CN116819573B - Long-term model construction method for weakening GPS (Global positioning System) related LOD (LOD) system errors - Google Patents
Long-term model construction method for weakening GPS (Global positioning System) related LOD (LOD) system errors Download PDFInfo
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Abstract
The application belongs to the technical field of satellite navigation, and particularly discloses a long-term model construction method for weakening GPS (Global positioning System) related LOD (LOD) system errors, which comprises the following steps: firstly, a correlation analysis method is utilized to find GPS satellite acceleration parameters related to LOD statistics; then fixing ERP as an accurate value, and solving a time sequence of the ERP aiming at the selected acceleration parameter; modeling the acquired acceleration parameter time sequence; finally, the model is provided for a user to solve LOD; through verification, the method has obvious effect on weakening systematic errors in LOD sequences solved by using GPS observations.
Description
Technical Field
The application belongs to the field of satellite navigation, and particularly relates to a long-term model construction method for weakening GPS (Global positioning System) related LOD (LOD) system errors.
Background
ERP describes the relative orientation between the inertial and ground-fixed systems, which are important transformation parameters between the two coordinate systems. Plays an important role in the fields of satellite navigation, deep space exploration and the like, which is difficult to replace. The time series of ERP also contains important geophysical information, so that the ERP is also an important input for researches on geophysics, extreme weather and the like. LOD (Length Of Day), also known as the solar length parameter, is an important component of ERP to represent changes in the earth's spin rate.
GNSS comprises four large systems, namely a global positioning system (Global Positioning System, GPS for short), a Geranos (GLONASS), a Beidou (BeiDou) and a Galileo (Galileo), and is an important observation means for solving rotation parameters of the earth such as LOD. Although the GNSS observation means cannot realize accurate solution of the UT1-UTC parameters due to the fact that the ascending intersection point (Right Ascension of Ascending Node, RAAN) parameter describing the space orientation of the orbit surface of the artificial earth satellite is strongly related to the UT1-UTC parameter, the change rate of the UT1-UTC day, namely the LOD parameter, solved by using the GNSS observation value has higher precision.
Currently, internationally, an international GNSS service organization (International GNSS Service, abbreviated as IGS) and an international GNSS monitoring and evaluation system (International GNSS Monitoring & evaluation, abbreviated as IGMAS) initiated by china use GNSS observations to issue ERP products including LOD parameters periodically. However, the LOD parameters obtained by using GNSS observations have a significant problem that the international earth rotation service organization (International Earth Rotation Service, abbreviated as ies) 14 c04 product, which is relatively authoritative and is de-fused by multiple observations, has significant systematic errors. The analysis in the publication shows that the LOD systematic errors are mainly related to the GPS system, which can be as high as 20 mus.
Currently, there are four general categories of methods for attenuating systematic errors in LOD data products solved using GPS observations in the prior art:
1. the reference is the IERS Bulletin A product, the LOD data product is calibrated by utilizing a sliding window algorithm, and the required exogenous data product is calculated by a very long baseline interferometry (Very Long Baseline Interferometry, abbreviated as VLBI) observation value. Currently IGS corrects its LOD data product in the manner described above.
2. The sliding window algorithm is also adopted, and the LOD solution systematic error value obtained by using the observations of other GNSS systems such as BeiDou is considered to be smaller, and is usually better than 5 mu s. And correcting the GPS LOD solution by adopting other GNSS LOD solutions to replace the IERS Bulletin A product.
3. LOD is solved by combining the observations of the multiple GNSS systems.
4. The data processing time period when the LOD was calculated was extended from 1 day to 3 days.
In the process of implementing the present application, the inventor finds that at least the following problems exist in the prior art:
1. the method of correcting LOD system errors using a sliding window algorithm requires waiting for historical data to accumulate. In addition, since the LOD system error varies with time, the method needs to adjust the sliding window length in time to ensure the correction effect. Up to now, two sliding window lengths of 21 days and 10 days have been adopted by IGS. In summary, the flexibility and convenience of the method are insufficient.
2. The analysis result of the existing literature shows that the method for solving the LOD by combining the multi-GNSS system observations has limited effect on weakening the LOD system error. The LOD solution obtained by using the observation values of the GPS, GLONASS, galileo three systems has a system error value of about 10 mu s.
3. Although the method for expanding the data processing time from 1 day to 3 days can effectively weaken LOD system errors, the requirement on a quality control algorithm for data processing is high, and the realization is relatively complex.
Disclosure of Invention
In order to solve the technical problems, the application provides a long-term model construction method for weakening GPS related LOD system errors, which adopts the following technical scheme:
a long-term model construction method for mitigating GPS-related LOD system errors, comprising:
step one: using a correlation analysis method to find GPS satellite acceleration parameters related to LOD statistics;
step two: fixing ERP to be an accurate value, and solving acceleration parameters found in the first step;
step three: modeling the acceleration parameter time sequence obtained in the second step;
step four: and (3) based on the model obtained in the step (III), inputting a time difference calculation model value of the current moment relative to the reference moment, and solving the LOD.
Specifically, in the first step, the method for analyzing the correlation includes:
solving LOD by using the GPS observation value, and outputting a covariance matrix among parameters to be estimated;
based on the covariance matrix, calculating a correlation coefficient between parameters to be estimated;
evaluating the correlation between parameters to be estimated;
wherein the parameters to be estimated include acceleration parameters and LOD.
Specifically, the method for calculating the correlation coefficient uses the following formula:
（1）
wherein,representing parameters to be estimatedX，YThe correlation coefficient between the two,Cov(X, Y)representing parameters to be estimatedX，YThe covariance of the two is obtained by the method,Cov(X, X)representing parameters to be estimatedXIs a function of the variance of (a),Cov(Y, Y)representing parameters to be estimatedYIs a variance of (2);
wherein the method comprises the steps ofThe absolute value of (2) is closer to 1X，YThe stronger the correlation between them; and when->If the absolute value of (2) is greater than the set threshold, then the acceleration parameter is considered to be correlated with LOD.
Specifically, the threshold is set to 0.2.
Specifically, in the third step, modeling is performed on the acceleration time sequence acquired in the second step, and the model is represented by the following formula:
（2）
wherein the method comprises the steps ofThe reference time is the starting time of the time sequence for modeling;nfor the selected model order;a i , b i , c i is the i-th order coefficient of the model.
Specifically, the order of the model is not lower than 3.
In particular, in the model,a i , b i , c i and (3) fitting the acceleration parameter time sequence obtained in the step two to obtain the numerical value of (2).
Specifically, in the second step:
when the acceleration parameters are solved, each GPS satellite solves a group, and the solving interval is 1 day;
when ERP is fixed to an accurate value, the resolving time is more than 1 year.
The application has the following beneficial effects:
(1) Compared with the method for correcting LOD system errors by utilizing a sliding window algorithm, the application provides
The model of the model is effective for a long time, and a user does not need to wait for accumulation of historical data and does not need to adjust algorithm parameters;
(2) Compared with a method for solving LOD by combining multiple GNSS system observations, the method has better correction effect on LOD system errors, and the corrected LOD system errors can be better than 5 mu s;
(3) Compared with a method for expanding the data processing time length from 1 day to 3 days, the method can achieve a better LOD system error correction effect under the condition that the data processing time length is 1 day, and has no special requirement on a quality control algorithm of data processing;
(4) Compared with the method that the accurate priori value of the satellite acceleration parameter is calculated at first in fixed ERP and then used for LOD solving, the method provided by the application does not need to update the input parameter every day.
Drawings
FIG. 1 is a schematic flow chart of the present application;
FIG. 2 is a graph showing the comparison of LOD results obtained in the present application with the LOD results obtained in the prior art, wherein the three line diagrams from top to bottom are respectively: the LOD result corresponding to the model, the LOD result corresponding to the IGS method result with the sliding window length of 10 days and the LOD result corresponding to the IGS method with the sliding window length of 21 days are provided by the application;
the results in fig. 2 are referenced by the ies 14 c04 product, and respectively show timing diagrams of LOD results solved by the present application versus the ies 14 c04 product differences;
FIG. 3 is a table comparing the mean and RMS of the LOD results of the present application versus the product variance of IERS 14C 04; wherein the mean indicator is used to measure the systematic error magnitude of the LOD result relative to the ies 14 c04 product; the RMS index is used for evaluating the precision of the LOD result; the larger the mean value, the larger the systematic error between the LOD result and the ies 14 c04 product; the greater the RMS value, the lower the accuracy of the LOD result.
Detailed Description
In order that the above-recited objects, features and advantages of the present application will be more fully understood, a more particular description of the application will be rendered by reference to the appended drawings, which are given in connection with FIGS. 1-3 and detailed description thereof. It should be noted that, without conflict, the embodiments of the present application and features in the embodiments may be combined with each other. The described embodiments are only some, but not all, embodiments of the application. Further, technical means not specifically described in the examples are conventional means well known to those skilled in the art.
The application provides a long-term model construction method for weakening GPS related LOD system errors, which has a flow shown in a figure 1, specifically, an accurate priori value Of an acceleration parameter is modeled for satellite acceleration parameters statistically related to the LOD parameter, and the method is used for LOD solving based on GPS observation values, and LOD is a Length Of Day parameter (LOD) for short in the application. The specific steps of the application are as follows:
step one: using a correlation analysis method to find GPS satellite acceleration parameters related to LOD statistics;
specifically, in the first step, the method of correlation analysis is as follows: when solving for LOD using GPS observations, a covariance matrix between the parameters to be estimated is typically output.
Based on the covariance matrix, a correlation coefficient between two parameters to be estimated (acceleration parameter and LOD) can be calculated to evaluate the correlation between them. The method for calculating the correlation coefficient is as follows:
（1）
wherein,representing parameters to be estimatedX，YThe correlation coefficient between the two,Cov(X, Y)representing parameters to be estimatedX，YThe covariance of the two is obtained by the method,Cov(X, X)representing parameters to be estimatedXIs a function of the variance of (a),Cov(Y, Y)
representing parameters to be estimatedYIs a variance of (c).The absolute value of (2) is closer to 1X，YThe stronger the correlation between them. The application adopts 0.2 as a threshold value, and if the absolute value of the correlation coefficient between the acceleration parameter and the LOD is larger than the threshold value, the acceleration parameter is considered to be correlated with the LOD.
Step two: fixing ERP to be an accurate value, and solving acceleration parameters;
specifically, in the second step, when the ERP is fixed to an accurate value, the ERP prior accurate value, such as the IERS 14C 04 product value, is substituted into the ERP variable in the observation equation, and the ERP is not used as a parameter to be estimated to be solved; the solving process of the acceleration is that the partial derivative of the pseudo range relative to the corresponding acceleration parameter is determined through theoretical deduction, and then a parameter estimation algorithm, such as a least square algorithm, is adopted to estimate the value of the acceleration parameter. When the acceleration parameters are solved, each GPS satellite solves a group, and the solving interval is 1 day. The ERP accurate value can adopt an IERS 14C 04 product, and the calculating time is recommended to be more than 1 year.
Step three: modeling the acceleration parameter time sequence;
specifically, in step three, the model form may be a sinusoidal progression. To ensure modeling effect, the model order should not be lower than 3. The specific form of the model is as follows:
（2）
wherein the method comprises the steps ofThe time difference between the current time and the reference time is given in days. The reference moments are time series for modelingStarting time.nFor the selected model order.a i , b i , c i The value of the coefficient is the ith order coefficient of the model, and can be obtained by fitting the acceleration parameter time sequence in the second step.
Step four: based on the model, the difference between the time of the current time and the reference time is inputTo calculate model values for the solution of LOD. After solving for LOD, as shown in figures 2 and 3,
experimental results show that LOD results solved based on the above method have significant features of small systematic errors relative to the ies 14 c04 product.
In addition, in the first step, according to the measurement adjustment theory, the calculation method of the LOD waiting estimation parameter and the calculation method of the covariance matrix are as follows:
for the matrix form of the GNSS observations equation:
（3）
where y is the vector of observations, A is the design matrix,for the parameter vector to be estimated including LOD, V is the residual vector. Setting the approximate value of the parameter vector to be estimated to be X 0 Then->Can be expressed as:
（4）
in the middle ofIs the correction relative to the approximation and there is the following relationship:
（5）
（6）
(6) Wherein y is 0 For an approximation of y,representing the correction of y. Substitution of formulas (4), (5) and (6) into (3) can result in:
（7）
using the least squares principle, it is possible to:
（8）
middle and upper markT Representing a transpose of the matrix, P being the weight matrix, min represents the goal of parameter estimation to minimize the value to the left of the equation. The method can be used for obtaining the following steps:
（9）
and finally substituting the step (7) into the step (2), so that the LOD waiting estimation parameter can be solved.
Parameter vector to be estimatedThe covariance matrix is mathematically defined as follows, and the covariance matrix is denoted by D.
（10）
(10) In the method, in the process of the application,E representing mathematical expectations. Due to X 0 Substituting (2) into (8) is constant, and can be obtained:
（11）
combining (7) the propagation law of variances to obtain a covariance matrix:
（12）
wherein the method comprises the steps ofError in unit weight, its estimate is:
（13）
in the method, in the process of the application,ris the number of redundant observations.
Compared with the prior art, the application has the characteristics of flexibility and convenience. The application provides a solution for finding out satellite acceleration parameters related to LOD statistics through a correlation analysis method and further modeling the accurate priori values of the selected acceleration parameters. The acceleration prior value is derived from a result solved when the ERP is fixed to an accurate value. The application has the following specific technical advantages:
(1) Compared with a method for correcting LOD system errors by utilizing a sliding window algorithm, the model provided by the application is effective for a long time, and a user does not need to wait for accumulation of historical data and does not need to adjust algorithm parameters;
(2) Compared with a method for solving LOD by combining multiple GNSS system observations, the method has better correction effect on LOD system errors, and the corrected LOD system errors can be better than 5 mu s;
(3) Compared with a method for expanding the data processing time length from 1 day to 3 days, the method can achieve a better LOD system error correction effect under the condition that the data processing time length is 1 day, and has no special requirement on a quality control algorithm of data processing;
(4) Compared with the method that the accurate priori value of the satellite acceleration parameter is calculated at first in fixed ERP and then used for LOD solving, the method provided by the application does not need to update the input parameter every day.
Referring to fig. 2, a specific embodiment is given below:
this example uses the GPS satellite observations collected by 188 global stations for 4.5 years in length to illustrate the effect of the application. Of the selected stations, observation data of 99 stations are used for constructing a model; the observation data of the rest 89 measuring stations are not involved in model construction, and are only used for LOD calculation so as to verify the correction effect of the model on LOD system errors. For the selected data period, the observed data of the first 3.5 years is used to build the model; the last 1 year data is not involved in model construction, but is used only for LOD resolution to verify the long-term effect of the model. In addition, with the sliding window method currently used by IGS, a set of LODs was corrected using sliding window lengths of 10 days and 21 days, respectively, for comparison of model action effects.
The specific working process is as follows:
step one: the application is utilized to construct a long-term model.
Step two: the LOD is solved by using the long-term model constructed in the step one.
Step three: the LOD is solved without using a long-term model. And corrects for LOD results using a sliding window algorithm with a sliding window length of 10 days, with reference to the ier 14 c04 product.
Step four: the LOD is solved without using a long-term model. And corrects for LOD results using a sliding window algorithm with a sliding window length of 21 days, with reference to the ier 14 c04 product. And then calculating the difference between the LOD result and the IERS 14C 04 product in the second, third and fourth steps and the statistical value of the difference, and finding that the LOD result solved based on the method has the obvious characteristic of small systematic error relative to the IERS 14C 04 product.
The corrective effect of the different strategies is given in fig. 2. In fig. 2, the ordinate indicates the difference size of the LOD calculation compared to the ier 14 c04 product, and the dotted line is used to distinguish between the first 3.5 years and the second 1 year. The Mean and Root Mean Square error (RMS) statistics of the differences under different schemes are given in the table of figure 3. In fig. 2 and 3, REF represents a reference experimental result directly calculated using GPS observations without any correction. Long-term represents the model proposed by the present application. IGS-10d represents the IGS method results for a sliding window length of 10 days. IGS-21d represents the IGS method results for a sliding window length of 21 days.
Referring to fig. 3, it can be seen from the mean value result that the algorithm proposed by the present application has a significant effect on weakening systematic errors in LOD sequences solved by using GPS observations, compared to the sliding window method. For the period of the previous 3.5 years when the observed value participates in the model construction and the period of the later 1 year when the observed value does not participate in the model construction, the corrected LOD system error is better than 5 mu s, and the correction effect of the model on the LOD system error is long-term effective.
The above embodiments are only illustrative of the preferred embodiments of the present application and are not intended to limit the scope of the present application, and various modifications, variations, alterations, substitutions made by those skilled in the art to the technical solution of the present application should fall within the protection scope defined by the claims of the present application without departing from the spirit of the design of the present application.
Claims (5)
1. A long-term model construction method for attenuating GPS-related LOD system errors, comprising:
step one: using a correlation analysis method to find GPS satellite acceleration parameters related to LOD statistics;
step two: fixing ERP to be an accurate value, and solving acceleration parameters found in the first step;
step three: modeling the acceleration parameter time sequence obtained in the second step;
step four: based on the model obtained in the step three, inputting a time difference calculation model value of the current moment relative to the reference moment for solving LOD;
in the first step, the correlation analysis method comprises the following steps:
solving LOD by using the GPS observation value, and outputting a covariance matrix among parameters to be estimated;
based on the covariance matrix, calculating a correlation coefficient between parameters to be estimated;
evaluating the correlation between parameters to be estimated;
wherein the parameters to be estimated comprise acceleration parameters and LOD;
the calculation method of the correlation coefficient adopts the following formula:
，
wherein the parameters to be estimated are representedX，YThe correlation coefficient between the two,Cov(X, Y)representing parameters to be estimatedX，YThe covariance of the two is obtained by the method,Cov (X, X)representing parameters to be estimatedXIs a function of the variance of (a),Cov(Y, Y)representing parameters to be estimatedYIs a variance of (2);
the absolute value of the absolute value is close to 1X，YThe stronger the correlation between them; and when the absolute value is greater than the set threshold, then the acceleration parameter is considered to be correlated to LOD;
in the third step, modeling is performed on the acceleration time sequence obtained in the second step, and the model is represented by the following formula:
，
wherein is the difference in time of the current time relative to a reference time, the reference time being the starting time of the time series for modeling;nfor the selected model order;a i , b i , c i is the i-th order coefficient of the model.
2. The method of claim 1, wherein the threshold is set to 0.2.
3. The method of claim 1, wherein the model has an order of not less than 3.
4. A long term model construction method for mitigating GPS-related LOD systematic errors of claim 1, wherein, in the model,a i , b i , c i and (3) fitting the acceleration parameter time sequence obtained in the step two to obtain the numerical value of (2).
5. The method for constructing a long-term model for attenuating GPS-related LOD system errors according to claim 1, wherein in said step two:
when the acceleration parameters are solved, each GPS satellite solves a group, and the solving interval is 1 day;
when ERP is fixed to an accurate value, the resolving time is more than 1 year.
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