Method for resolving weights in inter-satellite baseline based on elevation angle grouping and variance component estimation

Abstract

The application relates to the technical field of satellite orbit calculation, and discloses an inter-satellite baseline solution weight determination method based on elevation angle grouping and variance component estimation, which comprises the following steps: S1) obtaining inter-station single-difference observation values; S2) pre-processing the observation values; S3) determining the weights of the observation values used for parameter estimation based on the elevation angle grouping and variance component estimation method, iteratively performing parameter estimation and orbit integration until convergence, and generating high-precision inter-satellite baseline and outputting the same. The inter-satellite baseline solution weight determination method based on the elevation angle grouping and variance component estimation determines the noise variances of observation values in different elevation angle intervals by using the variance component estimation method, establishes a more accurate and objective random model, and greatly improves the inter-satellite baseline precision.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of satellite orbit calculation, in particular to an inter-satellite baseline solution weight determination method based on elevation angle grouping and variance component estimation. BACKGROUND

[0002] High-precision inter-satellite baseline solution is the key to the completion of the mission of low-orbit satellite formation, such as synthetic aperture radar interferometry (InSAR) satellites (such as Landesat, Gaojing series satellites) and gravity satellites (such as GRACE, GRACE-FO) and other tasks, and the precision directly determines the quality of scientific achievements such as global terrain modeling, ground deformation and mass migration.

[0003] In the determination of inter-satellite baseline based on dynamics method, data preprocessing (cycle slip and gross error detection), parameter estimation, residual editing, orbit integration and other steps are usually involved. Among them, the observation value weight determination is the key link of parameter estimation, which directly affects the precision and reliability of baseline solution. At present, the demand for baseline precision of low-orbit satellite formation mission is higher and higher, and some tasks need to reach millimeter or even sub-millimeter level, so the role of observation value weight determination in inter-satellite baseline solution is increasingly significant.

[0004] The traditional method does not consider the influence of elevation angle on observation noise, and gives the same weight to the observation values of different elevation angles, that is, it is assumed that the observation values of different elevation angles have the same random error level. As a result, low-precision observation values are given unreasonable weight, which amplifies the influence of low-quality observation on parameter solution, and further affects the precision of inter-satellite baseline solution.

[0005] Therefore, how to more accurately and objectively estimate the actual noise variance of observation values in different elevation angle intervals, and accordingly realize optimal weight determination to effectively improve the precision of inter-satellite baseline determination, is a technical problem to be solved in the field. SUMMARY

[0006] The purpose of the present application is to solve the above technical problems, and provide an inter-satellite baseline solution weight determination method based on elevation angle grouping and variance component estimation, which uses variance component estimation method to determine the noise variance of observation values in different elevation angle intervals, establishes a more accurate and objective random model, and greatly improves the precision of inter-satellite baseline.

[0007] To achieve the above purpose, the inter-satellite baseline solution weight determination method based on elevation angle grouping and variance component estimation according to the present application comprises the following steps:

[0008] S1) obtaining inter-station single-difference observation values;

[0009] S2) preprocessing the observation values;

[0010] S3) The observations used for parameter estimation are weighted based on the elevation angle grouping and variance component estimation method. The parameter estimation and orbit integration are iterated until convergence, and a high-precision inter-satellite baseline is generated and output.

[0011] Preferably, in step S3), the weighting based on elevation angle grouping and variance component estimation includes the following steps: the observations at different elevation angles are divided into several sets of observations according to elevation angle intervals, and iteratively performed. In the first iteration, the estimated values ​​are initialized when parameter estimation is performed, and the estimated values ​​for the next iteration are calculated. Then, the variance of the observation set for the next iteration is obtained. Based on the variance, the weights of the observations used for the next iteration are obtained. After multiple iterations until the convergence condition is met, the weights of the observations in each set of observations remain unchanged, and a high-precision inter-satellite baseline is generated and output.

[0012] Preferably, the convergence condition is that the absolute value of the difference between the ratio of the observation weights used in the parameter estimation of two adjacent iterations and 1 is less than the convergence threshold.

[0013] Preferably, during the calculation, the observed values ​​at different elevation angles are divided into b sets of observation values ​​at elevation angle intervals of a°, where a*b=90, and then iterated. The estimated value for parameter estimation in the k-th iteration is given. When k=1, it is... After assigning initial values, the estimated values ​​obtained from the parameter estimation in the (k+1)th iteration are:

[0014]

[0015] In the formula, N k The normal matrix of all sets of observations is summed, N k = N 1,k + N 2,k +…+ N b,k , where the m-th set of observations y m The normal matrix N in the k-th iteration m,k for:

[0016]

[0017] In the formula, 1≤m≤b, A m Let y be the set of observations for the m-th group. m The design matrix W m,k Let y be the set of observations for the m-th group. m The observation weights in the k-th iteration, Let n be the set of observations y of the m-th group. m The number of observations included. Let y be the set of observations for the m-th group.m The variance at the kth iteration, when k=1, is is initialized, I n is an identity matrix, then the mth set of observations y m The variance at the k+1th iteration is:

[0018]

[0019] The mth set of observations y

[0020]

[0021] v m,k+1 =[v 1,k+1 , v 2,k+1 , …, v n-1,k+1 , v n,k+1 ] T , trace is the trace of a matrix, according to the variance at the k+1th iteration , the observation weight used for parameter estimation at the k+2th iteration is obtained , multiple iterations are performed until the convergence condition is reached, the observation weight of each set of observations is unchanged, a high-precision inter-satellite baseline is generated and output.

[0022] Preferably, the convergence condition is .

[0023] Preferably, the matrix A m designed in the step S3) is a matrix of observation sets y m The partial derivative of the parameter to be estimated in the parameter estimation.

[0024] Preferably, in the step S2), the observation values obtained in the step S1) are subjected to cycle slip detection and gross error elimination, and clean observation values for parameter estimation are obtained.

[0025] Preferably, the iteration for parameter estimation and residual editing is continued, and cycle slip detection and gross error elimination are performed.

[0026] Preferably, the parameters for parameter estimation in the step S3) include satellite initial position and velocity, clock error, ambiguity and dynamic parameters.

[0027] Preferably, the orbit integration in the step S3) is based on the satellite initial position and velocity obtained by parameter estimation, and the position and velocity of the satellite at subsequent time are obtained by numerical integration.

[0028] Compared with the prior art, the present application has the following advantages:

[0029] 1. The variance component estimation method is used to determine the observation value noise variance of different group elevation angle intervals, so that a more accurate and objective random model is established;

[0030] 2. The inter-satellite baseline solution weighting method based on elevation angle grouping and variance component estimation generates a dynamic baseline with higher precision than the dynamic baseline under the traditional equal weight model. BRIEF DESCRIPTION OF DRAWINGS

[0031] Figure 1 The flowchart of the inter-satellite baseline solution weighting method based on elevation angle grouping and variance component estimation;

[0032] Figure 2 The KBR check residual STD comparison chart of the GRACE_FO satellite dynamic inter-satellite baseline in January 2019 obtained by the weighting method based on elevation angle grouping and variance component estimation and the equal weight model. DETAILED DESCRIPTION

[0033] The technical solutions of the present application will be described clearly and completely in combination with the drawings and examples. Obviously, the described examples are part of the examples of the present application, rather than all the examples. Based on the examples in the present application, all other examples obtained by those skilled in the art without creative labor belong to the scope of protection of the present application.

[0034] An inter-satellite baseline solution weighting method based on elevation angle grouping and variance component estimation, comprising the following steps:

[0035] S1) Obtain inter-station single difference observation values;

[0036] S2) Preprocess the observation values;

[0037] S3) Weight the observation values used for parameter estimation based on the elevation angle grouping and variance component estimation method, iterate parameter estimation and orbit integration until convergence, generate high-precision inter-satellite baseline and output.

[0038] In step S3), the weight setting based on the elevation angle grouping and the variance component estimation comprises the following steps: the observation values of different elevation angles are divided into a plurality of group observation value sets according to elevation angle intervals, iteration is performed, the estimated value for parameter estimation in the next iteration is calculated by assigning an initial value to the estimated value in the first iteration, and then the variance of the next iteration of the group observation value set is obtained. According to the variance, the observation value weight used for parameter estimation in the next iteration is obtained. Multiple iterations are performed until the convergence condition is reached, the observation value weight of each group observation value set is unchanged, a high-precision inter-satellite baseline is generated, and output is performed. The convergence condition is that the absolute value of the difference between the ratio of the observation value weight used for parameter estimation in the next iteration and the observation value weight used for parameter estimation in the previous iteration and 1 is less than a convergence threshold.

[0039] Specifically, in step S3), when the calculation is performed, the observation values of different elevation angles are divided into b group observation value sets according to a° elevation angle intervals, a*b=90, iteration is performed, The estimated value for parameter estimation in the kth iteration is when k=1, The initial value is assigned, and the estimated value obtained by parameter estimation in the k+1th iteration is:

[0040]

[0041] In the formula, N k is the normal matrix of all group observation value sets, N k = N 1,k + N 2,k +…+ N b,k , wherein the mth group observation value set y m In the kth iteration, the normal matrix N m,k is:

[0042]

[0043] In the formula, 1≤m≤b, A m is the design matrix of the mth group observation value set y m , , W m,k is the observation value weight of the mth group observation value set y m in the kth iteration, , n is the number of observation values contained in the mth group observation value set y m , is the variance of the mth group observation value set y m in the kth iteration, and when k=1, The initial value is assigned, and I n is a unit matrix, then the variance of the mth group observation value set y m in the k+1th iteration is:

[0044]

[0045] The posterior residual of the mth group of observation sets for parameter estimation in the k+1th iteration is:

[0046]

[0047] v m,k+1 =[v 1,k+1 、v 2,k+1 、…、v n-1,k+1 、v n,k+1 ] T , trace is the trace of the matrix, and the observation weight used for parameter estimation in the k+2th iteration is obtained according to the variance of the k+1th iteration. Multiple iterations are performed until the observation weight of each group of observation sets is unchanged after the convergence condition is reached, and the high-precision inter-satellite baseline is generated and output.

[0048] The matrix A is designed in step S3) m for the observation set y m .

[0049] In step S2), the observation values obtained in step S1) are subjected to cycle slip detection and gross error elimination when the observation values are preprocessed, and clean observation values for parameter estimation are obtained. The cycle slip detection and gross error elimination can also be iterated for parameter estimation and residual editing.

[0050] The parameters for parameter estimation in step S3) include satellite initial position and velocity, clock error, ambiguity and dynamic parameters, and the orbit integration in step S3) is based on the satellite initial position and velocity obtained by parameter estimation, and the position and velocity of the satellite at subsequent time are obtained by numerical integration.

[0051] Taking the space-borne GNSS observation values of the GRACE_FO satellite in January 2019 as an example, as shown in Figure 1 , the inter-satellite baseline solution weight determination method based on elevation angle grouping and variance component estimation includes the following steps:

[0052] S1) Obtain inter-station single-difference observation values;

[0053] S2) Preprocess the observation values, and perform cycle slip detection and gross error elimination on the observation values obtained in step S1) to obtain clean observation values for parameter estimation. The cycle slip detection and gross error elimination can also be iterated for parameter estimation and residual editing.

[0054] S3) considering that the observation value weights of different elevation angles for the same type of observation quantity (such as carrier phase and pseudorange) are determined by variance component estimation, the observation values used for parameter estimation are weighted based on elevation angle grouping and variance component estimation method, iterative parameter estimation and orbit integration are performed until convergence, high-precision inter-satellite baselines are generated and output, and the parameters of parameter estimation include satellite initial position and velocity, clock error, ambiguity and dynamic parameters, and the orbit integration is performed based on the satellite initial position and velocity obtained by parameter estimation, and the positions and velocities of satellites at subsequent time points are obtained by numerical integration.

[0055] In step S3), the weighting based on elevation angle grouping and variance component estimation includes the following steps: the observation values at different elevation angles are divided into a plurality of sets of observation values according to elevation angle intervals, iteration is performed, the initial value of the estimated value is assigned when the parameter estimation is performed for the first time, the estimated value for the next iteration of parameter estimation is calculated, and then the variance of the next iteration of the set of observation values is obtained, the observation value weight used for the next iteration of parameter estimation is obtained according to the variance, and the iteration is performed multiple times until the convergence condition is reached, the observation value weights of each set of observation values are unchanged, high-precision inter-satellite baselines are generated and output. The convergence condition is that the absolute value of the difference between the ratio of the observation value weights used for the parameter estimation of the next iteration and the previous iteration and 1 is less than the convergence threshold.

[0056] Specifically, in step S3), the observation values at different elevation angles are divided into 90 sets of observation values according to 1° elevation angle intervals, iteration is performed, is the estimated value for the kth iteration of parameter estimation, and when k = 1, it is is assigned, and the orbit can be solved by precise point positioning, and the estimated value obtained by the k+1th iteration of parameter estimation is:

[0057]

[0058] In the formula, N k is the normal matrix of all sets of observation values, N k = N 1,k + N 2,k +…+ N 90,k , wherein the mth set of observation values y m is: m,k

[0059]

[0060] In the formula, 1≤m≤b, A m is the design matrix of the mth set of observation values y m , the design matrix A m is the design matrix of the observation value set y​m The matrix for taking partial derivatives of the parameters to be estimated in parameter estimation. W m,k Let y be the set of observations for the m-th group. m The observation weights in the k-th iteration, Let n be the set of observations y of the m-th group. m The number of observations included. Let y be the set of observations for the m-th group. m The variance in the k-th iteration, when k=1, is... Assign an initial value to I n If y is the identity matrix, then the set of observations for the m-th group is... m Variance in the (k+1)th iteration:

[0061]

[0062] Wherein, the post-hoc residual of the m-th set of observations after the (k+1)-th iteration for parameter estimation is:

[0063]

[0064] v m,k+1 =[v 1,k+1 v 2,k+1 ..., v n-1,k+1 v n,k+1 ] T The trace is the trace of the matrix, calculated based on the variance of the (k+1)th iteration. Obtain the observation weights used for parameter estimation in the (k+2)th iteration. After multiple iterations until the convergence condition is met, the observation weights of each set of observations remain unchanged, generating and outputting a high-precision inter-satellite baseline. In this embodiment, the convergence condition is... .

[0065] Similarly, taking the onboard GNSS observations of the GRACE_FO satellite in January 2019 as an example, in step S3), the weights are determined based on the equal weight model, that is, it is assumed that for the same type of observations (such as carrier phase and pseudorange), the observations at different elevation angles have the same weight. Parameter estimation and orbit integration iteration are performed until convergence, and a high-precision inter-satellite baseline is generated and output. The parameter estimation is based on the traditional least squares method.

[0066] like Figure 2 The figure shows a comparison of the dynamic inter-satellite baseline KBR check residual STD of the GRACE_FO satellite in January 2019 obtained by the weighting method based on elevation angle grouping and variance component estimation (Scheme B) and the weighting method based on the equal weight model (Scheme A). It can be seen that the accuracy of the inter-satellite baseline generated by the present invention is 38% higher than that of the equal weight model weighting method.

[0067] The application is based on an inter-satellite baseline solution weighting method based on elevation angle grouping and variance component estimation, noise variances of observation values in different elevation angle intervals are determined by using the variance component estimation method, so that a more accurate and objective random model is established; through the inter-satellite baseline solution weighting method based on elevation angle grouping and variance component estimation, the generated dynamic baseline has higher precision than the dynamic baseline under the traditional equal weight model.

[0068] Here, it should be noted that the description of the above technical solutions is exemplary, and the specification can be embodied in different forms, and should not be interpreted as being limited to the technical solutions set forth herein. On the contrary, providing these descriptions will make the present disclosure be thorough and complete, and will fully convey the scope disclosed by the present specification to those skilled in the art. In addition, the technical solutions of the present application are only limited by the scope of the claims.

[0069] The aspects disclosed for describing the specification and claims are only examples, and therefore the specification and claims are not limited to the details shown. In the above description, when detailed description of relevant known functions or configurations is determined to unnecessarily obscure the focus of the specification and claims, detailed description will be omitted.

[0070] Finally, it should be noted that the above content is a further detailed description of the application in combination with the specific embodiments, and the specific embodiments of the application cannot be considered to be limited to these descriptions. For ordinary skilled in the art to which the present application belongs, simple substitutions made without departing from the concept of the present application should be considered to be within the protection scope of the present application. The above examples are only more representative examples of the present application. Obviously, the present application is not limited to the above examples, and there can be many variations. Any simple modification, equivalent change and modification made according to the technical essence of the present application to the above examples should be considered to be within the protection scope of the present application.

Claims

1. An inter-satellite baseline resolving weight determination method based on elevation angle grouping and variance component estimation, characterized in that: The method comprises the following steps: S1) obtaining inter-station single-difference observation values; S2) pre-processing the observation values; S3) weighting the observation values used for parameter estimation based on elevation angle grouping and variance component estimation, iteratively performing parameter estimation and orbit integration until convergence, generating high-precision inter-satellite baselines and outputting the baselines; In the step S3), the weighting based on elevation angle grouping and variance component estimation comprises the following steps: dividing the observation values of different elevation angles into a plurality of sets of observation values according to elevation angle intervals, performing iteration, assigning initial values to the estimated values and the variances of the sets of observation values when performing parameter estimation in the first iteration, then obtaining the observation value weights of the sets of observation values in the current iteration, calculating the estimated values for the next iteration of parameter estimation in combination with the observation value weights, and calculating the variances of the sets of observation values for the next iteration, obtaining the observation value weights used for the next iteration of parameter estimation according to the variances, performing multiple iterations until the observation value weights of the sets of observation values remain unchanged when the convergence condition is reached, generating high-precision inter-satellite baselines and outputting the baselines.

2. The method of claim 1, wherein the method is characterized by: The convergence condition is that the absolute value of the difference between the ratio of the variances calculated in the parameter estimation of the next iteration and the previous iteration and 1 is less than a convergence threshold.

3. The method of claim 1, wherein the method is characterized by: When performing calculations, the observed values ​​at different elevation angles are arranged according to... a ° Altitude angle interval is divided into b Set of observations a * b =90, proceed with iteration. For the first k The estimated value of the parameters in the next iteration, when k= At 1 o'clock, it is Assign initial values, the first k The parameter estimates obtained after +1 iterations are: In the formula, N k The normal matrix of all sets of observations is summed, N k = N 1,k + N 2,k +…+ N b,k , among which, the m Set of observations y m In the k The normal matrix N of the next iteration m,k for; In the formula, 1≤ m ≤ b A m For the first m Set of observations y m The design matrix W m,k For the first m Set of observations y m In the k The observation weights for the next iteration. , n For the first m Set of observations y m The number of observations included. For the first m Set of observations y m In the k The variance of the next iteration, when k= At 1 o'clock, it is Assign initial values, I n If is the identity matrix, then the _i ... m Set of observations y m In the k+ Variance of 1st iteration: wherein the first m The first k The posterior residual of the parameter estimation with the first iteration is: v m,k+1 [ v 1,k+1 、 v 2,k+1 、…、 v n-1,k+1 、 v n,k+1 ] T , trace is the trace of the matrix, according to the first k+ 1 iteration variance , get the observation weight used for parameter estimation in the second k+ 2 iteration , multiple iterations until the convergence condition is reached, the observation weight of each set of observation values is unchanged, and high-precision inter-satellite baseline is generated and output.

4. The method of claim 3, wherein the method further comprises: The convergence condition is .

5. The method of claim 3, wherein the method further comprises: determining the weight of each satellite based on the elevation angle grouping and the variance component estimation. The design matrix A in the step S3 m The observation value set y m The matrix of partial derivatives of the parameters to be estimated in the parameter estimation.

6. The method of claim 1, wherein the method is characterized by: In the step S2), the observation values obtained in the step S1) are subjected to cycle slip detection and gross error elimination to obtain clean observation values for parameter estimation.

7. The method of claim 6, wherein the method further comprises: determining the weight of each baseline based on the elevation angle grouping and the variance component estimation. The iteration of parameter estimation and residual editing is continued, and cycle slip detection and gross error elimination are performed.

8. The method of claim 1, wherein the method is characterized by: The parameters for parameter estimation in the step S3) include satellite initial position and velocity, clock error, ambiguity and dynamic parameters.

9. The inter-satellite baseline calculation and weighting method based on elevation angle grouping and variance component estimation as described in claim 1, characterized in that: The orbit integration in the step S3) is performed based on the satellite initial position and velocity obtained by parameter estimation, and the position and velocity of the satellite at subsequent time points are obtained by numerical integration.

Images