Pseudo-range precision optimization quantification method based on GNSS redundant pseudo-range observation

Abstract

The application discloses a pseudo-range precision optimization quantization method based on GNSS redundant pseudo-range observation, and relates to the field of satellite navigation and positioning. The method comprises the following steps: constructing a double-difference mathematical model according to GNSS pseudo-range and carrier phase observation, and obtaining a baseline vector floating point solution variance-covariance matrix by using a least square method; adding a redundant pseudo-range observation to the double-difference mathematical model, and obtaining a baseline vector floating point solution variance-covariance matrix after adding the redundant pseudo-range observation by using the least square method; constructing an original pseudo-range precision optimization quantization formula after adding the redundant pseudo-range observation according to the baseline vector floating point solution variance-covariance matrix before and after adding the redundant pseudo-range observation; obtaining a value required for original pseudo-range precision optimization quantization according to a given ADOP value; and adding the redundant pseudo-range observation to the double-difference mathematical model until the calculated value of the original pseudo-range precision optimization quantization is not greater than the value required for the original pseudo-range precision optimization quantization, so that the given ADOP value and GNSS reliable precise positioning are realized.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning, specifically to a method for optimizing and quantifying pseudorange accuracy based on GNSS redundant pseudorange observations. Background Technology

[0002] In Global Navigation Satellite System (GNSS), accurate fixation of the ambiguity vector is crucial for precise positioning using the GNSS double-difference mathematical model. The higher the accuracy of the floating-point solution of the GNSS ambiguity vector, the greater the probability of correctly fixing the ambiguity vector. Adding redundant pseudorange observations to GNSS can improve the probability of correctly fixing the ambiguity vector by increasing the accuracy of the floating-point solution. Essentially, adding redundant pseudorange observations is equivalent to optimizing the accuracy of the original pseudorange observations.

[0003] However, due to the current lack of a quantitative method for measuring the degree to which redundant pseudorange observations optimize the accuracy of the original pseudorange observations, it is difficult to directly control the added redundant pseudorange observations by calculating the quantified value of the original pseudorange observations' accuracy optimization. The improvement in the accuracy of the ambiguity vector floating-point solution can only be evaluated by calculating the variance-covariance matrix of the floating-point solution after adding redundant pseudorange observations. This method increases computational complexity and affects the efficiency of precise positioning. Furthermore, due to the lack of a quantitative method for optimizing the accuracy of the original pseudorange observations based on GNSS redundant pseudorange observations, existing methods cannot reveal the mechanism by which the spatial distribution, accuracy, and quantity of redundant pseudorange observations affect the accuracy of the original pseudorange observations. Summary of the Invention

[0004] To address the aforementioned technical shortcomings, the purpose of this invention is to provide a method for optimizing and quantifying pseudorange accuracy based on redundant pseudorange observations in GNSS. This method solves the problem that traditional methods can only assess the improvement in the accuracy of the floating-point solution of the ambiguity vector by calculating the variance-covariance matrix of the floating-point solution after adding redundant pseudorange observations. It reduces the complexity of the algorithm and improves the efficiency of precise positioning. This method has significant theoretical implications for improving the success rate and reliability of GNSS ambiguity vector fixation and provides methodological support for studying the influence mechanism of the spatial distribution, accuracy, and quantity of redundant pseudorange observations on the accuracy of the original pseudorange observations.

[0005] To solve the above-mentioned technical problems, the present invention adopts the following technical solution: The present invention provides a pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations, including:

[0006] S1: Based on GNSS pseudorange observations and carrier phase observations, construct a single-epoch GNSS double-difference mathematical model, and use the least squares method to obtain the baseline vector floating-point solution variance-covariance matrix;

[0007] S2: Add redundant GNSS pseudorange observations to a single-epoch GNSS double-difference mathematical model, and use the least squares method to obtain the floating-point solution variance-covariance matrix of the baseline vector after adding redundant GNSS pseudorange observations.

[0008] S3: Based on the floating-point solution variance-covariance matrix of the baseline vector in S1 and the floating-point solution variance-covariance matrix of the baseline vector after adding GNSS redundant pseudorange observations in S2, construct the quantization formula for optimizing the accuracy of pseudorange observations in S1 after adding GNSS redundant pseudorange observations.

[0009] S4: Based on ADOP theory, according to the ADOP approximation formula and the given ADOP value, obtain the accuracy required for GNSS pseudorange observations in S1 to achieve the given ADOP value;

[0010] S5: Based on the accuracy of GNSS pseudorange observations in S1 and the required accuracy of GNSS pseudorange observations, obtain the value required for optimizing and quantizing the accuracy of GNSS pseudorange observations in S1.

[0011] S6: Based on the quantization formula for optimizing the pseudorange observation accuracy in S1 after adding redundant pseudorange observations, obtain the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 after adding redundant pseudorange observations. Compare whether the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 is not greater than the value required for the optimized quantization of the GNSS pseudorange observation accuracy. Otherwise, continue to add redundant pseudorange observations to the single-epoch GNSS double-difference mathematical model until the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 is not greater than the value required for the optimized quantization of the GNSS pseudorange observation accuracy.

[0012] Preferably, S1 includes:

[0013] S1.1: Constructing a single-epoch multi-frequency GNSS double-difference mathematical model:

[0014] Defined as the observation of GNSS at a certain epoch. t Frequency 1 satellite, of which For the first k Number of observation satellites at different frequencies k =1, 2,……, t If a primary satellite is selected within each frequency range to form a double-difference mathematical model, then the result is N=M- t A single-epoch multi-frequency GNSS double-difference mathematical model consisting of one double-difference pseudorange observation and N double-difference carrier phase observations:

[0015] ;

[0016] ;

[0017] In the formula, and They are respectively and Expectations and They are respectively and The variance; , , and These are, respectively, the double-difference pseudorange observations of multi-frequency GNSS, the N-dimensional double-difference carrier phase observations, the double-difference ambiguity vector, and the N×3 order baseline vector double-difference coefficient matrix. and The first k Frequency double-difference pseudorange observation, double-difference carrier phase observation, double-difference ambiguity vector, and baseline vector double-difference coefficient matrix. k =1,2,…, t ; , ,and The first k The carrier wavelength and the dimension of the double-difference ambiguity vector at each frequency. k =1, 2,…, t , is an identity matrix of order ; A 3D baseline vector for multi-frequency GNSS; , , , , The first k The double-difference observable cofactor array, the accuracy of the non-difference pseudorange observable, and the accuracy of the non-difference carrier phase observable at each frequency. for zero-order matrix;

[0018] S1.2: Constructing a single-epoch, single-frequency GNSS double-difference mathematical model:

[0019] When only one frequency is observed at a certain epoch m When a satellite is in use, it can form a system composed of... One double-difference pseudorange observation and n A single-epoch, single-frequency, single-system GNSS double-difference mathematical model consisting of two double-difference carrier phase observations:

[0020] ;

[0021] ;

[0022] In the formula, and These are single-frequency double-difference pseudorange observations. and single-frequency double-difference carrier phase observations Expectations; and They are respectively and The variance; and These are the 3D baseline vectors for single-frequency GNSS and n 3D double-difference ambiguity vector; , For single-frequency carrier wavelength, for An identity matrix of order 1. The double-difference coefficient matrix of the baseline vector of a single-frequency GNSS; It is a cofactor matrix of two-difference observations; and These are the accuracy measurements of non-difference pseudorange and carrier phase observations for single-frequency GNSS, respectively. for A zero matrix of order zero.

[0023] Preferably, in S1, obtaining the floating-point solution variance-covariance matrix of the GNSS baseline vector using the least squares method includes:

[0024] According to S1.1 Chinese style Japanese style Using the least squares method, floating-point solutions for the baseline vector and ambiguity vector for multi-frequency GNSS are obtained. and and variance-covariance matrix and :

[0025] ;

[0026] ;

[0027] According to S1.2 Chinese style Japanese style The baseline vector for single-frequency GNSS is obtained using the least squares method. and ambiguity vector Floating-point solution and and variance-covariance matrix and :

[0028] ;

[0029] .

[0030] Preferably, in S2, GNSS redundant pseudorange observations are added to the single-epoch GNSS double-difference mathematical model, and the baseline vector floating-point solution variance-covariance matrix after adding GNSS redundant pseudorange observations is obtained using the least squares method, including:

[0031] S2.1: Add Frequency Redundant pseudorange observations from several observation satellites, among which For redundant pseudorange observations s Number of observation satellites at different frequencies s =1, 2, …, Then it forms One double-difference redundant pseudorange observation;

[0032] Add it to S1.1 Chinese style and The formula yields:

[0033] ;

[0034] ;

[0035] In the formula, and These are the GNSS redundant double-difference pseudorange observations and their corresponding baseline vector double-difference coefficient matrices, respectively. and The first s Redundant double-difference pseudorange observations at frequencies and their corresponding baseline vector double-difference coefficient matrices. s =1, 2, …, , for zero-order matrix; , and The first s The accuracy of the double-difference cofactor matrix and the non-difference pseudorange observations of frequency redundancy pseudorange observations;

[0036] Based on Japanese style Using the least squares method, the baseline vector for multi-frequency GNSS is obtained after adding GNSS redundant pseudorange observations. Floating-point solution and its variance-covariance matrix :

[0037] ;

[0038] In the formula, ;

[0039] S2.2: Will be added frequency The redundant pseudorange observations formed by the observation satellite A double-difference redundant pseudorange observation is added to S1.2. Japanese style From:

[0040] ;

[0041] ;

[0042] In the formula, for zero-order matrix;

[0043] Based on Japanese style Using the least squares method, the single-frequency GNSS baseline vector after adding GNSS redundant pseudorange observations is obtained. Floating-point solution and its variance-covariance matrix :

[0044] ;

[0045] In the formula, .

[0046] Preferably, in S3, the quantization formula for optimizing the pseudorange observation accuracy in S1 after adding GNSS redundant pseudorange observations includes a multi-frequency pseudorange observation accuracy optimization quantization formula and a single-frequency pseudorange observation accuracy optimization quantization formula, specifically including:

[0047] S3.1: When the GNSS double-difference mathematical model before adding redundant pseudorange observations corresponds to multiple frequencies, the quantification formula for optimizing the accuracy of multi-frequency pseudorange observations in S1.1 after adding redundant pseudorange observations is:

[0048] ;

[0049] In the formula, To improve the accuracy of multi-frequency GNSS pseudorange observations in S1.1 after adding redundant GNSS pseudorange observations. Optimized quantization value, ; , , and They are respectively , , and The determinant of;

[0050] S3.2: When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to a single frequency, the quantification formula for optimizing the accuracy of single-frequency pseudorange observations in S1.2 after adding GNSS redundant pseudorange observations is:

[0051] ;

[0052] In the formula, To improve the accuracy of single-frequency GNSS pseudorange observations in S1.2 after adding redundant GNSS pseudorange observations. Optimized quantization value; , , and They are respectively , , and The determinant of .

[0053] Preferably, in S4:

[0054] Define the ambiguity vector floating-point solution variance-covariance matrix And fuzzy vector dimension x Functions:

[0055] ;

[0056] In the formula, for The determinant of ADOP, where Cycle is the unit of ADOP;

[0057] ADOP is used to measure the integer least squares success rate of the ambiguity vector. for:

[0058] ;

[0059] In the formula, and These represent the success rates based on ADOP and the success rates based on integer sequential rounding, respectively. It is the standard normal distribution function; and All are monotonically decreasing functions of ADOP;

[0060] The ADOP approximation for multi-frequency GNSS is:

[0061] ;

[0062] In the formula, , , For the first k Frequency The weights of the observation satellites, k =1,2,…, t The higher the observation accuracy, the greater the weight. , and The first k The standard deviation of the non-difference of frequency pseudorange and carrier phase observations k =1, 2, …, t ;

[0063] The ADOP approximation for single-frequency GNSS is:

[0064] ;

[0065] In the formula, For single-frequency The weights of the observation satellites, i =1, 2,…, m， The higher the observation accuracy, the greater the weight.

[0066] Preferably, in S4:

[0067] Fixed success rate based on the required ambiguity Through the formula Determine or give the ADOP value of a fixed-dimensional ambiguity vector. ;

[0068] When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to multiple frequencies, according to the formula... The required accuracy for multi-frequency GNSS pseudorange observations in S1.1 The formula is:

[0069] ;

[0070] In the formula, For multi-frequency GNSS observations ;

[0071] When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to a single frequency, according to the formula... The required accuracy for single-frequency GNSS pseudorange observations in S1.2 The formula is:

[0072] ;

[0073] In the formula, For single-frequency GNSS observations .

[0074] Preferably, in S5, obtaining the values ​​required for GNSS pseudorange observation accuracy optimization and quantization in S1 includes the values ​​required for multi-frequency GNSS pseudorange observation accuracy optimization and quantization and the values ​​required for single-frequency GNSS pseudorange observation accuracy optimization and quantization, specifically including:

[0075] According to S1.1 Chinese style Japanese style Average accuracy of multi-frequency GNSS pseudorange observations and the required accuracy for multi-frequency GNSS pseudorange observations The required values ​​for optimizing and quantizing the accuracy of multi-frequency GNSS pseudorange observations in S1.1 are obtained:

[0076] ;

[0077] According to S1.2 Chinese style Japanese style single-frequency GNSS pseudorange observation accuracy and the required accuracy for single-frequency GNSS pseudorange observations The required values ​​for optimizing the quantization of single-frequency GNSS pseudorange observation accuracy are obtained:

[0078] .

[0079] Preferably, S6 specifically includes:

[0080] S6.1: Sort the redundant pseudorange observations of GNSS according to the elevation angle of their corresponding satellites from high to low;

[0081] S6.2: Add redundant pseudorange observations of GNSS to the single-epoch GNSS double-difference mathematical model according to the elevation angle from high to low;

[0082] If the added GNSS redundant pseudorange observations include If a frequency is added for the first time, then at least two redundant GNSS pseudorange observations are added for each frequency; if it is not added for the first time, then at least one redundant GNSS pseudorange observation is added for each frequency, and together with the previously added redundant GNSS pseudorange observations of the same frequency, they form a double-difference mathematical model.

[0083] S6.3: According to formula or Obtain the optimized quantized values ​​of the multi-frequency GNSS pseudorange observation accuracy in S1.1 after adding GNSS redundant pseudorange observations. Alternatively, the optimized quantization calculation value of single-frequency GNSS pseudorange observation accuracy in S1.2 after adding redundant GNSS pseudorange observations. ;

[0084] S6.4: Judgment or Is it valid?

[0085] S6.5: If the condition in S6.4 is met, then stop adding redundant GNSS pseudorange observations; otherwise, continue adding redundant GNSS pseudorange observations to the single-epoch GNSS double-difference mathematical model in S1, and repeat steps S6.2, S6.3, S6.4 and S6.5 until the condition in S6.4 is met.

[0086] The beneficial effects of this invention are as follows: This invention utilizes GNSS pseudorange and carrier phase observations to construct a single-epoch GNSS double-difference mathematical model. By adding redundant pseudorange observations to the single-epoch GNSS double-difference mathematical model, and using the least squares method, the variance-covariance matrix of the baseline vector floating-point solution before and after adding redundant pseudorange observations is obtained. Based on the variance-covariance matrix of the baseline vector floating-point solution before and after adding redundant pseudorange observations, an optimization quantization formula for the accuracy of the original pseudorange observations after adding redundant pseudorange observations is constructed. For the single-epoch GNSS double-difference mathematical model before adding redundant pseudorange observations, the accuracy is optimized using a given ambiguity vector precision factor. The method obtains the required accuracy values ​​for the original pseudorange observations and the required values ​​for optimizing and quantizing the accuracy of the original pseudorange observations by calculating the ADOP value. Redundant pseudorange observations are added from high to low according to the corresponding satellite elevation angles until the calculated value for optimizing and quantizing the accuracy of the original pseudorange observations is no greater than the required value. This achieves a given ADOP value and precise and reliable GNSS positioning. It solves the problem that traditional methods can only assess the improvement in the accuracy of the ambiguity vector floating-point solution by calculating the variance-covariance matrix of the added redundant pseudorange observations. This reduces the complexity of the algorithm and improves the efficiency of precise positioning. It has significant theoretical implications for improving the success rate and reliability of GNSS ambiguity vector fixing and confirmation, and provides methodological support for studying the influence mechanism of the spatial distribution, accuracy, and quantity of redundant pseudorange observations on the accuracy of the original pseudorange observations. Attached Figure Description

[0087] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0088] Figure 1 The flowchart shows the pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations provided by this invention. Detailed Implementation

[0089] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0090] Example: This invention provides a pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations, including the following steps:

[0091] S1: Based on GNSS pseudorange observations and carrier phase observations, a single-epoch GNSS double-difference mathematical model is constructed, and the least squares method is used to obtain the baseline vector floating-point solution variance-covariance matrix.

[0092] S1.1: Construct a single-epoch multi-frequency GNSS double-difference mathematical model, and use the least squares method to obtain the variance-covariance matrix of the baseline vector floating-point solution for multi-frequency GNSS:

[0093] Specifically, assuming GNSS is observed at a certain epoch t Frequency 1 satellite, of which ( k =1, 2,……, t ) is the first k If the number of observation satellites at each frequency is determined by selecting a master satellite within each frequency to form a double-difference mathematical model, then the formula N=M- can be used to form a mathematical model. t A single-epoch multi-frequency GNSS double-difference mathematical model consisting of one double-difference pseudorange observation and N double-difference carrier phase observations:

[0094] (1);

[0095] (2);

[0096] In the formula, and They are respectively and Expectations and They are respectively and The variance; , , and These are, respectively, the double-difference pseudorange observations of multi-frequency GNSS, the N-dimensional double-difference carrier phase observations, the double-difference ambiguity vector, and the N×3 order baseline vector double-difference coefficient matrix. and The first kFrequency double-difference pseudorange observation, double-difference carrier phase observation, double-difference ambiguity vector, and baseline vector double-difference coefficient matrix. k =1,2,…, t ; , and The first k The carrier wavelength and the dimension of the double-difference ambiguity vector at each frequency. k =1, 2,…, t , for An identity matrix of order 1; A 3D baseline vector oriented towards multiple frequencies; , The first k The double-difference observable cofactor array, the accuracy of the non-difference pseudorange observable, and the accuracy of the non-difference carrier phase observable at each frequency. for A zero matrix of order zero.

[0097] Based on equations (1) and (2), the baseline vector for multi-frequency GNSS can be obtained using the least squares method. and ambiguity vector Floating-point solution and and its variance-covariance matrix and :

[0098] (3);

[0099] (4);

[0100] S1.2: Construct a single-epoch, single-frequency GNSS double-difference mathematical model, and use the least squares method to obtain the floating-point solution variance-covariance matrix of the baseline vector for single-frequency GNSS:

[0101] Suppose that only one frequency is observed at a certain epoch. m A single satellite can then form a series of double-difference pseudorange observations and n A single-epoch, single-frequency, single-system GNSS double-difference mathematical model consisting of two double-difference carrier phase observations:

[0102] (5);

[0103] (6);

[0104] In the formula, and These are single-frequency double-difference pseudorange observations. and single-frequency double-difference carrier phase observations Expectations; and They are respectively and The variance; and These are 3D baseline vectors for single frequency and n 3D double-difference ambiguity vector; , For single-frequency carrier wavelength, For the order identity matrix The double-difference coefficient matrix of the baseline vector of a single-frequency GNSS; It is a cofactor matrix of two-difference observations; and These are the accuracy measurements of non-difference pseudorange and carrier phase observations for single-frequency GNSS, respectively. for A zero matrix of order zero.

[0105] Based on equations (5) and (6), the baseline vector for single-frequency GNSS can be obtained using the least squares method. and ambiguity vector Floating-point solution and and its variance-covariance matrix and :

[0106] (7);

[0107] (8);

[0108] According to equations (3) and (4) or equations (7) and (8), the fixed solution of the ambiguity vector and the fixed solution of the baseline vector can be obtained by using the least squares ambiguity decorrelation adjustment method to achieve precise positioning.

[0109] S2: Add redundant GNSS pseudorange observations to a single-epoch GNSS double-difference mathematical model, and use the least squares method to obtain the floating-point solution variance-covariance matrix of the baseline vector after adding redundant GNSS pseudorange observations.

[0110] Specifically, in this embodiment, redundant or redundant pseudorange observations based on multiple frequencies are added to the single-epoch GNSS double-difference mathematical model (i.e., equations (1) and (2), and equations (5) and (6)); at the same time, in order to facilitate the construction and expression of the double-difference mathematical model, it is assumed that the main satellite is selected in the added redundant pseudorange observations and each frequency selects its own main satellite to form a double-difference mathematical model of redundant pseudorange observations.

[0111] Specifically, it includes:

[0112] S2.1: Add Frequency Redundant pseudorange observations from several observation satellites, among which For redundant pseudorange observations s Number of observation satellites at different frequencies s =1, 2, …, Then it forms Adding a double-difference redundant pseudorange observation to equations (1) and (2) yields:

[0113] (9);

[0114] (10);

[0115] In the formula, and These are the GNSS redundant double-difference pseudorange observations and their corresponding baseline vector double-difference coefficient matrices, respectively. and The first s Redundant double-difference pseudorange observations at frequencies and their corresponding baseline vector double-difference coefficient matrices. s =1, 2, …, , for zero matrix of order 1; The first s The accuracy of the double-difference cofactor array and the non-difference pseudorange observations of frequency redundancy pseudorange.

[0116] Based on equations (9) and (10), the baseline vector for multi-frequency GNSS after adding redundant pseudorange observations can be obtained using the least squares method. Floating-point solution and its variance-covariance matrix :

[0117] (11);

[0118] In the formula, .

[0119] S2.2: If by frequency The redundant pseudorange observations of the observation satellites constitute Adding a double-difference redundant pseudorange observation to equations (5) and (6), we can obtain:

[0120] (12);

[0121] (13);

[0122] In the formula, for A zero matrix of order zero.

[0123] Based on equations (12) and (13), the baseline vector for single-frequency GNSS after adding redundant pseudorange observations can be obtained using the least squares method. Floating-point solution and its variance-covariance matrix :

[0124] (14);

[0125] In the formula, .

[0126] S3: Based on the baseline vector floating-point solution variance-covariance matrix in S1 and the baseline vector floating-point solution variance-covariance matrix after adding GNSS redundant pseudorange observations in S2, construct the quantization formula for optimizing the accuracy of pseudorange observations in S1 after adding GNSS redundant pseudorange observations.

[0127] Specifically, adding redundant GNSS double-difference pseudorange observations to the single-epoch GNSS double-difference mathematical model can improve the accuracy and probability of correct fixation of the ambiguity vector floating-point solution. That is, the accuracy of the ambiguity vector floating-point solution calculated by equations (9) and (10) is better than that calculated by equations (1) and (2); similarly, the accuracy of the ambiguity vector floating-point solution calculated by equations (12) and (13) is better than that calculated by equations (5) and (6). The essence of the above results is that adding redundant GNSS pseudorange observations is equivalent to optimizing the accuracy of pseudorange observations in S1.1 and S1.2.

[0128] Specifically, it includes:

[0129] S3.1: When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to multiple frequencies (i.e., equations (1) and (2)), the quantification formula for optimizing the accuracy of multi-frequency pseudorange observations in S1.1 after adding GNSS redundant pseudorange observations is:

[0130] (15);

[0131] In the formula, To improve the accuracy of multi-frequency GNSS pseudorange observations in S1.1 after adding redundant GNSS pseudorange observations. Optimized quantization value, ; , , and They are respectively , , and The determinant of; , .

[0132] because , Weighted double-difference coefficient matrix of multi-frequency redundant pseudorange observations All are positive definite matrices and If the matrix is ​​positive definite or positive semi-definite, according to the Peter-Weyl theory, Its establishment improves upon the original multi-frequency pseudorange. The accuracy.

[0133] S3.2: When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to a single frequency (i.e., equations (5) and (6)), the quantification formula for optimizing the accuracy of single-frequency pseudorange observations in S1.2 after adding GNSS redundant pseudorange observations is:

[0134] (16);

[0135] In the formula, To improve the accuracy of single-frequency GNSS pseudorange observations in S1.2 after adding redundant GNSS pseudorange observations. Optimized quantization value; , , and They are respectively , , and The determinant of; , .

[0136] Similarly, because , Weighted double-difference coefficient matrix of multi-frequency redundant pseudorange observations All are positive definite matrices and If the matrix is ​​positive definite or positive semi-definite, according to the Peter-Weyl theory, Established, this improves upon the original single-frequency pseudorange. The accuracy.

[0137] S4: Based on ADOP theory, according to the ADOP approximation formula and the given ADOP value, obtain the GNSS pseudorange observation accuracy required to achieve the given ADOP value.

[0138] Specifically, ADOP is an easily computed scalar factor used to measure the accuracy of ambiguity vector estimation; it is a floating-point solution variance-covariance matrix of the ambiguity vector. And fuzzy vector dimension x The function is defined as follows:

[0139] (17);

[0140] In the formula, for The determinant of ADOP, where Cycle is the unit of ADOP.

[0141] ADOP can also be used to measure the integer least squares success rate of the ambiguity vector. :

[0142] (18);

[0143] In the formula, and These represent the success rates based on ADOP and the success rates based on integer sequential rounding, respectively. It is the standard normal distribution function; and All are monotonically decreasing functions of ADOP.

[0144] To achieve advance estimation of ambiguity vector accuracy and fixed success rate, an approximate formula for ADOP is given, where ADOP based on Multiple Frequency (ADOP) is used for multi-frequency GNSS. The approximate formula is:

[0145] (19);

[0146] In the formula, , , For the first k Frequency i The weight of each observation satellite is determined by its observation accuracy; the higher the observation accuracy, the greater the weight. and The first k The standard deviation of the frequency pseudorange and carrier phase observations k =1, 2, …, t .

[0147] ADOP based on Single Frequency GNSS The approximate formula is:

[0148] (20);

[0149] In the formula, For single-frequency i The weight of each observation satellite is determined by its observation accuracy; the higher the observation accuracy, the greater the weight.

[0150] Fixed success rate based on the required ambiguity By using equation (18), the value of the ambiguity vector ADOP with a fixed dimension can be determined or given. ,according to The implementation can be obtained by approximating the ADOP formula. The required pseudorange observation accuracy. When facing a GNSS double-difference mathematical model based on multi-frequency observations (i.e., equations (1) and (2)), according to equation (19), the required accuracy of multi-frequency GNSS pseudorange observations in S1.1 is... The formula is:

[0151] (twenty one);

[0152] In the formula, For multi-frequency GNSS observations When facing a GNSS double-difference mathematical model based on single-frequency observations (i.e., equations (5) and (6)), according to equation (20), the required accuracy formula for single-frequency GNSS pseudorange observations in S1.2 is:

[0153] (twenty two)

[0154] In the formula, For single-frequency GNSS observations .

[0155] Specifically, based on the required pseudorange observation accuracy and the existing pseudorange observation accuracy, the value required for optimizing and quantizing the pseudorange observation accuracy can be obtained. When facing a GNSS double-difference mathematical model based on multi-frequency observations (i.e., equations (1) and (2)), the average pseudorange observation accuracy of multi-frequency GNSS can be obtained from equations (1) and (2). and the required accuracy for multi-frequency GNSS pseudorange observations This allows us to obtain the values ​​required for optimizing and quantizing the accuracy of multi-frequency GNSS pseudorange observations in S1.1. :

[0156] (twenty three);

[0157] When dealing with a GNSS double-difference mathematical model based on single-frequency observations (i.e., equations (5) and (6)), the accuracy of single-frequency GNSS pseudorange observations in equations (5) and (6) is determined. and the required accuracy for single-frequency GNSS pseudorange observations This allows us to obtain the values ​​required for optimizing and quantizing the accuracy of single-frequency GNSS pseudorange observations in S1.2. :

[0158] (twenty four).

[0159] S6: Based on the quantization formula for optimizing the pseudorange observation accuracy in S1 after adding redundant pseudorange observations, obtain the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 after adding redundant pseudorange observations. Compare whether the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 is not greater than the value required for the optimized quantization of the GNSS pseudorange observation accuracy. Otherwise, continue to add redundant pseudorange observations to the single-epoch GNSS double-difference mathematical model until the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 is not greater than the value required for the optimized quantization of the GNSS pseudorange observation accuracy.

[0160] Specifically, it includes:

[0161] S6.1: Sort the redundant pseudorange observations of GNSS according to the elevation angle of their corresponding satellites from high to low;

[0162] S6.2: Add redundant pseudorange observations of GNSS from high to low elevation angle to a single-epoch GNSS double-difference mathematical model (i.e., equations (1) and (2) or equations (5) and (6)).

[0163] If the added GNSS redundant pseudorange observations include If a frequency is added for the first time, then at least two redundant GNSS pseudorange observations are added for each frequency; if it is not added for the first time, then at least one redundant GNSS pseudorange observation is added for each frequency, and together with the previously added redundant GNSS pseudorange observations of the same frequency, they form a double-difference mathematical model.

[0164] S6.3: Obtain the optimized quantitative calculation value of the multi-frequency GNSS pseudorange observation accuracy in S1.1 after adding GNSS redundant pseudorange observations according to equation (15) or equation (16). Alternatively, the optimized quantization calculation value of single-frequency pseudorange observation accuracy in S1.2 after adding GNSS redundant pseudorange observations. ;

[0165] S6.4: Determine the optimized quantization value of pseudorange observation accuracy in S1 after adding GNSS redundant pseudorange observations. Is it not greater than the value required for pseudorange observation accuracy optimization and quantization? ,Right now Is it valid?

[0166] S6.5: If the condition in S6.4 is met, then stop adding redundant GNSS pseudorange observations; otherwise, continue adding redundant GNSS pseudorange observations to the single-epoch GNSS double-difference mathematical model (i.e., equations (1) and (2) or equations (5) and (6)), and repeat steps S6.2, S6.3, S6.4 and S6.5 until the condition in S6.4 is met.

[0167] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations, characterized in that, include: S1: Based on GNSS pseudorange observations and carrier phase observations, construct a single-epoch GNSS double-difference mathematical model, and use the least squares method to obtain the baseline vector floating-point solution variance-covariance matrix; S2: Add redundant GNSS pseudorange observations to a single-epoch GNSS double-difference mathematical model, and use the least squares method to obtain the floating-point solution variance-covariance matrix of the baseline vector after adding redundant GNSS pseudorange observations. S3: Based on the floating-point solution variance-covariance matrix of the baseline vector in S1 and the floating-point solution variance-covariance matrix of the baseline vector after adding GNSS redundant pseudorange observations in S2, construct the quantization formula for optimizing the accuracy of pseudorange observations in S1 after adding GNSS redundant pseudorange observations. S4: Based on ADOP theory, according to the ADOP approximation formula and the given ADOP value, obtain the accuracy required for GNSS pseudorange observations in S1 to achieve the given ADOP value; S5: Based on the accuracy of GNSS pseudorange observations in S1 and the required accuracy of GNSS pseudorange observations, obtain the value required for optimizing and quantizing the accuracy of GNSS pseudorange observations in S1. S6: Based on the quantization formula for optimizing the pseudorange observation accuracy in S1 after adding redundant pseudorange observations, obtain the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 after adding redundant pseudorange observations. Compare whether the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 is not greater than the value required for the optimized quantization of the GNSS pseudorange observation accuracy. Otherwise, continue to add redundant pseudorange observations to the single-epoch GNSS double-difference mathematical model until the calculated value of the optimized quantization of the GNSS pseudorange observation accuracy in S1 is not greater than the value required for the optimized quantization of the GNSS pseudorange observation accuracy.

2. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 1, characterized in that, S1 includes: S1.1: Constructing a single-epoch multi-frequency GNSS double-difference mathematical model: Defined as the observation of GNSS at a certain epoch. t Frequency 1 satellite, of which For the first k Number of observation satellites at different frequencies k =1, 2,……, t If a primary satellite is selected within each frequency range to form a double-difference mathematical model, then the result is N=M- t A single-epoch multi-frequency GNSS double-difference mathematical model consisting of one double-difference pseudorange observation and N double-difference carrier phase observations: ； In the formula, and They are respectively and Expectations and They are respectively and The variance; , , and These are, respectively, double-difference pseudorange observations of multi-frequency GNSS, Double-difference carrier phase observations, double-difference ambiguity vectors, and The double difference coefficient matrix of the baseline vector. , , and The first k Frequency double-difference pseudorange observation, double-difference carrier phase observation, double-difference ambiguity vector, and baseline vector double-difference coefficient matrix. k =1,2,…, t ; , , and The first k The carrier wavelength and the dimension of the double-difference ambiguity vector at each frequency. k =1, 2,…, t , for An identity matrix of order 1; A 3D baseline vector for multi-frequency GNSS; , , , , ( k =1,2,…, t ) are respectively the first k The double-difference observable cofactor array, the accuracy of the non-difference pseudorange observable, and the accuracy of the non-difference carrier phase observable at each frequency. for zero-order matrix; S1.2: Constructing a single-epoch, single-frequency GNSS double-difference mathematical model: When only one frequency is observed at a certain epoch m When a satellite is in use, it can form a system composed of... One double-difference pseudorange observation and n A single-epoch, single-frequency, single-system GNSS double-difference mathematical model consisting of two double-difference carrier phase observations: ； In the formula, and These are single-frequency double-difference pseudorange observations. and single-frequency double-difference carrier phase observations Expectations; and They are respectively and The variance; and These are the 3D baseline vectors for single-frequency GNSS and n 3D double-difference ambiguity vector; , For single-frequency carrier wavelength, for An identity matrix of order 1. For single-frequency GNSS The double difference coefficient matrix of the baseline vector; It is a cofactor matrix of two-difference observations; and These are the accuracy measurements of non-difference pseudorange and carrier phase observations for single-frequency GNSS, respectively. for A zero matrix of order 1.

3. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 2, characterized in that, In S1, the floating-point solution variance-covariance matrix of the GNSS baseline vector is obtained using the least squares method, including: According to S1.1 Chinese style Japanese style The baseline vector for multi-frequency GNSS is obtained using the least squares method. and ambiguity vector Floating-point solution and and variance-covariance matrix and : ； ； According to S1.2 Chinese style Japanese style The baseline vector for single-frequency GNSS is obtained using the least squares method. and ambiguity vector Floating-point solution and and variance-covariance matrix and : ； 。 4. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 2, characterized in that, In S2, redundant GNSS pseudorange observations are added to the single-epoch GNSS double-difference mathematical model. The least squares method is used to obtain the floating-point solution variance-covariance matrix of the baseline vector after adding redundant GNSS pseudorange observations, including: S2.1: Add Frequency Redundant pseudorange observations from several observation satellites, among which For redundant pseudorange observations s Number of observation satellites at different frequencies s =1, 2, …, Then it forms One double-difference redundant pseudorange observation; Add it to S1.1 Chinese style Japanese style From: ； ； In the formula, and These are the GNSS redundant double-difference pseudorange observations and their corresponding baseline vector double-difference coefficient matrices, respectively. and The first s Redundant double-difference pseudorange observations at frequencies and their corresponding baseline vector double-difference coefficient matrices. s =1, 2, …, , for zero-order matrix; , and The first s The accuracy of the double-difference cofactor matrix and the non-difference pseudorange observations of frequency redundancy pseudorange observations; Based on Japanese style Using the least squares method, the baseline vector for multi-frequency GNSS is obtained after adding GNSS redundant pseudorange observations. Floating-point solution and its variance-covariance matrix : ； In the formula, , , ; S2.2: Will be by frequency The redundant pseudorange observations formed by the observation satellite A double-difference redundant pseudorange observation is added to S1.

2. Japanese style From: ； ； In the formula, for zero-order matrix; Based on Japanese style Using the least squares method, the single-frequency GNSS baseline vector after adding GNSS redundant pseudorange observations is obtained. Floating-point solution and its variance-covariance matrix : ； In the formula, , , .

5. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 2, characterized in that, In S3, the quantization formula for optimizing the pseudorange observation accuracy in S1 after adding GNSS redundant pseudorange observations includes a multi-frequency pseudorange observation accuracy optimization quantization formula and a single-frequency pseudorange observation accuracy optimization quantization formula, specifically including: S3.1: When the GNSS double-difference mathematical model before adding redundant pseudorange observations corresponds to multiple frequencies, the quantification formula for optimizing the accuracy of multi-frequency pseudorange observations in S1.1 after adding redundant pseudorange observations is: ； In the formula, To improve the accuracy of multi-frequency GNSS pseudorange observations in S1.1 after adding redundant GNSS pseudorange observations. Optimized quantization value, ; , , and They are respectively , , and The determinant of; S3.2: When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to a single frequency, the quantification formula for optimizing the accuracy of single-frequency pseudorange observations in S1.2 after adding GNSS redundant pseudorange observations is: ； In the formula, To improve the accuracy of single-frequency GNSS pseudorange observations in S1.2 after adding redundant GNSS pseudorange observations. Optimized quantization value; , , and They are respectively , , and The determinant of .

6. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 2, characterized in that, In S4: Define the ambiguity vector floating-point solution variance-covariance matrix And fuzzy vector dimension x Functions: ； In the formula, for The determinant of ADOP, where Cycle is the unit of ADOP; ADOP is used to measure the integer least squares success rate of the ambiguity vector. for: ； In the formula, and These represent the success rates based on ADOP and the success rates based on integer sequential rounding, respectively. It is the standard normal distribution function; and All are monotonically decreasing functions of ADOP; The ADOP approximation for multi-frequency GNSS is: ； In the formula, , , For the first k Frequency i The weights of the observation satellites, k =1,2,…, t , The higher the observation accuracy, the greater the weight. and The first k The standard deviation of the frequency pseudorange and carrier phase observations k =1, 2, …, t ; The ADOP approximation for single-frequency GNSS is: ； In the formula, For single-frequency i The weights of the observation satellites, i =1, 2,…, m The higher the observation accuracy, the greater the weight.

7. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 6, characterized in that, In S4: Fixed success rate based on the required ambiguity Through the formula Determine or give the ADOP value of a fixed-dimensional ambiguity vector. ; When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to multiple frequencies, according to the formula... The required accuracy for multi-frequency GNSS pseudorange observations in S1.1 The formula is: ； In the formula, For multi-frequency GNSS observations ; When the GNSS double-difference mathematical model before adding GNSS redundant pseudorange observations corresponds to a single frequency, according to the formula... The required accuracy for single-frequency GNSS pseudorange observations in S1.2 The formula is: ； In the formula, For single-frequency GNSS observations .

8. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 2, characterized in that, In S5, the values ​​required for optimizing and quantizing the accuracy of GNSS pseudorange observations in S1 include both multi-frequency GNSS pseudorange observation accuracy optimization and quantization values ​​and single-frequency GNSS pseudorange observation accuracy optimization and quantization values, specifically including: According to S1.1 Chinese style Japanese style Average accuracy of multi-frequency GNSS pseudorange observations and the required accuracy for multi-frequency GNSS pseudorange observations The required values ​​for optimizing and quantizing the accuracy of multi-frequency GNSS pseudorange observations in S1.1 are obtained: ； According to S1.2 Chinese style Japanese style single-frequency GNSS pseudorange observation accuracy and the required accuracy for single-frequency GNSS pseudorange observations The required values ​​for optimizing the quantization of single-frequency GNSS pseudorange observation accuracy are obtained: 。 9. The pseudorange accuracy optimization and quantization method based on GNSS redundant pseudorange observations as described in claim 8, characterized in that, S6 specifically includes: S6.1: Sort the redundant pseudorange observations of GNSS according to the elevation angle of their corresponding satellites from high to low; S6.2: Add redundant pseudorange observations of GNSS to the single-epoch GNSS double-difference mathematical model according to the elevation angle from high to low; If the added GNSS redundant pseudorange observations include If a frequency is added for the first time, then at least two redundant GNSS pseudorange observations are added for each frequency; if it is not added for the first time, then at least one redundant GNSS pseudorange observation is added for each frequency, and together with the previously added redundant GNSS pseudorange observations of the same frequency, they form a double-difference mathematical model. S6.3: According to formula or Obtain the optimized quantized values ​​of the multi-frequency GNSS pseudorange observation accuracy in S1.1 after adding GNSS redundant pseudorange observations. Alternatively, the optimized quantization calculation value of single-frequency GNSS pseudorange observation accuracy in S1.2 after adding redundant GNSS pseudorange observations. ; S6.4: Determine " "or" "Whether it is valid; S6.5: If the condition in S6.4 is met, then stop adding redundant GNSS pseudorange observations; otherwise, continue adding redundant GNSS pseudorange observations to the single-epoch GNSS double-difference mathematical model in S1, and repeat steps S6.2, S6.3, S6.4 and S6.5 until the condition in S6.4 is met.

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