Δ Δ &dtri; &dtri; {ϵ ϵ}_{A A,, B B}^{i i,, j j} (({t t}_{i i})) - - - - - - ((55))$

其中，

为载波相位的双差观测值，

为双差站星距离，为双差整周模糊度，

为双差电离层延迟，

为双差对流层延迟，

为双差多路径效应引起的误差，

为双差非模型误差；in,

is the double-differenced observation of the carrier phase,

is the double-difference station-satellite distance, is the double-differenced integer ambiguity,

is the double-differenced ionospheric delay,

is the double-differenced tropospheric delay,

is the error caused by the double-difference multipath effect,

is the double-differenced non-model error;

在CORS网中，双差整周模糊度在初始化后得到。根据CORS网中高采样率、历元间误差的强相关性，通过上一个历元的双差对流层和电离层误差值近似，如公式(6)；In CORS nets, double-differenced integer ambiguities are obtained after initialization. According to the high sampling rate in the CORS network and the strong correlation of errors between epochs, the error values of the troposphere and ionosphere are approximated by the double difference of the previous epoch, as shown in formula (6);

假设CORS基站网中组成的基线中的一个站A的坐标精确已知，另外一个站B的坐标作为参数进行估计，在无周跳且双差模糊度已知的情况下，则可得到误差方程为：Assuming that the coordinates of one station A in the baseline composed of the CORS base station network are known accurately, and the coordinates of the other station B are estimated as parameters, in the case of no cycle slip and known double-difference ambiguity, the error equation can be obtained for:

${V V}_{A A,, B B}^{i i,, j j} = = Bx Bx - - {L L}_{A A,, B B}^{i i,, j j} - - - - - - ((77))$

其中in

x＝[dx dy dz]^T，B为系数矩阵；

x=[dx dy dz] ^T , B is the coefficient matrix;

在以上的误差方程中，假设有一颗非参考卫星在某一站点上发生了周跳，则会引起粗差，如果是参考卫星发生了周跳，则此周跳将会带入到所有的误差方程，从而产生系统性误差，将(7)式加入系统参数可得：In the above error equation, assuming that a non-reference satellite has a cycle slip on a certain site, it will cause gross errors. If the reference satellite has a cycle slip, this cycle slip will bring all the errors Equation, resulting in a systematic error, adding (7) to the system parameters can be obtained:

${V V}_{A A,, B B}^{i i,, j j} = = Bx Bx + + Ey Ey - - {L L}_{A A,, B B}^{i i,, j j} - - - - - - ((88))$

其中，y＝[y₁，y₂]^T分别为参考卫星L1和L2载波相位观测值中的周跳；Wherein, y=[y ₁ , y ₂ ] ^T are the cycle slips in the carrier phase observations of the reference satellites L1 and L2 respectively;

假设在某一历元，跟踪到了n颗卫星，并且在前一个历元，这n颗卫星的整周模糊度都已固定，则可得到此历元的误差方程组为：Assuming that in a certain epoch, n satellites are tracked, and in the previous epoch, the ambiguities of the n satellites have been fixed, then the error equations for this epoch can be obtained as:

$\underset{(n - 1) \times 1}{V_{1}} = \underset{(n - 1) \times 3}{B} \underset{3 \times 1}{x} + \underset{(n - 1) \times 1}{E_{1}} \underset{1 \times 1}{y_{1}} - \underset{(n - 1) \times 1}{L_{1}}$ (9) $\underset{(no - 1) \times 1}{V_{1}} = \underset{(no - 1) \times 3}{B} \underset{3 \times 1}{x} + \underset{(no - 1) \times 1}{{E.}_{1}} \underset{1 \times 1}{{they}_{1}} - \underset{(no - 1) \times 1}{L_{1}}$ (9)

$\underset{((n no - - 11)) \times \times 11}{{V V}_{22}} = = \underset{((n no - - 11)) \times \times 33}{B B} \underset{33 \times \times 11}{x x} + + \underset{((n no - - 11)) \times \times 11}{{E E.}_{22}} \underset{11 \times \times 11}{{y the y}_{22}} - - \underset{((n no - - 11)) \times \times 11}{{L L}_{22}}$

分别为L1和L2载波上的误差方程式；are the error equations on the L1 and L2 carriers, respectively;

根据电离层残差法周跳探测结果，对实时双差载波观测值分为四组，第一组为无周跳的L1的双差观测方程构成的误差方程，用L₁₁表示，权值为P₁₁，第二组为存在周跳的L1的双差观测方程构成的误差方程，用L₂₁表示，权值为P₂₁，第三组为无周跳的L2的双差观测方程构成的误差方程，用L₁₂表示，权值为P₁₂，第四组为存在周跳的L2的双差观测方程构成的误差方程，用L₂₂表示，权值为P₂₂；则可得误差方程为：According to the cycle-slip detection results of the ionospheric residual method, the real-time double-difference carrier observations are divided into four groups. The first group is the error equation formed by the double-difference observation equation of L1 without cycle slip, represented by _L11 , and the weight is P ₁₁ , the second group is the error equation formed by the double-difference observation equation of L1 with cycle slip, denoted by L ₂₁ , the weight is P ₂₁ , the third group is the error equation formed by the double-difference observation equation of L2 without cycle slip The equation is represented by L ₁₂ and the weight is P ₁₂ . The fourth group is the error equation formed by the double-difference observation equation of L2 with cycle slip, which is represented by L ₂₂ and the weight is P ₂₂ ; then the error equation can be obtained as:

$\begin{matrix} {V V}_{1111} = = {B B}_{1111} x x + + {E E.}_{1111} {y the y}_{11} - - {l l}_{1111} \\ {V V}_{21 twenty one} = = {B B}_{21 twenty one} x x + + {E E.}_{21 twenty one} {y the y}_{11} - - {l l}_{21 twenty one} \\ {V V}_{1212} = = {B B}_{1212} x x + + {E E.}_{1212} {y the y}_{22} - - {l l}_{1212} \\ {V V}_{1212} = = {B B}_{22 twenty two} x x + + {E E.}_{22 twenty two} {y the y}_{22} - - {l l}_{22 twenty two} \end{matrix}\}$ $P P = = (\begin{matrix} {P P}_{1111} & O o & O o & O o \\ O o & {P P}_{21 twenty one} & O o & O o \\ O o & O o & {P P}_{1212} & O o \\ O o & O o & O o & {P P}_{22 twenty two} \end{matrix}) - - - - - - ((1010))$

对上述四组双差观测方程构成的误差方程进一步分为两类，即第一类为无周跳的L1和L2的双差观测方程构成的误差方程，第二类为存在周跳的L1和L2的双差观测方程构成的误差方程，则上式可表示为：The error equations composed of the above four sets of double-difference observation equations are further divided into two categories, that is, the first category is the error equations composed of double-difference observation equations of L1 and L2 without cycle slips, and the second category is the error equations of L1 and L2 with cycle slips. The error equation formed by the double-difference observation equation of L2, the above formula can be expressed as:

$\begin{matrix} {V V}_{11} = = {B B}_{11} x x + + {E E.}_{11} y the y - - {l l}_{11} \\ {V V}_{22} = = {B B}_{22} x x + + {E E.}_{22} y the y - - {l l}_{22} \end{matrix}\}$ $P P = = (\begin{matrix} {P P}_{11} & O o \\ O o & {P P}_{22} \end{matrix}) - - - - - - ((1111))$

其中：in:

${V V}_{11} = = (\begin{matrix} {V V}_{1111} \\ {V V}_{1212} \end{matrix})$ ${V V}_{22} = = (\begin{matrix} {V V}_{21 twenty one} \\ {V V}_{22 twenty two} \end{matrix}),,$ ${B B}_{11} = = (\begin{matrix} {B B}_{1111} \\ {B B}_{1212} \end{matrix})$ ${B B}_{22} = = (\begin{matrix} {B B}_{21 twenty one} \\ {B B}_{22 twenty two} \end{matrix}),,$ ${l l}_{11} = = (\begin{matrix} {l l}_{1111} \\ {l l}_{1212} \end{matrix})$ ${l l}_{22} = = (\begin{matrix} {l l}_{21 twenty one} \\ {l l}_{22 twenty two} \end{matrix})$

${E E.}_{11} = = (\begin{matrix} {E E.}_{1111} \\ {E E.}_{1212} \end{matrix})$ ${E E.}_{22} = = (\begin{matrix} {E E.}_{21 twenty one} \\ {E E.}_{22 twenty two} \end{matrix}),,$ $y the y = = (\begin{matrix} {y the y}_{11} \\ {y the y}_{22} \end{matrix}),,$ ${P P}_{11} = = (\begin{matrix} {P P}_{1111} & O o \\ O o & {P P}_{1212} \end{matrix}),,$ ${P P}_{22} = = (\begin{matrix} {P P}_{21 twenty one} & O o \\ O o & {P P}_{22 twenty two} \end{matrix})$

x为流动站坐标改正参数，y为参考卫星L1和L2载波观测值中的周跳；x is the coordinate correction parameter of the rover, and y is the cycle slip in the carrier observation values of the reference satellite L1 and L2;

3)用第一类双差观测方程构成的误差方程进行参数估计3) Use the error equation composed of the first kind of double-difference observation equation to estimate the parameters

将第二类存在周跳的L1和L2的双差观测方程作为存在粗差的观测方程处理，则假设P₂＝0，也即在解算中不起任何作用，则可直接使用第一类无周跳的L1和L2的载波观测方程解算x和y参数，按最小二乘准则V^TPV＝min，可得法方程：The second type of double-difference observation equations of L1 and L2 with cycle slips are treated as observation equations with gross errors, and assuming that P ₂ =0, that is, it does not play any role in the solution, then the first type can be directly used Solve the x and y parameters of the carrier observation equations of L1 and L2 without cycle slip, according to the least square criterion V ^T PV = min, the normal equation can be obtained:

$(\begin{matrix} {B B}_{11}^{T T} {P P}_{11} {B B}_{11} & {B B}_{11}^{T T} {P P}_{11} {E E.}_{11} \\ {E E.}_{11}^{T T} {P P}_{11} {B B}_{11} & {E E.}_{11}^{T T} {P P}_{11} {E E.}_{11} \end{matrix}) (\begin{matrix} \overset{^^}{x x} \\ \overset{^^}{y the y} \end{matrix}) = = (\begin{matrix} {B B}_{11}^{T T} {P P}_{11} {l l}_{11} \\ {E E.}_{11}^{T T} {P P}_{11} {l l}_{11} \end{matrix}) - - - - - - ((1212))$

令 $N_{11} = B_{1}^{T} P_{1} B_{1},$ $N_{12} = N_{21}^{T} = B_{1}^{T} P_{1} E_{1},$ $N_{22} = E_{1}^{T} P_{1} E_{1},$ $W_{1} = B_{1}^{T} P_{1} l_{1},$ $W_{2} = E_{1}^{T} P_{1} l_{1},$ make $N_{11} = B_{1}^{T} P_{1} B_{1},$ $N_{12} = N_{twenty one}^{T} = B_{1}^{T} P_{1} {E.}_{1},$ $N_{twenty two} = {E.}_{1}^{T} P_{1} {E.}_{1},$ $W_{1} = B_{1}^{T} P_{1} l_{1},$ $W_{2} = {E.}_{1}^{T} P_{1} l_{1},$

则上式可写为：Then the above formula can be written as:

$(\begin{matrix} {N N}_{1111} & {N N}_{1212} \\ {N N}_{21 twenty one} & {N N}_{22 twenty two} \end{matrix}) (\begin{matrix} \overset{^^}{x x} \\ \overset{^^}{y the y} \end{matrix}) (\begin{matrix} {W W}_{11} \\ {W W}_{22} \end{matrix}) - - - - - - ((1313))$

由分块求逆公式得From the block inversion formula to get

$(\begin{matrix} \overset{^^}{x x} \\ \overset{^^}{y the y} \end{matrix}) (\begin{matrix} {N N}_{1111}^{- - 11} + + {N N}_{1111}^{- - 11} {N N}_{1212} {M m}^{- - 11} {N N}_{21 twenty one} {N N}_{1111}^{- - 11} & - - {N N}_{1111}^{- - 11} {N N}_{1212} {M m}^{- - 11} \\ - - {M m}^{- - 11} {N N}_{21 twenty one} {N N}_{1111}^{- - 11} & {M m}^{- - 11} \end{matrix}) (\begin{matrix} {W W}_{11} \\ {W W}_{22} \end{matrix}) - - - - - - ((1414))$

式中In the formula

$M m = = {N N}_{22 twenty two} - - {N N}_{21 twenty one} {N N}_{1111}^{- - 11} {N N}_{1212} - - - - - - ((1515))$

若参考卫星不存在周跳，则If there is no cycle slip in the reference satellite, then

$\overset{^^}{x x} = = {N N}_{1111}^{- - 11} {W W}_{11} - - - - - - ((1616))$

根据系统误差的估值

得到参考卫星L1和L2载波上的周跳值为：Estimation according to systematic error

The cycle slip values on the reference satellite L1 and L2 carriers are obtained as:

$\{\begin{matrix} {Slip Slip}_{11} = = \frac{{\overset{^^}{y the y}}_{11}}{{λ λ}_{11}} \\ {Slip Slip}_{22} = = \frac{{\overset{^^}{y the y}}_{22}}{{λ λ}_{22}} \end{matrix} - - - - - - ((1717))$

其中Slip₁，Slip₂分别表示参考卫星L1和L2载波相位观测值的周跳；Among them, Slip ₁ and Slip ₂ represent the cycle slips of the carrier phase observations of reference satellites L1 and L2, respectively;

4)非参考卫星周跳修复值的计算4) Calculation of non-reference satellite cycle slip repair value

将

及

带入V₂＝B₂x+E₂y-l₂，可得相应非参考卫星的周跳值为：Will

and

Inserting V ₂ =B ₂ x+E ₂ yl ₂ , the cycle slip value of the corresponding non-reference satellite can be obtained as:

$\{\begin{matrix} {slip slip}_{22} = = \frac{{V V}_{21 twenty one}}{{λ λ}_{11}} \\ {slip slip}_{22} = = \frac{{V V}_{22 twenty two}}{{λ λ}_{22}} \end{matrix} - - - - - - ((1818))$

其中slip₁，slip₂分别表示非参考卫星L1和L2载波相位观测值的周跳；where slip ₁ and slip ₂ represent the cycle slips of the non-reference satellite L1 and L2 carrier phase observations, respectively;

5)确定周跳发生的基站及周跳的修复5) Determine the base station where the cycle slip occurs and the repair of the cycle slip

在探测出基线中出现周跳卫星后，根据三角网中基站对应的两条基线确定出现周跳的基站，如三角网ABC，有三条基线A→B，B→C，C→A，如果基线A→B中探测出了周跳，基线B→C也存在周跳，且周跳的大小相等，符号相反，则周跳出现在基站B上，根据基站在基线中作为基准点解算还是流动点解算来判断周跳的正负号，对于一条基线中，如果周跳发生在基准点上，则周跳结果与残差值符号正好相反，如果发生在流动点上，则周跳结果与残差值符号相同，在基线A→B中，B点作为流动点，所以将基线A→B探测出的周跳值作为基站B的周跳修复值。同样的方法，根据基线C→A和基线A→B修复基站A的周跳，根据基线B→C和基线C→A修复基站C的周跳值。After detecting the cycle-slip satellite in the baseline, determine the base station with cycle-slip according to the two baselines corresponding to the base station in the triangulation network, such as the triangulation network ABC, there are three baselines A→B, B→C, C→A, if the baseline A cycle slip is detected in A→B, and there is also a cycle slip in the baseline B→C, and the size of the cycle slip is equal and the sign is opposite, then the cycle slip appears on base station B, and it is calculated according to whether the base station is used as a reference point in the baseline or it is a flow point For a baseline, if the cycle slip occurs at the reference point, the sign of the cycle slip is exactly opposite to that of the residual value; if it occurs at the flow point, the cycle slip result is the same as the residual value The sign of the difference is the same, in the baseline A→B, point B is used as the flow point, so the cycle slip value detected by the baseline A→B is taken as the cycle slip repair value of the base station B. In the same way, the cycle slip of base station A is repaired according to baseline C→A and baseline A→B, and the cycle slip value of base station C is repaired according to baseline B→C and baseline C→A.

本发明的优点及有益效果：Advantage of the present invention and beneficial effect:

本发明基于分类最小二乘估计的周跳探测与修复方法，由于直接利用了CORS网的精确坐标以及双差对流层、电离层等误差的时间强相关性，能非常有效的减少其他系统性误差对模型的影响，从而能准确的进行周跳的探测和修复，是一种非常有效的周跳整体探测和修复的方法。基于天津CORS实验参考站网络的实验表明：传统的周跳探测方法对于小周跳的探测较为困难，而基于分类最小二乘估计的周跳探测与修复方法可以探测的精度为0.01周。本专利源于国家自然科学基金(41074021)：CORS系统完备性监测理论与方法研究及“十一五”国家科技支撑计划重点项目：“农村土地实时监测技术研究与系统研制”的子课题：网络化数字调查技术开发。The cycle slip detection and repair method based on the classification least squares estimation of the present invention can effectively reduce the impact of other systematic errors due to the direct use of the precise coordinates of the CORS network and the strong temporal correlation of errors such as double-difference troposphere and ionosphere. It is a very effective method for the overall detection and repair of cycle slips. Experiments based on the Tianjin CORS experimental reference station network show that the traditional cycle slip detection method is difficult to detect small cycle slips, while the cycle slip detection and repair method based on classification least squares estimation can detect with an accuracy of 0.01 cycle. This patent originates from the National Natural Science Foundation of China (41074021): CORS System Integrity Monitoring Theory and Method Research and the "Eleventh Five-Year" National Science and Technology Support Program Key Project: "Rural Land Real-time Monitoring Technology Research and System Development" Sub-project: Network Development of digitized survey technology.

附图说明 Description of drawings

图1是VRS与参考站网关系图；Figure 1 is a diagram of the relationship between VRS and the reference station network;

图2是周跳探测流程图；Fig. 2 is a flow chart of cycle slip detection;

图3是天津CORS试验参考站网络分布；Figure 3 is the network distribution of Tianjin CORS test reference stations;

图4是基线解算误差；Figure 4 is the baseline solution error;

图5基线DG→XQ周跳探测结果，其中图5(a)为30号卫星的周跳探测结果，图5(b)为32号卫星的周跳探测结果；Figure 5 baseline DG→XQ cycle slip detection results, where Figure 5(a) is the cycle slip detection result of No. 30 satellite, and Fig. 5(b) is the cycle slip detection result of No. 32 satellite;

图6基线XQ→NH周跳探测结果，其中图6(a)为30号卫星的周跳探测结果，图6(b)为32号卫星的周跳探测结果。Figure 6. Baseline XQ→NH cycle-slip detection results, where Fig. 6(a) is the cycle-slip detection result of No. 30 satellite, and Fig. 6(b) is the cycle-slip detection result of No. 32 satellite.

具体实施方式 Detailed ways

本发明方法是根据CORS网中已知的精确坐标以及对流层、电离层误差的时间相关性及初始化后已知的整周模糊度，依据非参考卫星引起单个双差观测方程出现粗差、而参考卫星引起所有双差观测方程中出现系统性误差的性质，首先使用电离层残差法进行周跳探测，确定存在周跳的卫星及所对应的观测值，然后根据周跳探测结果，建立单历元双差观测方程，将单历元双差观测方程分为两类，第一类为无周跳方程，第二类为存在周跳的的方程，将非参考卫星产生的周跳作为粗差，参考卫星产生的周跳作为系统误差，使用第一类方程进行参数估计，确定参考卫星的周跳，将第一类方程估计出的参数带入第二类方程，计算改正数，得到非参考卫星的周跳值，最后根据CORS三角网中基线间的关系修复发生周跳的基站观测数据。周跳探测与修复流程图参见图2所示。The method of the present invention is based on the known precise coordinates in the CORS network and the time correlation of troposphere and ionosphere errors and the known integer ambiguity after initialization, and the gross error occurs in the single double-difference observation equation caused by non-reference satellites, while the reference Satellites cause systematic errors in all double-difference observation equations. First, use the ionospheric residual method to detect cycle slips, determine the satellites with cycle slips and the corresponding observations, and then establish a single calendar based on the cycle slip detection results. The single-epoch double-difference observation equation is divided into two types, the first type is the equation without cycle slip, and the second type is the equation with cycle slip, and the cycle slip generated by the non-reference satellite is used as gross error , the cycle slip generated by the reference satellite is used as the system error, and the first type of equation is used for parameter estimation to determine the cycle slip of the reference satellite, and the parameters estimated by the first type of equation are brought into the second type of equation to calculate the correction number and obtain the non-reference The cycle slip value of the satellite, and finally repair the observation data of the base station where the cycle slip occurs according to the relationship between the baselines in the CORS triangulation network. The flow chart of cycle slip detection and repair is shown in Figure 2.

实施例：在天津CORS试验参考站中使用本方法，天津CORS试验参考站网络包括大港(DG)、西青(XQ)、NH(NH)等15个连续运行参考站，实验采用2009年12月11日网中的DG、XQ、NH三个基站的数据，采样间隔1s，取其中5分钟的数据。如图3所示。其中，所有跟踪卫星均未发生周跳，为分析周跳探测与修复的能力，人为的加入周跳，其中，选择了在参考卫星PRN＝14，高度角为60°的PRN＝30卫星，高度角为10°的PRN＝32卫星。具体周跳值见下表1：Embodiment: use this method in Tianjin CORS test reference station, Tianjin CORS test reference station network includes 15 continuous operation reference stations such as Dagang (DG), Xiqing (XQ), NH (NH), and experiment adopts December, 2009 The data of the three base stations DG, XQ, and NH in the 11th network, the sampling interval is 1s, and the data of 5 minutes is taken. As shown in Figure 3. Among them, all tracking satellites have no cycle slips. In order to analyze the ability of cycle slip detection and repair, cycle slips are added artificially. Among them, the reference satellite PRN=14 and the altitude angle of 60° are selected. PRN=30 satellites, altitude PRN = 32 satellites with an angle of 10°. The specific cycle slip values are shown in Table 1 below:

表1加入的待检测的周跳数Number of cycle slips to be detected added in Table 1

使用电离层残差法进行周跳的探测，根据周跳探测结果对观测值进行了分类，使用本方法对网中的基线进行单历元解算，估计出坐标变化量及参考卫星的周跳值，表2表示DG→XQ周跳探测结果，表3表示基线XQ→NH进行探测结果。Use the ionospheric residual method to detect the cycle slip, and classify the observed values according to the cycle slip detection results, use this method to solve the baseline in the network in a single epoch, and estimate the coordinate change and the cycle slip of the reference satellite Table 2 shows the detection results of DG→XQ cycle slips, and Table 3 shows the detection results of the baseline XQ→NH.

表2基线DG→DL周跳探测结果Table 2 Baseline DG→DL cycle slip detection results

表3基线DL→TG周跳探测结果Table 3 Baseline DL→TG cycle slip detection results

从表2和表3中可以看出，周跳探测的结果与表1中加入的周跳值具有非常强的一致性，说明本方法对周跳的修复非常有效。It can be seen from Table 2 and Table 3 that the results of cycle slip detection are very consistent with the cycle slip value added in Table 1, which shows that this method is very effective for repairing cycle slip.

图4表示对基线DG→XQ(图4(a))和基线XQ→NH(图4(b))的解算结果，结果表明周跳对通过分类之后进行的基线解算影响非常小。由计算结果可知，残差法可以判断出双差组合观测中是否存在周跳，至于是哪一个站上发生，还需要根据前后基线进行比较才可以确定周跳所在的站点及周跳的大小，比如在基线DG→XQ中如果探测出了周跳，而在基线XQ→NH中没有探测到，说明周跳出现在基站DG上，探测出周跳出现的站点后，还需要根据站点在基线中作为基站解算还是流动站解算来判断周跳的正负号，比如在基站的参考卫星上加1周周跳(如历元40)，残差探测结果为负值，在流动站参考卫星上加1周周跳(如历元120)，残差结果正负号一致，根据实验数据分析可以得到如下结论：(1)如果两条前后连接的基线同时探测到周跳，并且周跳大小相等，符号相反，说明周跳出现在公共站点上，如果只有一条基线中探测出了周跳，说明周跳发生在本条基线非公共站点上；(2)对于一条基线中，如果周跳发生在基站上，则周跳结果与残差值符号正好相反，如果发生在流动站，则周跳结果与残差值符号相同。Figure 4 shows the solution results for the baseline DG→XQ (Figure 4(a)) and baseline XQ→NH (Figure 4(b)). The results show that the cycle slip has very little effect on the baseline solution after classification. It can be seen from the calculation results that the residual method can determine whether there is a cycle slip in the double-difference combined observation. As for which station it occurs on, it is necessary to compare the base line before and after to determine the station where the cycle slip is located and the size of the cycle slip. For example, if a cycle slip is detected in the baseline DG→XQ, but not detected in the baseline XQ→NH, it means that the cycle slip occurs on the base station DG. The sign of the cycle slip is judged by the calculation of the base station or the rover station. For example, if a cycle slip is added to the reference satellite of the base station (such as epoch 40), the residual detection result is a negative value. On the reference satellite of the rover station Adding 1 cycle slip (such as epoch 120), the sign of the residual error is the same. According to the analysis of experimental data, the following conclusions can be obtained: (1) If two baselines connected back and forth detect cycle slips at the same time, and the magnitude of the cycle slips is equal , the signs are opposite, indicating that the cycle slip occurs on the public station. If only one baseline detects the cycle slip, it indicates that the cycle slip occurs on the non-public station of this baseline; (2) For one baseline, if the cycle slip occurs on the base station , the sign of the cycle slip result is just opposite to that of the residual value. If it occurs at the rover, the sign of the cycle slip result is the same as that of the residual value.

图5表示对基线DG→XQ的30号卫星(图5(a))和32号卫星(图5(b))的周跳探测结果。图6表示对基线DG→XQ的30号卫星(图6(a))和32号卫星(图6(b))的周跳探测结果。最后根据三角网中基线之间的关系确定出现周跳的基站，并对观测数据进行周跳的修复。比如在基线DG→XQ中如果探测出了周跳，并且在基线XQ→NH中也有周跳探测到，说明周跳出现在基站XQ上，探测出周跳出现的站点后，根据站点在基线中作为基准点解算还是流动点解算来判断周跳的正负号。比如在基站的参考卫星上加1周周跳(如历元40)，残差探测结果为负值，在流动站参考卫星上加1周周跳(如历元120)，残差结果正负号一致，在基线DG→XQ中，DG作为基准点，所以将基线DG→XQ探测出的结果取负号作为基站DG的周跳修复值。Fig. 5 shows the cycle-slip detection results of satellite No. 30 (Fig. 5(a)) and No. 32 satellite (Fig. 5(b)) of baseline DG→XQ. Fig. 6 shows the cycle-slip detection results of satellite No. 30 (Fig. 6(a)) and No. 32 satellite (Fig. 6(b)) of baseline DG→XQ. Finally, according to the relationship between the baselines in the triangulation network, the base stations with cycle slips are determined, and the cycle slips are repaired for the observation data. For example, if a cycle slip is detected in the baseline DG→XQ, and a cycle slip is also detected in the baseline XQ→NH, it means that the cycle slip occurs on the base station XQ. The reference point solution or flow point solution is used to judge the sign of the cycle slip. For example, if a cycle slip is added to the reference satellite of the base station (such as epoch 40), the residual detection result will be negative, and if a cycle slip is added to the reference satellite of the rover (such as epoch 120), the residual result will be positive or negative. In the baseline DG→XQ, DG is used as the reference point, so the negative sign of the detection result of the baseline DG→XQ is taken as the cycle slip repair value of the base station DG.

根据以上实验表明，本方法能够实现在一个历元中多颗卫星同时出现周跳时的准确探测与修复，当卫星高度角很低，在10°左右时仍能准确探测，并且计算出周跳值。According to the above experiments, this method can realize accurate detection and repair when multiple satellites have cycle slips at the same time in one epoch. When the satellite altitude angle is very low, it can still detect accurately when the satellite altitude angle is about 10°, and calculate the cycle slip value.

Claims

1. A CORS base station cycle slip detection and repair method is characterized in that: according to the known precise coordinates in the CORS network and the time correlation of the troposphere and ionosphere errors and the known integer ambiguity after initialization, according to non-reference Satellites cause gross errors in a single double-difference observation equation, while reference satellites cause systematic errors in all double-difference observation equations. The ionospheric residual method is used to detect cycle slips. According to the cycle slip detection results, a single-epoch double-difference difference observation equation, and finally perform cycle slip repair, including the following steps:

1) The cycle slip is detected according to the ionospheric residual method, the satellites with cycle slip and the corresponding observation values are determined, and the single-epoch double-difference observation equation is established;

2) Divide the double-difference observation equation into two types, the first type is the double-difference observation equation without cycle slip, and the second type is the double-difference observation equation with cycle slip. The cycle slip of the satellite is used as the systematic error;

3) Use the first type of double-difference observation equation for parameter estimation to determine the cycle slip of the reference satellite;

4) Bring the estimated parameters of the first type of double-difference observation equation into the second type of double-difference observation equation, calculate the correction number, and obtain the cycle slip value of the non-reference satellite;

5) According to the relationship between the baselines in the CORS triangulation, the observation data of the base station where the cycle slip occurs is repaired;

The specific method in the above steps is as follows:

1) Ionospheric residual method for cycle slip detection

The basic observation equation of GPS carrier phase non-difference observation is:

Among them, t is the observation epoch; i represents the corresponding L1 and L2 carriers;

The difference between the L1 and L2 carrier phase observations can be obtained:

Where I(t) is the difference between the ionospheric errors of L1 and L2 carrier observations; ε is the single-difference non-model error of L1 and L2 carrier observations;

Calculate the difference between the above ionospheric errors between epochs, we can get:

According to the nature of the ionosphere, for a CORS system with a sampling rate of 1 second, the ionosphere changes in a small amount in a short period of time, and the ionosphere residual error will not exceed 0.1 cycle when no cycle slip occurs in the observed value. If If it exceeds 0.1 cycle, it is considered that there is a cycle slip in the observation value, so that the cycle slip is detected, and the double-difference observation value is classified according to the detection result of the cycle slip;

2) Classification of double-difference observation equations

Using the double-difference observation equation for carrier phase observations, the double-difference observation equation is:

in,

is the double-differenced observation of the carrier phase,

is the double-difference station-satellite distance,

is the double-differenced integer ambiguity,

is the double-differenced ionospheric delay,

is the double-differenced tropospheric delay, is the error caused by the double-difference multipath effect,

is the double-differenced non-model error;

In the CORS network, the double-difference integer ambiguity is obtained after initialization. According to the high sampling rate in the CORS network and the strong correlation of errors between epochs, it is approximated by the double-difference troposphere and ionosphere error values of the previous epoch, that is, the formula (6);

Assuming that the coordinates of one station A in the baseline composed of the CORS base station network are known accurately, and the coordinates of the other station B are estimated as parameters, in the case of no cycle slip and known double-difference ambiguity, the error equation can be obtained for:

{V V}_{A A,, B B}^{i i,, j j} = = Bx Bx - - {L L}_{A A,, B B}^{i i,, j j} - - - - - - ((77))

in

x=[dx dy dz] ^T , B is the coefficient matrix;

In the above error equation, assuming that a non-reference satellite has a cycle slip on a certain site, it will cause gross errors. If the reference satellite has a cycle slip, this cycle slip will bring all the errors Equation, resulting in a systematic error, adding (7) to the system parameters can be obtained:

{V V}_{A A,, B B}^{i i,, j j} = = Bx Bx + + Ey Ey - - {L L}_{A A,, B B}^{i i,, j j} - - - - - - ((88))

Among them, y=[y ₁ ,y ₂ ] ^T are the cycle slips in the carrier observation values of the reference satellite L1 and L2 respectively;

Assuming that in a certain epoch, n satellites are tracked, and in the previous epoch, the ambiguities of the n satellites have been fixed, then the error equations for this epoch can be obtained as:

\underset{(no - 1) \times 1}{V_{L 1}} = \underset{(no - 1) \times 3}{B} \underset{3 \times 1}{x} + \underset{(no - 1) \times 1}{{E.}_{L 1}} \underset{1 \times 1}{{the y}_{1}} - \underset{(no - 1) \times 1}{L_{L 1}}

(9)

\underset{((n no - - 11)) \times \times 11}{{V V}_{L L 22}} = = \underset{((n no - - 11)) \times \times 33}{B B} \underset{33 \times \times 11}{x x} + + \underset{((n no - - 11)) \times \times 11}{{E E.}_{L L 22}} \underset{11 \times \times 11}{{y the y}_{22}} - - \underset{((n no - - 11)) \times \times 11}{{L L}_{L L 22}}

are the error equations on the L1 and L2 carriers, respectively;

According to the cycle-slip detection results of the ionospheric residual method, the real-time double-difference carrier observations are divided into four groups. The first group is the error equation formed by the double-difference observation equation of L1 without cycle slip, represented by _L11 , and the weight is P ₁₁ , the second group is the error equation formed by the double-difference observation equation of L1 with cycle slip, denoted by L ₂₁ , the weight is P ₂₁ , the third group is the error equation formed by the double-difference observation equation of L2 without cycle slip The equation is represented by L ₁₂ and the weight is P ₁₂ . The fourth group is the error equation formed by the double-difference observation equation of L2 with cycle slip, which is represented by L ₂₂ and the weight is P ₂₂ ; then the error equation can be obtained as:

\begin{matrix} {V V}_{1111} = = {B B}_{1111} x x + + {E E.}_{1111} {y the y}_{11} - - {l l}_{1111} \\ {V V}_{21 twenty one} = = {B B}_{21 twenty one} x x + + {E E.}_{21 twenty one} {y the y}_{11} - - {l l}_{21 twenty one} \\ {V V}_{1212} = = {B B}_{1212} x x + + {E E.}_{1212} {y the y}_{22} - - {l l}_{1212} \\ {V V}_{22 twenty two} = = {B B}_{22 twenty two} x x + + {E E.}_{22 twenty two} {y the y}_{22} - - {l l}_{22 twenty two} \end{matrix}\}

P P = = (\begin{matrix} {P P}_{1111} & O o & O o & O o \\ O o & {P P}_{21 twenty one} & O o & O o \\ O o & O o & {P P}_{1212} & O o \\ O o & O o & O o & {P P}_{22 twenty two} \end{matrix}) - - - - - - ((1010))

P is the weight matrix. The error equations composed of the above four sets of double-difference observation equations are further divided into two categories. The error equation formed by the double-difference observation equations of L1 and L2 of the jump, then the above formula can be expressed as:

\begin{matrix} V V 11 = = {B B}_{11} x x + + {E E.}_{11} y the y - - {l l}_{11} \\ V V 22 = = {B B}_{22} x x + + {E E.}_{22} y the y - - {l l}_{22} \end{matrix}\}

P P = = (\begin{matrix} {P P}_{11} & O o \\ O o & {P P}_{22} \end{matrix}) - - - - - - ((1111))

in:

V V 11 = = (\begin{matrix} {V V}_{1111} \\ {V V}_{1212} \end{matrix})

V V 22 = = (\begin{matrix} {V V}_{21 twenty one} \\ {V V}_{22 twenty two} \end{matrix}),,

{B B}_{11} = = (\begin{matrix} {B B}_{1111} \\ {B B}_{1212} \end{matrix})

{B B}_{22} = = (\begin{matrix} {B B}_{21 twenty one} \\ {B B}_{22 twenty two} \end{matrix}),,

{l l}_{11} = = (\begin{matrix} {l l}_{1111} \\ {l l}_{1212} \end{matrix})

{l l}_{22} = = (\begin{matrix} {l l}_{21 twenty one} \\ {l l}_{22 twenty two} \end{matrix})

{E E.}_{11} = = (\begin{matrix} {E E.}_{1111} \\ {E E.}_{1212} \end{matrix})

{E E.}_{22} = = (\begin{matrix} {E E.}_{21 twenty one} \\ {E E.}_{22 twenty two} \end{matrix}),,

y the y = = (\begin{matrix} {y the y}_{11} \\ {y the y}_{22} \end{matrix}),,

{P P}_{11} = = (\begin{matrix} {P P}_{1111} & O o \\ O o & {P P}_{1212} \end{matrix}),,

{P P}_{22} = = (\begin{matrix} {P P}_{21 twenty one} & O o \\ O o & {P P}_{22 twenty two} \end{matrix})

x is the coordinate correction parameter of the rover, and y is the cycle slip in the carrier observation values of the reference satellite L1 and L2;

3) Use the error equation composed of the first kind of double-difference observation equation to estimate the parameters

The second type of double-difference observation equations of L1 and L2 with cycle slips are treated as observation equations with gross errors, and assuming that P ₂ =0, that is, it does not play any role in the solution, then the first type can be directly used Solve the x and y parameters of the carrier observation equations of L1 and L2 without cycle slip, according to the least square criterion V ^T PV=min, the normal equation can be obtained:

(\begin{matrix} {B B}_{11}^{T T} {P P}_{11} {B B}_{11} & {B B}_{11}^{T T} {P P}_{11} {E E.}_{11} \\ {E E.}_{11}^{T T} {P P}_{11} {B B}_{11} & {E E.}_{11}^{T T} {P P}_{11} {E E.}_{11} \end{matrix}) (\begin{matrix} \overset{^^}{x x} \\ \overset{^^}{y the y} \end{matrix}) = = (\begin{matrix} {B B}_{11}^{T T} {P P}_{11} {l l}_{11} \\ {E E.}_{11}^{T T} {P P}_{11} {l l}_{11} \end{matrix}) - - - - - - ((1212))

make

N_{11} = B_{1}^{T} P_{1} B_{1},

N_{12} = N_{twenty one}^{T} = B_{1}^{T} P_{1} {E.}_{1},

N_{twenty two} = {E.}_{1}^{T} P_{1} {E.}_{1},

W_{1} = B_{1}^{T} P_{1} l_{1},

W_{2} = {E.}_{1}^{T} P_{1} l_{1},

Then the above formula can be written as:

(\begin{matrix} {N N}_{1111} & {N N}_{1212} \\ {N N}_{21 twenty one} & {N N}_{22 twenty two} \end{matrix}) (\begin{matrix} \overset{^^}{x x} \\ \overset{^^}{y the y} \end{matrix}) = = (\begin{matrix} {W W}_{11} \\ {W W}_{22} \end{matrix}) - - - - - - ((1313))

From the block inversion formula to get

(\begin{matrix} \overset{^^}{x x} \\ \overset{^^}{y the y} \end{matrix}) = = (\begin{matrix} {N N}_{1111}^{- - 11} + + {N N}_{1111}^{- - 11} {N N}_{1212} {M m}^{- - 11} {N N}_{21 twenty one} {N N}_{1111}^{- - 11} & - - {N N}_{1111}^{- - 11} {N N}_{1212} {M m}^{- - 11} \\ - - {M m}^{- - 11} {n no}_{21 twenty one} {N N}_{1111}^{- - 11} & {M m}^{- - 11} \end{matrix}) (\begin{matrix} {W W}_{11} \\ {W W}_{22} \end{matrix}) - - - - - - ((1414))

In the formula

M m = = {N N}_{22 twenty two} - - {N N}_{21 twenty one} {N N}_{1111}^{- - 11} {N N}_{1212} - - - - - - ((1515))

If there is no cycle slip in the reference satellite, then

\overset{^^}{x x} = = {N N}_{1111}^{- - 11} {W W}_{11} - - - - - - ((1616))

Estimation according to systematic error The cycle slip values on the reference satellite L1 and L2 carriers are obtained as:

\{\begin{matrix} {Slip Slip}_{11} = = \frac{{\overset{^^}{y the y}}_{11}}{{λ λ}_{11}} \\ {Slip Slip}_{22} = = \frac{{\overset{^^}{y the y}}_{22}}{{λ λ}_{22}} \end{matrix} - - - - - - ((1717))

Among them, Slip ₁ and Slip ₂ represent the cycle slips of the carrier phase observations of reference satellites L1 and L2, respectively;

4) Calculation of non-reference satellite cycle slip repair value

Will

and

Substituting V2=B ₂ x+E ₂ yl ₂ , the cycle slip value of the corresponding non-reference satellite can be obtained as:

\{\begin{matrix} {slip slip}_{11} = = \frac{{V V}_{21 twenty one}}{{λ λ}_{11}} \\ s the s {lip the lips}_{22} = = \frac{{V V}_{22 twenty two}}{{λ λ}_{22}} \end{matrix} - - - - - - ((1818))

where slip ₁ and slip ₂ represent the cycle slips of the non-reference satellite L1 and L2 carrier phase observations, respectively;

5) Determine the base station where the cycle slip occurs and the repair of the cycle slip

After the cycle-slip satellite is detected in the baseline, the base station with cycle-slip is determined according to the two baselines corresponding to the base station in the triangulation network. The triangulation network ABC has three baselines A→B, B→C, and C→A. If baseline A A cycle slip is detected in →B, and there is also a cycle slip in the baseline B→C, and the size of the cycle slip is equal and the sign is opposite, then the cycle slip appears on the base station B, and it is calculated according to whether the base station is used as a reference point in the baseline or a flow point solution Calculate to judge the sign of the cycle slip. For a baseline, if the cycle slip occurs at the reference point, the sign of the cycle slip is exactly opposite to that of the residual value. If it occurs at the flow point, the result of the cycle slip is the same as the residual The value signs are the same, in the baseline A→B, point B is used as the flow point, so the cycle slip value detected by the baseline A→B is used as the cycle slip repair value of the base station B; in the same way, according to the baseline C→A and the baseline A →B repairs the cycle slip of base station A, and repairs the cycle slip value of base station C according to baseline B→C and baseline C→A.