A single-epoch GNSS double-difference parameter conversion method for arbitrary primary satellites

Abstract

The present invention discloses a single-epoch GNSS double-difference parameter conversion method for any master satellite, relating to the field of satellite navigation and positioning technology. The method comprises: constructing a master satellite conversion matrix and a double-difference observation quantity sequential transformation matrix and their inverse matrices between any two master satellites based on a single-epoch single-frequency single-system GNSS double-difference mathematical model, and obtaining the invariance and orthogonality of the inverse transformation of the matrix; constructing a single-epoch multi-frequency multi-system master satellite conversion matrix and a double-difference observation quantity sequential transformation matrix and their inverse matrices with inverse transformation invariance and orthogonality by establishing a single-epoch multi-frequency multi-system double-difference mathematical model and analogical deduction; constructing a single-epoch GNSS double-difference model parameter and estimated parameter conversion and inverse transformation formulas between any two or two groups of master satellites based on the above matrices and properties; and performing single-epoch double-difference parameter conversion.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation and positioning technology, and in particular to a single-epoch GNSS double-difference parameter conversion method for any main satellite. Background Art

[0002] Single-epoch differential technology based on the Global Navigation Satellite System (GNSS) can provide all-weather, all-day, fully automatic real-time positioning services. It has broad application prospects in shared vehicle management, unmanned driving, smart city construction, geological disaster monitoring, and other aspects. The correct fixation of the single-epoch ambiguity vector is a prerequisite for using GNSS differential technology to provide precise, real-time positioning services for the above applications.

[0003] Due to the short observation time and lack of verification information of single-epoch GNSS positioning, the accuracy of its ambiguity vector estimation and the reliability of its fixation face severe challenges; although it is possible to use the common double-difference ambiguity vector of the epoch that has been correctly fixed before the current epoch to enhance the estimation accuracy and fixation reliability of the double-difference ambiguity vector corresponding to the current epoch, the problem of primary satellite transformation between observation epochs will lead to changes in the model parameters (such as double-difference ambiguity vector, double-difference pseudorange / carrier observation, etc.) and estimation parameters (such as double-difference floating point / fixed deambiguation vector, ambiguity precision dilution ADOP, etc.) of the single-epoch GNSS double-difference mathematical model. It is difficult to directly use the ambiguity vector correctly fixed in the previous epoch to enhance the estimation accuracy and fixation reliability of the ambiguity vector of the current epoch. It is necessary to convert the double-difference parameters (model parameters and estimation parameters) of two or two groups of arbitrary different primary satellites between the observation epochs. However, the existing methods are only for the conversion of double-difference model parameters and estimated parameters between the first observation satellite as the main satellite and other observation satellites as the main satellite. There is a lack of double-difference mathematical model parameter and estimated parameter conversion methods for any two or two groups of main satellites, making it difficult to realize the conversion of double-difference ambiguity vectors and other estimated parameters between any different main satellites in adjacent epochs. Summary of the Invention

[0004] The embodiment of the present invention provides a single-epoch GNSS double-difference parameter conversion method for any master satellite, which can solve the problem in the prior art that it is difficult to convert double-difference ambiguity vectors and other estimated parameters between any different master satellites in adjacent epochs.

[0005] An embodiment of the present invention provides a single-epoch GNSS double-difference parameter conversion method for any primary satellite, comprising the following steps:

[0006] Constructed with i The single-epoch single-frequency single-system GNSS double-difference mathematical model of the observation satellite as the main satellite is obtained, and thei Single-epoch single-frequency single-system GNSS double-difference estimation parameters of the main satellite of the observation satellite;

[0007] Constructed with i The observation satellite is converted to the main satellite j The master satellite conversion matrix and double-difference observation quantity sequence transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model when the observation satellite is the master satellite;

[0008] Construct the master satellite conversion matrix and the inverse matrix of the double-difference observation sequence transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model, and obtain the invariance of the inverse transformation of the master satellite conversion matrix and the orthogonality of the inverse transformation of the double-difference observation sequence transformation matrix;

[0009] Constructed with A single-epoch multi-frequency multi-system GNSS double-difference mathematical model with an observation satellite as the main satellite is provided. The single-epoch multi-frequency multi-system GNSS is composed of multiple frequencies of multiple GNSS systems. According to the independence of double-difference observations between multiple frequencies of the single-epoch multi-frequency multi-system GNSS, the invariance of the inverse transformation of the main satellite transformation matrix, and the orthogonality of the inverse transformation of the double-difference observation quantity sequence transformation matrix, the main satellite transformation matrix and the double-difference observation quantity sequence transformation matrix of the double-difference mathematical model of multiple frequencies in the single-epoch multi-frequency multi-system GNSS are respectively arranged diagonally in blocks to obtain the double-difference mathematical model to be formed by the first observation satellite. The observation satellite was converted to The main satellite conversion matrix and double-difference observation quantity sequence transformation matrix of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model with the observation satellite as the main satellite, as well as the invariance of the inverse transformation of the main satellite conversion matrix and the orthogonality of the inverse transformation of the double-difference observation quantity sequence transformation matrix for the single-epoch multi-frequency multi-system GNSS; and Both represent multiple observation satellites;

[0010] According to the invariance of the main satellite conversion matrix and the double-difference observation sequence transformation matrix of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model, as well as the orthogonality of the inverse transformation of the main satellite conversion matrix and the double-difference observation sequence transformation matrix, a new method based on the first The observation satellite was converted to The conversion formulas and inverse transformation formulas of the model parameters and estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model when the observation satellite is the main satellite are used to perform the conversion between the single-epoch GNSS double-difference model parameters and estimated parameters.

[0011] The embodiment of the present invention provides a single-epoch GNSS double-difference parameter conversion method for any primary satellite. Compared with the prior art, the method has the following advantages:

[0012] The present invention constructs a master satellite conversion matrix and an observation quantity sequence transformation matrix of a single-epoch single-frequency single-system GNSS double-difference mathematical model between any two master satellites, and constructs the inverse matrix of the master satellite conversion matrix and the observation quantity sequence transformation matrix and obtains the inverse transformation invariance and orthogonality. Then, based on the construction process of the master satellite conversion matrix and the observation quantity sequence transformation matrix of the single-frequency single-epoch single-system GNSS double-difference mathematical model, a single-epoch multi-frequency multi-system GNSS double-difference mathematical model is constructed to obtain a single-epoch multi-frequency multi-system GNSS double-difference with inverse transformation invariance and orthogonality. The main satellite conversion matrix and observation sequence transformation matrix of the mathematical model and their inverse matrix are used to obtain the model parameter and estimation parameter conversion formulas and inverse transformation formulas for the single-epoch single-frequency single-system GNSS double-difference mathematical model and the single-epoch multi-frequency multi-system GNSS double-difference mathematical model, and perform double-difference parameter conversion, thereby realizing the conversion of double-difference ambiguity vectors and other estimated parameters between any two or two groups of different main satellites in adjacent epochs. This has important theoretical value and practical guiding significance for constructing a single-epoch GNSS parameter estimation enhancement model and improving the ambiguity fixation success rate and fixation reliability. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 A schematic diagram of the main flow of a single-epoch GNSS double-difference parameter conversion method for any primary satellite provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0014] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, specific embodiments of the present invention are described in detail below with reference to the accompanying drawings. The following description sets forth many specific details to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar modifications without violating the scope of the present invention. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0015] See also Figure 1 The embodiment of the present invention provides a single-epoch GNSS double-difference parameter conversion method for any master satellite, comprising: constructing a master satellite conversion matrix of a single-epoch single-frequency single-system GNSS double-difference mathematical model between any two master satellites. Z ; Construct the double-difference observation sequence transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model L ; Establish the above transformation matrix Z and the transformation matrix L The inverse matrix of the inverse transformation is analyzed and the invariance and orthogonality of its inverse transformation are analyzed; by analogy with the above-mentioned single-epoch single-frequency single-system transformation matrix and observation sequence transformation matrix, the main satellite transformation matrix of the single-epoch multi-frequency multi-system GNSS with inverse transformation invariance and orthogonality is derived. Zand double difference observation order transformation moment L and its inverse matrix; establish a single-epoch GNSS double-difference model parameter and estimated parameter conversion method for any two or two groups of main satellites.

[0016] Specifically:

[0017] 1. Single epoch GNSS double-difference mathematical model and parameter estimation.

[0018] This part mainly includes the single-epoch double-difference mathematical model (function model and random model) based on the Global Navigation Satellite System (GNSS), double-difference parameter estimation, ambiguity precision index and positioning precision index, and ambiguity fixation reliability theory based on R-ratio test.

[0019] 1.1GNSS double-difference positioning model

[0020] If GNSS is used to observe at the same time m satellites, they can be composed of Single-epoch single-frequency single-system double-difference carrier observations and pseudorange observations , based on the observed and The single-epoch single-frequency single-system GNSS double-difference mathematical model (function model E and random models D ) can be expressed as:

[0021] (1)

[0022] (2)

[0023] in, and Respectively represent The expectation and variance of and Respectively represent The expectation and variance of b and a are the double difference baseline vector and double difference ambiguity vector respectively; B for b The column-full rank double difference coefficient matrix of ; , is the carrier wavelength; is the cofactor matrix of double-difference observations; and are the standard deviations of the undifferenced pseudorange and carrier observations, respectively. and its inverse matrix are all symmetric positive definite matrices. Using the least squares method, according to formula (1) and formula (2), we can get and Floating-point solution of and and its variance-covariance matrix and :

[0024] (3)

[0025] (4)

[0026] in: and They are all symmetric positive definite matrices, and the least squares ambiguity reduction correlation adjustment method can be obtained and Fixed solution and :

[0027] (5)

[0028] in: for and The mutual factor matrix of .

[0029] 1.2 Single epoch ADOP and PDOP theory.

[0030] The Dilution of Precision (DOP) is a scalar factor that is easy to calculate. The DOPs involved in this invention include the Ambiguity DOP (ADOP) and the Positioning DOP (PDOP). The ADOP is primarily used to measure the accuracy of ambiguity estimation and the success rate of ambiguity fixation. It is defined as follows:

[0031] (6)

[0032] in: for The determinant of m - t is the fuzziness vector dimension, t The number of main satellites. For single-frequency single-system GNSS, t = 1. PDOP is mainly used to measure GNSS positioning accuracy and is defined as follows:

[0033] (7)

[0034] Where: trace( )for Generally speaking, the smaller the PDOP is, the higher the positioning accuracy is.

[0035] 1.3 Fuzziness Test Based on R-ratio

[0036] Ambiguity checking is an important step in high-precision positioning using GNSS, which determines whether to accept the optimal integer solution of the ambiguity vector. is a fixed solution. Fuzzy test methods mainly include the success rate / failure rate index method, the statistical difference test method, and a combination of the two methods. The most commonly used one is the R-ratio test method, which belongs to the statistical difference test method and is defined as follows:

[0037] (8)

[0038] in: is the suboptimal integer solution for the ambiguity vector, is the threshold. In general, The values ​​are empirical values ​​such as 1.5, 2.0, 2.5, 3.0, etc.

[0039] 2. Single-epoch single-frequency single-system GNSS double-difference conversion matrix Z and the transformation matrix L .

[0040] According to formula (1) and formula (2), i Single-epoch single-frequency single-system GNSS double-difference function model with two observation satellites as main satellites E and random models D They can be written as:

[0041] (9)

[0042] (10)

[0043] in: and Respectively The expectation and variance of and Respectively The expectation and variance of 、 、 、 、 and Respectively i Parameters of the single-epoch single-frequency single-system GNSS double-difference model with the observation satellite as the main satellite 、 、 B 、 Q 、 aand b ; b and a denote the double difference baseline vector and double difference ambiguity vector respectively; B express b The column-full rank double difference coefficient matrix of ; ; Indicates the carrier wavelength; The cofactor matrix representing the double-difference observations; and Represent the standard deviation of the undifferenced pseudorange and carrier observations respectively; single epoch single frequency single system GNSS double difference model parameters 、 、 、 and They are:

[0044] (11)

[0045] in: 、 and ( l =1, 2,…, m ) are respectively l The single-difference pseudorange observations, single-difference carrier observations and single-difference ambiguities between the receivers of the observation satellites; For the first i Single-epoch single-frequency single-system GNSS differential coefficient matrix of the observation satellite as the main satellite , for The identity matrix of order, The elements are all 1 dimensional column vector, For all elements to be 0 rank matrix, , , in particular, when i =1, ,when i = m hour, ; G is the non-difference unit direction vector between the receiver and the satellite. According to equations (3)-(5) and (9)-(11), i The single-epoch single-frequency single-system GNSS double-difference parameter estimation result of the observation satellite as the main satellite can be written as:

[0046] (12)

[0047] in: 、 、 、 、 、 、 、 and For the first i Single-epoch single-frequency single-system GNSS double-difference estimation parameters of the main satellite 、 、 、 、 、 、 、 and , for and In addition, according to formula (6)-formula (8), the first i The ADOP, PDOP and R-ratio of the single-epoch single-frequency single-system GNSS with two observation satellites as the main satellite can be written as 、 and :

[0048] (13)

[0049] 2.1 Single-epoch single-frequency single-system GNSS primary satellite conversion matrix Z .

[0050] When the i The observation satellite is converted to the main satellite j When the single-epoch single-frequency single-system GNSS double-difference mathematical model of the main satellite is used ( ), due to the replacement of the main satellite, all model parameters in Equations (9) to (11) need to be converted to the main satellite, which involves the main satellite conversion matrix of the single epoch single frequency single system GNSS double difference mathematical model , The construction of mainly faces two situations, namely and ; can be expressed as:

[0051] ① When The main satellite conversion matrix of the single epoch single frequency single system GNSS double difference mathematical model is Expressed as:

[0052] (14)

[0053] in: Representation matrix of( x , y )element;" " indicates single epoch single frequency single system GNSS with the i The observation satellite is converted to the main satellite j The symbol of the observation satellite is the main satellite.

[0054] ②When The main satellite conversion matrix of the single epoch single frequency single system GNSS double difference mathematical model is Expressed as:

[0055] (15)

[0056] To facilitate the construction of the matrix , you can make The initial matrix , and then use formula (14) and formula (15) to assign values ​​to the corresponding elements.

[0057] 2.2 Single-epoch single-frequency single-system GNSS double-difference observation sequence transformation matrix L .

[0058] ① When When , the matrix defined by formula (14) The order of double-difference observations in the converted single-epoch single-frequency single-system GNSS double-difference mathematical model will change, and it needs to be transformed. j The order of the double-difference observations is adjusted to i -1, original j +1 to i -1 double-difference observation quantity order minus 1, the corresponding double-difference observation quantity order transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model It can be written as:

[0059] (16)

[0060] in: Representation matrix of( x , y ) elements; in particular, when hour, , that is, no need to The double-difference observations of the converted mathematical model are transformed sequentially.

[0061] ②When When , the matrix defined by formula (15) The order of the converted single-epoch single-frequency single-system GNSS double-difference observations also needs to be changed. j- 1 double difference observation is adjusted to the first i , the original i toj -The order of the two double-difference observations is increased by 1, and the corresponding double-difference observation order transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model is It can be written as:

[0062] (17)

[0063] In particular, when hour, , that is, no need to The double-difference observations of the converted mathematical model are transformed sequentially.

[0064] To facilitate the construction of the matrix , you can make The initial matrix , and then use formula (16) and formula (17) to assign values ​​to the corresponding elements.

[0065] 2.3 Single-epoch single-frequency single-system GNSS conversion matrix Z With the transformation matrix L Properties and its inverse matrix.

[0066] The master satellite conversion matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model described above and the double-difference observation order transformation matrix It has the following three important properties:

[0067] ①Matrix Z and L The integer property of and From the definition of , we can see that and The elements in are integers such as 0, 1 or -1, that is, Z conversion and L The transformed ambiguity vector still has integer characteristics.

[0068] ②Matrix Z and L The reversibility and integer characteristics of the inverse matrix elements; According to the properties of elementary row / column transformations of determinants, 、 and Established, that is and are all reversible matrices; according to the adjoint matrix and the matrix determinant Inverse matrix Formula It can be seen that and The elements in the inverse matrix are also integers. This property ensures that the matrixZ and matrix L The inverse transformed ambiguity vector still has integer characteristics.

[0069] ③Matrix Z and L Invariance and orthogonality of inverse matrices; with the help of reversible matrices A The relationship , Established, that is It has inverse transformation invariance; by block reversible matrix Perform elementary row transformations, Established, that is Has orthogonal invariance. The matrix and The above properties ensure that Z and L Transformation or Z and L The inverse transformed ambiguity vector still maintains the integer property.

[0070] 3. Single epoch multi-frequency multi-system GNSS double-difference conversion matrix Z and the transformation matrix L .

[0071] Assume that the same frequency or different frequencies of different systems select the main satellite in each system's respective frequency to form a double difference mathematical model and the multi-frequency multi-system GNSS includes d frequency, then d The double difference observations of the frequencies are independent or irrelevant to each other and are based on the first Double-difference function model of single-epoch multi-frequency multi-system GNSS with two observation satellites as main satellites E and random models D They can be written as:

[0072] (18)

[0073] (19)

[0074] in: 、 、 、 and Respectively Model parameters of single-epoch multi-frequency multi-system GNSS with observation satellites as main satellites 、 、 、 and , ( k =1, 2,…,d ) is the k Frequency i observation satellites; , and ( k =1, 2,…, d ) are the first k The wavelength of the frequency and the dimension of the double-difference ambiguity vector; The single-epoch multi-frequency multi-system GNSS differential coefficient matrix and double-difference cofactor matrix of the observation satellite as the main satellite are and ; 、 、 、 、 and ( k =1, 2,…, d ) are respectively k Frequency i Double difference model parameters of the observation satellite as the main satellite 、 、 B 、 a 、 and Q , can be constructed with the help of the definition of relevant parameters in formula (11); , According to equations (18) and (19), the least square method and the least square ambiguity reduction correlation adjustment method are used to obtain Double-difference estimation parameters of single-epoch multi-frequency multi-system GNSS with two observation satellites as main satellites 、 、 、 、 、 、 、 、 and , using the model parameters and estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model in equations (18) and (19) to replace the model parameters and estimated parameters of the single-epoch single-frequency single-system GNSS double-difference mathematical model in equation (12), we can obtain The specific analytical expressions of the single-epoch multi-frequency multi-system GNSS double-difference estimation parameters with the observation satellite as the main satellite are given.

[0075] With the help of the single epoch multi-frequency multi-system GNSS double difference mathematical model dThe independence of the double-difference observations of the frequencies is obtained by diagonally arranging the main satellite conversion matrix and the double-difference observation sequence transformation matrix of multiple single-frequency single-system double-difference mathematical models in the multi-frequency multi-system GNSS. The observation satellite is converted to the main satellite The double-difference mathematical model of single-epoch multi-frequency multi-system GNSS when the observation satellite is the main satellite and the main satellite conversion matrix and the double-difference observation order transformation matrix , respectively expressed as:

[0076] (20)

[0077] (twenty one)

[0078] in:" " indicates that the single epoch multi-frequency multi-system GNSS is The observation satellite is converted to the main satellite The symbol of the observation satellite as the main satellite; , ( k =1, 2,…, d ) is the k Frequency j observation satellites, ; s , For the k The number of satellites observing at the same frequency, and ( k =1, 2,…, d ) are respectively k The master satellite conversion matrix of the frequency and the double difference observation sequence transformation matrix are used to convert the first The double difference mathematical model of the observation satellite as the main satellite is converted into the The double difference mathematical model of the observation satellite as the main satellite can be based on and The numerical relationship between them is constructed using formula (14)-formula (17). In particular, when hour, .

[0079] Factors (20) and (21) are both diagonal matrices, and the matrix and Properties ①-③ are also applicable to the master satellite conversion matrix of the single epoch multi-frequency multi-system GNSS double-difference mathematical model and the double-difference observation order transformation matrix ; Therefore, the matrix and The ambiguity vector after transformation or inverse transformation still has integer characteristics.

[0080] 4. Single-epoch GNSS double-difference parameter conversion method for any two or two groups of main satellites.

[0081] According to the master satellite conversion matrix of the single epoch multi-frequency multi-system GNSS double-difference mathematical model in Equations (20) and (21), and the double-difference observation order transformation matrix ,Depend on" The general formula for model parameter conversion of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model can be written as:

[0082] (twenty two)

[0083] in: 、 、 and Respectively Parameters of the single-epoch multi-frequency multi-system GNSS double-difference model with an observation satellite as the main satellite 、 、 and , ( k =1, 2,…, d ) is the k Frequency j observation satellites; The single-epoch multi-frequency multi-system GNSS differential coefficient matrix and double-difference cofactor matrix of the observation satellite as the main satellite are and ; 、 、 、 、 and ( k =1, 2,…, d ) are respectively k Frequency j Double difference model parameters of the observation satellite as the main satellite 、 、 B 、 a 、 and Q ; and .

[0084] According to the equations (18) and (19), The single-epoch multi-frequency multi-system GNSS double-difference estimation parameters of the observation satellite as the main satellite are obtained by The general formula for parameter conversion of single-epoch multi-frequency multi-system GNSS double-difference estimation can be written as:

[0085] (twenty three)

[0086] (twenty four)

[0087] in, 、 、 、 、 、 and They are respectively for single epoch multi-frequency multi-system GNSS Observation satellites are the main satellites 、 、 、 、 、 and ; Can be further simplified to At the same time, ADOP definition (6), PDOP definition (7) and R-ratio definition (8) can be obtained by " The general formula for the conversion of single-epoch multi-frequency multi-system GNSS double-difference estimation parameters ADOP, PDOP and R-ratio is:

[0088] (25)

[0089] in, 、 and For single epoch multi-frequency multi-system GNSS The ADOP, PDOP and R-ratio values ​​of the observation satellites as the main satellites; In particular, when it is a single-epoch single-frequency single-system GNSS, according to equations (22) to (25), by “ The general formulas for the conversion of single-epoch single-frequency single-system GNSS double-difference model parameters and estimated parameters can be expressed as:

[0090] (26)

[0091] (27)

[0092] Among them: superscript " j " means the j An observation satellite is the main satellite; .

[0093] According to the invariance of the inverse transformation of the main satellite conversion matrix and the orthogonality of the inverse transformation of the double difference observation sequence transformation matrix and equations (22) to (25), we can get “ The general formulas for the inverse transformation of model parameters and estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model are respectively expressed as:

[0094] (28)

[0095] (29)

[0096] in: ;" "express" "Inverse transformation; other single epoch multi-frequency multi-system GNSS double difference estimation parameters 、 、 、 , ADOP, PDOP and R-ratio and Remain unchanged.

[0097] When it is a single-epoch single-frequency single-system GNSS, according to equations (26)-(27), “ The general formulas for the inverse transformation of the parameters and the estimated parameters of the single-epoch single-frequency single-system GNSS double-difference model can be expressed as follows:

[0098] (30)

[0099] (31)

[0100] in:" "express" "Inverse transformation of ;Other single-epoch single-frequency single-system GNSS double-difference estimation parameters 、 、 、 , ADOP, PDOP and R-ratio and remain unchanged;

[0101] According to equations (22) to (31), the single epoch GNSS double difference estimation parameters are 、 、 、 , ADOP, PDOP and R-ratio are all independent of the double-difference master satellite, that is, their values ​​are independent of the selection of the master satellite; single epoch GNSS double-difference estimation parameters 、 and and double-difference mathematical model parameters (double-difference pseudo-range observations , double-difference carrier observation , double difference coefficient matrix , double difference ambiguity vector parameters , difference coefficient matrix and the cofactor matrix of double-difference observations Q ) have double difference elementary transformation consistency, that is, their values ​​vary with the selection of the main satellite, but they can be transformed by the main satellite matrix Z and the double-difference observation order transformation matrix L to convert.

[0102] The above-described embodiments merely illustrate several implementations of the present invention, and while their descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent. It should be noted that a person skilled in the art would be able to make numerous variations and improvements without departing from the spirit of the present invention, all of which fall within the scope of protection of the present invention. Therefore, the scope of protection of the patent for this invention shall be determined by the appended claims.

Claims

1. A single-epoch GNSS double-difference parameter conversion method for any primary satellite, characterized in that: The following steps are involved: Construct a single-epoch single-frequency single-system GNSS double-difference mathematical model with the i-th observation satellite as the main satellite, and obtain its double-difference estimation parameters; Construct the master satellite conversion matrix Z and double-difference observation sequence transformation matrix L of the single-epoch single-frequency single-system GNSS double-difference mathematical model when converting from the i-th master satellite to the j-th master satellite; Construct the inverse matrices of matrix Z and matrix L, and obtain the invariance of the inverse transformation of matrix Z and the orthogonality of the inverse transformation of matrix L; Constructed with The double-difference mathematical model of single-epoch multi-frequency multi-system GNSS with a group of observation satellites as the main satellite is proposed. According to the independence of double-difference observations between multiple frequencies of single-epoch multi-frequency multi-system GNSS, the invariance of the inverse transformation of the matrix Z and the orthogonality of the inverse transformation of the matrix L, the matrices Z and L of the double-difference mathematical model of multiple frequencies in the single-epoch multi-frequency multi-system GNSS are arranged diagonally, and the double-difference mathematical model of multiple frequencies in the single-epoch multi-frequency multi-system GNSS is obtained. The primary satellite of the group switches to the The master satellite transformation matrix Z' and double-difference observation sequence transformation matrix L' of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model of the master satellite group, as well as the invariance of the inverse transformation of the matrix Z' and the orthogonality of the inverse transformation of the matrix L'; According to the main satellite conversion matrix Z' and the double difference observation sequence transformation matrix L', as well as the invariance of the inverse transformation of the matrix Z' and the orthogonality of the inverse transformation of the matrix L', the The primary satellite of the group switches to the The conversion formulas and inverse transformation formulas of the model parameters and estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model of the main satellite of the group are used to convert the single-epoch GNSS double-difference model parameters and estimated parameters.

2. The single-epoch GNSS double-difference parameter conversion method for any primary satellite according to claim 1, characterized in that: The method of constructing a single-epoch single-frequency single-system GNSS double-difference mathematical model with the i-th observation satellite as the primary satellite and obtaining its double-difference estimation parameters includes: When a single-system GNSS is used to observe m satellites at the same time, n = m - 1 single-epoch single-frequency single-system GNSS double-difference carrier observations Φ and pseudorange observations p with the i-th observation satellite as the primary satellite can be formed. The mathematical model of the single-epoch single-frequency single-system GNSS double-difference with the i-th observation satellite as the primary satellite, which is composed of the double-difference function model E of Φ and p and the double-difference random model D, is: Where: E[p i ] and D[p i ] represent p i The expectation and variance of E[Φ i ] and D[Φ i ] represent Φ i The expectation and variance of p i , Φ i 、B i , Q i 、a i and b i are the parameters p, Φ, B, Q, a and b of the single-epoch single-frequency single-system GNSS double-difference model with the i-th observation satellite as the main satellite; b and a represent the double-difference baseline vector and the double-difference ambiguity vector respectively; B represents the column-full-rank double-difference coefficient matrix of b; B λ =λ·I n×n ;λ represents the carrier wavelength; Q represents the cofactor matrix of the double-difference observation; σ p and are the standard deviations of the undifferenced pseudorange and carrier observations respectively; the single-epoch single-frequency single-system GNSS double-difference model parameter p i , Φ i 、B i , Q i and a i They are: Where: l 、φ l and a l are the single-difference pseudorange observations, single-difference carrier observations, and single-difference ambiguities between receivers of the l-th observation satellite, l = 1, 2, …, m; is the single-epoch single-frequency single-system GNSS differential coefficient matrix with the i-th observation satellite as the main satellite I γ×γ is the γ×γ order unit matrix, e γ is a γ-dimensional column vector whose elements are all 1, 0 γ×η is a γ×η matrix with all elements being 0, α=mi,β=i-1. In particular, when i=1, the differential coefficient is When i=m, G is the undifference unit direction vector between receiver and satellite; According to the formula of the single-epoch single-frequency single-system GNSS double-difference function model E and the double-difference random model D, the single-epoch single-frequency single-system GNSS parameter b with the i-th observation satellite as the main satellite is obtained using the least squares method. i and a i Floating-point solution of and and its variance-covariance matrix and Respectively expressed as: in: and The least squares ambiguity reduction correlation adjustment method is used to obtain the single-epoch single-frequency single-system GNSS parameters b with the i-th observation satellite as the main satellite. i and a i Fixed solution and and The variance-covariance matrix of Expressed as: in, for and According to the definition of parameters ADOP, PODP and R-ratio, the single-epoch single-frequency single-system GNSS double-difference estimation parameter ADOP with the i-th observation satellite as the main satellite is obtained. i PDOP i and R-ratio i , respectively expressed as:

3. The single-epoch GNSS double-difference parameter conversion method for any master satellite according to claim 2, characterized in that: The method of constructing the master satellite conversion matrix Z and the double-difference observation quantity sequence transformation matrix L of the single-epoch single-frequency single-system GNSS double-difference mathematical model when converting from the i-th master satellite to the j-th master satellite includes: When converting from the \(i\)-th observation satellite as the main satellite to the \(j\)-th observation satellite as the main satellite in the single-epoch single-frequency single-system GNSS double-difference mathematical model, due to the replacement of the main satellite, all model parameters in the double-difference mathematical model need to be converted for the main satellite, which involves the construction of the main satellite conversion matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model There are mainly two cases, namely \(i > j\) and \(i < j\), which are respectively expressed as: When i>j, the main satellite conversion matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model Expressed as: Where: z xy Representation matrix The (x,y) element of ; "i→j" indicates the symbol transition from a single-epoch single-frequency single-system GNSS with the i-th observation satellite as the primary satellite to a symbol transition with the j-th observation satellite as the primary satellite; Main satellite conversion matrix The order of double-difference observations in the converted single-epoch single-frequency single-system GNSS double-difference mathematical model will change, and it needs to be transformed. The order of the j-th double-difference observation is adjusted to the i-1-th, and the order of the original j+1 to i-1-th double-difference observations is reduced by 1. The corresponding double-difference observation order transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model is Expressed as: Among them: xy Representation matrix (x,y) element; in particular, when j=i-1, That is, no need to The double-difference observations of the converted mathematical model are transformed sequentially; When i < j, the main satellite transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model is expressed as: Main satellite conversion matrix The order of the converted single-epoch single-frequency single-system GNSS double-difference observations needs to be transformed. The order of the j-1th double-difference observation is adjusted to the i-th, and the order of the original i-th to j-2th double-difference observations is increased by 1. The corresponding double-difference observation order transformation matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model is Expressed as: When j=i+1, No need to The double difference observations of the converted mathematical model are transformed in sequence; in order to facilitate the construction of the main satellite conversion matrix make The initial matrix Reuse the above z xy The two formulas assign values ​​to the corresponding elements; to construct the sequential transformation matrix make The initial matrix Using the above l xy The two formulas assign values ​​to the corresponding elements.

4. The single-epoch GNSS double-difference parameter conversion method for any master satellite according to claim 3, characterized in that: The obtaining of the invariance of the inverse transformation of the matrix Z and the orthogonality of the inverse transformation of the matrix L comprises: Depend on and The definition of and The elements in are integers of 0, 1 or -1. According to the properties of elementary row / column transformation of determinant, and The determinants are expressed as: but and are all reversible matrices; according to the adjoint matrix A * Sum matrix determinant |A| find the inverse matrix A -1 Formula A -1 =A * / |A|, and The elements in the inverse matrix are also integers, and The inverse matrix of is expressed as: By partitioning the block reversible matrix Perform elementary row transformations, The inverse matrix of is expressed as: Then the main satellite conversion matrix of the single epoch single frequency single system GNSS double difference mathematical model is The inverse transformation is invariant and the double difference observation order transformation matrix The inverse transform of has orthogonality.

5. The single-epoch GNSS double-difference parameter conversion method for any master satellite according to claim 1, characterized in that: The obtained The primary satellite of the group switches to the The master satellite conversion matrix Z' and double-difference observation sequence transformation matrix L' of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model of the master satellite group, as well as the invariance of the inverse transformation of the matrix Z' and the orthogonality of the inverse transformation of the matrix L', include: The same frequency or different frequencies of different GNSS systems all select the main satellite in their respective frequencies to form a double-difference mathematical model, and the multi-frequency multi-system GNSS includes d frequencies in total. Then the double-difference observations of the d frequencies are independent or irrelevant to each other and are based on the first The double difference function model E and random model D of the single epoch multi-frequency multi-system GNSS with 1 observation satellite as the main satellite can be expressed as follows: in: and Respectively The model parameters p, Φ, B, a and b of the single-epoch multi-frequency multi-system GNSS with the observation satellite as the main satellite, i k is the i-th observation satellite at the k-th frequency, where k = 1, 2, …, d; λ k and n k are the wavelength of the kth frequency in multi-frequency multi-system GNSS and the dimension of the double-difference ambiguity vector, where k = 1, 2, …, d; The single-epoch multi-frequency multi-system GNSS differential coefficient matrix and double-difference cofactor matrix of the observation satellite as the main satellite are and and are the double difference model parameters p, Φ, B, a, and and Q, where k = 1, 2, …, d; According to the above two equations, the least square method and the least square ambiguity reduction correlation adjustment method are used to obtain the Double-difference estimation parameters of single-epoch multi-frequency multi-system GNSS with two observation satellites as main satellites and According to the independence between the double-difference observations of d frequencies in the single-epoch multi-frequency multi-system GNSS double-difference mathematical model, the main satellite conversion matrix and the double-difference observation sequence transformation matrix of multiple single-frequency single-system double-difference mathematical models in the multi-frequency multi-system GNSS are arranged diagonally to obtain the first The observation satellite was converted to The double-difference mathematical model of single-epoch multi-frequency multi-system GNSS when the observation satellite is the main satellite and the main satellite conversion matrix and the double-difference observation order transformation matrix Respectively expressed as: in: Indicates single epoch multi-frequency multi-system GNSS with the The observation satellite was converted to The symbol of the observation satellite as the main satellite; j k is the jth observation satellite at the kth frequency, where k = 1, 2, ..., d, m k is the number of observation satellites at the kth frequency, and are the master satellite conversion matrix and double-difference observation order transformation matrix of the kth frequency, where k = 1, 2, ..., d, to transform the i-th frequency k The double difference mathematical model of the jth observation satellite is converted into the k The double difference mathematical model of the observation satellite as the main satellite is based on i k and j k The numerical relationship between them is used and Definitional construction and when i k =j k hour, According to the main satellite conversion matrix of the single-epoch single-frequency single-system GNSS double-difference mathematical model Invariance of Inverse Transformation and Sequential Transformation Matrix of Double-Difference Observations Orthogonality of inverse transformation, master satellite conversion matrix of single epoch multi-frequency multi-system GNSS double-difference mathematical model The inverse transformation is invariant and the double difference observation order transformation matrix The inverse transform of has orthogonality.

6. The single-epoch GNSS double-difference parameter conversion method for any primary satellite according to claim 5, characterized in that: The construction starts from The primary satellite of the group switches to the The conversion formulas for the model parameters and estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model of the primary satellite of the group include: According to the main satellite conversion matrix and the double-difference observation order transformation matrix By The model parameter conversion formula of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model is expressed as: in: and Respectively The single-epoch multi-frequency multi-system GNSS double-difference model parameters p, Φ, B and a,j of the observation satellite as the main satellite k is the jth observation satellite of the kth frequency, where k = 1, 2, ..., d; The single-epoch multi-frequency multi-system GNSS differential coefficient matrix and double-difference cofactor matrix of the observation satellite as the main satellite are and and are the double difference model parameters p, Φ, B, a, and and Q, where k = 1, 2, …, d; and Depend on The conversion formula of the single-epoch multi-frequency multi-system GNSS double-difference estimation parameters is expressed as: in, and They are respectively for single epoch multi-frequency multi-system GNSS Observation satellites are the main satellites and Simplified to According to the definitions of ADOP, PDOP and R-ratio, The conversion formula of single epoch multi-frequency multi-system GNSS double-difference estimation parameters ADOP, PDOP and R-ratio is expressed as: in: and They are respectively for single epoch multi-frequency multi-system GNSS The ADOP, PDOP and R-ratio values ​​of the observation satellite are the main satellites; when it is a single-epoch single-frequency single-system GNSS, the conversion formulas of the double-difference model parameters and estimated parameters from "i→j" are respectively expressed as: Where: "j" means the j-th observation satellite is the main satellite; 7. The single-epoch GNSS double-difference parameter conversion method for any master satellite according to claim 6, characterized in that: The construction starts from The primary satellite of the group switches to the The inverse transformation formulas for the model parameters and estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model of the primary satellite of the group include: According to the invariance of the inverse transformation of the main satellite conversion matrix and the orthogonality of the inverse transformation of the double difference observation sequence transformation matrix, we have The formulas for inverse transformation of model parameters and inverse transformation of estimated parameters of the single-epoch multi-frequency multi-system GNSS double-difference mathematical model are respectively expressed as: in: express Inverse transformation of other single-epoch multi-frequency multi-system GNSS double-difference estimation parameters ADOP, PDOP and R-ratio and remain unchanged; When it is a single-epoch single-frequency single-system GNSS, the formulas for the inverse transformation of the double-difference model parameters and the inverse transformation of the estimated parameters from "i→j" are respectively expressed as: Among them: "j→i" represents the inverse transformation of "i→j"; Other single-epoch single-frequency single-system GNSS double-difference estimation parameters ADOP, PDOP and R-ratio and Remain unchanged.

8. The single-epoch GNSS double-difference parameter conversion method for any primary satellite according to claim 7, characterized in that: When converting the single epoch GNSS double difference model parameters and the estimated parameters, the single epoch GNSS double difference estimated parameters ADOP, PDOP and R-ratio are all independent of the double-difference primary satellite, which means that the double-difference parameter values ​​are independent of the selection of the primary satellite; Single epoch GNSS double-difference estimation parameters and And double difference mathematical model parameters: double difference pseudorange observation quantity p, double difference carrier observation quantity Φ, double difference coefficient matrix B, double difference ambiguity vector parameter a, difference coefficient matrix The double-difference observation cofactor matrix Q has double-difference elementary transformation consistency, which means that the double-difference parameter values ​​vary with the selection of the main satellite and are transformed through the main satellite transformation matrix Z and the double-difference observation sequence transformation matrix L.

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