Single-epoch GNSS-oriented PAR ambiguity precision factor determination method

Abstract

The invention discloses a single-epoch GNSS-oriented PAR ambiguity precision factor determination method, and relates to the technical field of satellite navigation and positioning. Comprising the following steps: dividing pseudo-range and carrier wave observed quantities in a GNSS double-difference mathematical model into two groups, and constructing a function relationship between a floating point solution # imgabs1 # and a floating point solution # imgabs2 # variance-covariance matrix of an ambiguity vector # imgabs0 #; constructing a single-frequency single-epoch single-system P-ADOP expression and establishing a shrinkage factor k de-inversion transformation analytic expression, and simultaneously obtaining a single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximation formula; and performing analogy derivation on the single-frequency single-epoch single-system non-inverse transformation P-ADOP approximate formula to obtain a single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP general approximate formula. The method has important theoretical value and practical guiding significance for GNSS optimal ambiguity subset rapid selection and positioning and partial ambiguity fixing success rate influence mechanism analysis.

Description

Technical Field

[0001] The present invention relates to the field of satellite navigation and positioning technology, and in particular to a method for determining a PAR ambiguity precision factor for a single-epoch GNSS. Background Art

[0002] Correct resolution of ambiguity is the key to high-precision relative positioning using the Global Navigation Satellite System (GNSS). The Ambiguity Dilution of Precision (ADOP) is an indicator factor that measures the success rate of ambiguity fixation, and its approximate formula can accurately predict the ADOP value based on the observed value.

[0003] In terms of dimension, ambiguity resolution can be divided into global ambiguity resolution and partial ambiguity resolution (PAR). Partial ambiguity resolution PAR is the optimal method for GNSS fast positioning.

[0004] However, the current ADOP approximation formula is only for overall ambiguity resolution, and there is still a lack of accurate estimation methods for the PAR ambiguity precision factor (ADOPBased on PAR, P-ADOP). In other words, the existing formulas or methods cannot accurately predict or estimate the PAR ambiguity precision factor P-ADOP based on the observed values. Summary of the invention

[0005] Based on this, it is necessary to provide a method for determining the PAR ambiguity precision factor for single-epoch GNSS in response to the above technical issues.

[0006] The embodiment of the present invention provides a method for determining the PAR ambiguity precision factor for a single-epoch GNSS, including: Construct a single epoch GNSS double-difference mathematical model and transform the pseudo-range observations in the model and carrier observations Divided into two groups ( , )and( , ), and the single-epoch GNSS double-difference mathematical model after the observations are split is obtained, and the overall ambiguity vector Divide into two groups accordingly ; Using the least squares method, we construct , Or Observable , and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of With the observed quantity and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of The functional relationship between them; using the determinant reduction theorem and the partial fuzzy vector in the functional relationship Floating point solution The variance-covariance matrix of , construct the partial ambiguity vector Floating point solution The single-frequency single-epoch single-system P-ADOP expression; Constructing the scaling factor when taking the first observed satellite as the reference satellite K middle The analytical formula for the inverse transformation; according to The de-inverse transform weighting coefficient matrix is ​​determined by the de-inverse transform analytical formula, and the shrinkage factor representing the theoretical relationship between P-ADOP and ADOP is established. k The analytical expression of the inverse transformation of ; Combined single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The de-inverse transform analytical expression is used to determine the PAR ambiguity precision factor P-ADOP.

[0007] Optionally, the single-epoch GNSS double-difference mathematical model after the observations are split is specifically: ; in, , " ” are , , B、 or ; , , and Respectively represent " The expectation and variance of is the pseudorange observation, is the carrier observation quantity, and are the baseline vector and the overall ambiguity vector respectively, , is the carrier wavelength, for The coefficient matrix of order , It is a cooperative factor array.

[0008] Optionally, construct a partial ambiguity vector Floating point solution The variance-covariance matrix of and the partial ambiguity vector Floating point solution The variance-covariance matrix of The functional relationship between them is as follows: ; in, and The observed quantities are , , , Or Observable , , The calculated partial ambiguity vector Floating point solution and the baseline vector b Floating point solution The variance-covariance matrix of is a positive definite or semi-positive definite matrix, , , For only and The calculated baseline vector b Floating point solution The variance-covariance matrix of is the standard deviation of the undifferenced pseudorange observations; If the partial ambiguity vector and the overall ambiguity vector Corresponding to t and The carrier observations of frequencies, then the partial ambiguity vector The corresponding observation double difference covariance matrix is , is the partial ambiguity vector Middle j The double-difference covariance matrix of the observations corresponding to the frequency ambiguity vector.

[0009] Optionally, construct a partial ambiguity vector Floating point solution The single-frequency single-epoch single-system P-ADOP expression includes: According to the definition of ambiguity precision dilution ADOP, the single-frequency single-epoch single-system partial ambiguity vector Floating point solution The P-ADOP formula is expressed as ; in, According to the partial ambiguity vector Floating point solution The variance-covariance matrix of Calculated partial ambiguity vector Floating point solution Ambiguity Dilution of Precision ADOP, , scaling factor K is a positive number less than 1 and has pseudorange accuracy properties; the single-frequency single-epoch single-system P-ADOP expression is used to characterize the partial ambiguity vector Floating point solution ADOP and scaling factors K the relationship between; Scaling Factor K The standard deviation of the undifferenced pseudorange observations The coefficient, shrinkage factor k Used to describe the standard deviation of undifferenced pseudorange observations , , then the partial ambiguity vector of the single-frequency single-epoch single-system is Floating point solution P-ADOP approximate expression and shrinkage factor k The analytical formula is: ; in, k is a positive shrinkage factor, is the standard deviation of the undifferenced carrier observation, and is the same as the partial ambiguity vector The corresponding coefficient matrix and cofactor matrix are, for The coefficient matrix of order , is the cofactor matrix, is the partial ambiguity vector The dimension of is the partial ambiguity vector The corresponding number of observed satellites.

[0010] Optionally, construct the shrinkage factor with the first observed satellite as the reference satellite k middle The analytical formula for the inverse transformation includes: Let the double difference coefficient matrix and double difference cofactor matrix when the first observed satellite is used as the reference satellite be: and , the double difference coefficient matrix and double difference cofactor matrix when the second observation satellite is used as the reference satellite are and , the relationship between the double difference coefficient matrix and the double difference cofactor matrix is ​​as follows: ; in, is a reversible matrix with determinant 1, Established, It has double difference reference satellite independence; The shrinkage factor when the first observed satellite is used as the reference satellite is k middle The analytical formula for the inverse transformation is: ; in, and are the double difference coefficient matrix and double difference cofactor matrix when the first observed satellite is used as the reference satellite, is the weight of the observation satellites other than the reference satellite. The weight of the reference satellite is ; according to To inverse transform analytical expression, the shrinkage factor when the first observed satellite is used as the reference satellite k The analytical formula for the inverse transformation is as follows: ; in, and They are oriented to the partial fuzzy vectors and the overall ambiguity vector The inverse transform weighting coefficient matrix of .

[0011] Optionally, construct a satellite with the first observation as the reference satellite The inverse transformation formula is as follows: ; Inverse Matrix and the adjoint matrix The functional relationship between them is: ; The analytical formula is: ; Among them, diag( ) is the vector " ” is a diagonal matrix with the main diagonal elements.

[0012] Optionally, when the pseudorange observations and carrier observations are single-frequency single-epoch single-system GNSS observations, the de-inverse transformation shrinkage factor isk In and Specifically: ; in, , is the imaginary unit of the complex number, , is the partial ambiguity vector The corresponding weighted double difference coefficient matrix, is the overall blur vector The corresponding weighted double difference coefficient matrix.

[0013] Optionally, the single-frequency single-epoch single-system P-ADOP expression and the shrinkage factor k The de-inverse transformation analytical formula is used to determine the PAR ambiguity precision factor P-ADOP, which includes: Combined single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The analytical formula for the inverse transformation is used to obtain the single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula; the single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula is analogically derived to obtain the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP general approximate formula; and the PAR ambiguity precision factor P-ADOP is determined by the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP general approximate formula; The single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula is specifically: ; When the pseudorange observations and carrier observations are single-frequency multi-system or multi-frequency single-epoch GNSS observations, adjust the weighting coefficients and ambiguity dimensions in the single-frequency single-epoch single-system GNSS non-inverse transform P-ADOP approximate formula, multiply the SMRW factors of each frequency, and average the wavelength, undifferenced pseudorange standard deviation, and undifferenced carrier standard deviation of each frequency to obtain the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transform P-ADOP general approximate formula; the single-frequency multi-system or multi-frequency single-epoch single baseline non-inverse transform P-ADOP general approximate formula is: ; in, is the partial ambiguity vector Middle j The ratio of the weighted sum of the frequencies to the weighted product, N is the partial ambiguity vector The dimension of and They are respectively oriented to the partial ambiguity vector and the overall ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix, and are the partial ambiguity vectors middle t The average value of the pseudorange and carrier undifference standard deviation for each frequency, is the partial ambiguity vector middle t The average value of the carrier wavelength at each frequency; The average value of carrier wavelength in the general approximate formula of single-frequency multi-system or multi-frequency single-epoch GNSS non-inverting transform P-ADOP , carrier non-difference standard deviation average , the average value of pseudorange non-difference standard deviation , partial ambiguity vector Middle j The ratio of the sum of the frequency weights to the product of the weights , partial ambiguity vector The dimension N, oriented to the partial ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix and the overall ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix Specifically: ; in, and Corresponding to j Frequency and , , , and Respectively j The undifferenced standard deviation of the frequency pseudorange and carrier, For the j The carrier wavelength of the frequency.

[0014] Compared with the prior art, the above-mentioned method for determining the PAR ambiguity precision factor for single-epoch GNSS provided by the embodiment of the present invention has the following beneficial effects: The present invention studies the influencing mechanism of the precision of partial ambiguity vector floating-point solution, derives the single-frequency single-epoch single-system P-ADOP expression, and demonstrates the independence of its double-difference reference satellite.

[0015] More importantly, the contraction factor that characterizes the theoretical relationship between P-ADOP and ADOP was constructed. k , analyze the shrinkage factor kThe shrinkage and pseudorange accuracy properties of the shrinkage factor are used to establish the inverse transformation analytical formula of the shrinkage factor; the single-frequency single-epoch single-system P-ADOP expression and the shrinkage factor k By combining and analogically deducing the combined results, a general approximate formula for the non-inverse transformation P-ADOP of single-frequency multi-system or multi-frequency single-epoch GNSS is formed, which can improve the ambiguity precision dilution ADOP theory and has important theoretical value and practical guiding significance for the rapid selection and positioning of the optimal ambiguity subset of GNSS and the analysis of the mechanism affecting the success rate of partial ambiguity fixation. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 The figure is a flow chart of a method for determining the PAR ambiguity precision factor for a single-epoch GNSS provided in an embodiment. DETAILED DESCRIPTION

[0017] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0018] In one embodiment, a method for determining PAR ambiguity precision factor for a single-epoch GNSS is provided, the method comprising: Construct a single epoch GNSS double-difference mathematical model and transform the pseudo-range observations in the model and carrier observations Divided into two groups ( , )and( , ), and the single-epoch GNSS double-difference mathematical model after the observations are split is obtained, and the overall ambiguity vector Divide into two groups accordingly .

[0019] Using the least squares method, we construct , Or Observable , and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of With the observed quantity and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of The functional relationship between them.

[0020] According to the definition of ambiguity precision dilution ADOP, the determinant reduction theorem and the partial ambiguity vector in the functional relationship are used. Floating point solution The variance-covariance matrix of , construct the partial ambiguity vector Floating point solution The single-frequency single-epoch single-system P-ADOP expression is used to characterize the partial ambiguity vector Floating point solution ADOP and scaling factors K The relationship between.

[0021] Constructing the scaling factor when taking the first observed satellite as the reference satellite K middle The analytical formula for the inverse transformation is The de-inverse transform weighting coefficient matrix is ​​determined by the de-inverse transform analytical formula, and the shrinkage factor representing the theoretical relationship between P-ADOP and ADOP is established. k The analytical expression for the inverse transformation of .

[0022] Combined single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The analytical formula for the inverse transformation is used to obtain the single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula. The single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula is derived by analogy, and the general approximate formula for the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP is obtained, and the PAR ambiguity precision factor P-ADOP is determined by the general approximate formula for the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP.

[0023] The specific implementation is: 1. Single epoch GNSS positioning model Assume that at the same time satellites, can form A single-frequency double-difference observation (pseudorange and carrier) equation: (1) , (2) In the formula, and Respectively represent " ”’s expectation and variance; is the pseudorange observation, is the carrier observation; and are the baseline vector and the overall ambiguity vector respectively; , is the carrier wavelength, for The coefficient matrix of order ; is the cofactor matrix, , and The reference satellite and j The co-factor of the undifferenced observations of the satellites, w The right to observe satellites; is the standard deviation of the undifferenced pseudorange observations, is the standard deviation of the non-difference carrier observation. and and its inverse matrix are both symmetric positive definite matrices. Using the least squares method, according to equations (1) and (2), we can get the baseline vector and the overall ambiguity vector Floating point solution and and its variance-covariance matrix and : (3) (4) In the formula, and They are all symmetric positive definite matrices. The baseline vector can be obtained by using the LAMBDA method. and the overall ambiguity vector Fixed solution and .

[0024] 2. Single epoch ADOP theory The ambiguity dilution of precision (ADOP) is an easy-to-calculate scalar factor proposed by Professor Teunissen in 1997. It can be used to measure the accuracy of ambiguity vector estimation and the success rate of resolution. Its definition is as follows: (5) In the formula, express" " The geometric-based multi-frequency single-epoch single-baseline model ADOP approximate formula can be written as: (6) In the formula, , For the j The frequency of the carrier wave, m - t is the overall fuzziness vector dimension, tis the frequency number (assuming the same frequency in different systems, reference satellites are selected in their respective systems); and Respectively j The undifferenced standard deviation of the frequency pseudorange and carrier, , ADOP can also be used to measure the integer least squares success rate of the ambiguity vector : (7) In the formula, and They are the success rate based on ADOP and the success rate of integer sequential rounding, respectively; is the standard normal distribution function. and They are all monotonically decreasing functions of ADOP.

[0025] 3.1. Mechanism affecting the accuracy of floating-point solutions of partial ambiguity vectors Construct a single epoch GNSS double-difference mathematical model (double-difference function model and double-difference random model) and transform the pseudo-range observations in the model and carrier observations Divided into two groups ( , )and( , ), and obtain the single-epoch GNSS double-difference mathematical model after the observations are split, and the function model coefficient matrix and the overall ambiguity vector Divided into two groups accordingly, and .

[0026] If the observations in equation (1) are divided into two groups, equations (1) and (2) can be written as: (8) (9) In the formula, , " ” are , , B、 or ; , , and Respectively represent " The expectation and variance of is the pseudorange observation, is the carrier observation quantity, and are the baseline vector and the overall ambiguity vector respectively, , is the carrier wavelength, for The coefficient matrix of order ; It is a cooperative factor array.

[0027] Using the least squares method, we construct , Or Observable , and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of With the observed quantity and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of Functional relationship between: According to equations (8) and (9), the partial ambiguity vector Floating point solution The variance-covariance matrix of and the partial ambiguity vector Floating point solution The variance-covariance matrix of The functional relationship between them is as follows: (10) in, and The observed quantities are , , , Or Observable , , The calculated partial ambiguity vector Floating point solution and the baseline vector b Floating point solution The variance-covariance matrix of is a positive definite or semi-positive definite matrix, , , For only and The calculated baseline vector b Floating point solution The variance-covariance matrix of is the standard deviation of the undifferenced pseudorange observations, is the standard deviation of the undifferenced carrier observation.

[0028] If the partial ambiguity vector and the overall ambiguity vector Corresponding to t and The carrier observations of frequencies, then the partial ambiguity vector The corresponding observation double difference covariance matrix is , is the partial ambiguity vector Middle j The double-difference covariance matrix of the observations corresponding to the frequency ambiguity vector.

[0029] Therefore, from formula (10), we can see that the partial ambiguity vector Floating point solution The accuracy is higher than that of the partial ambiguity vector Floating point solution The accuracy of the partial ambiguity vector Floating point solution The improvement in accuracy is only related to the pseudo-range observation Related to the carrier observation Not relevant.

[0030] 3.2. Single-frequency, single-epoch, single-system P-ADOP approximate formula According to the definition of ADOP and formula (10), using the determinant reduction theorem (in, A and R are all reversible square matrices), constructing partial ambiguity vectors Floating point solution The single-frequency single-epoch single-system P-ADOP expression is used to characterize the partial ambiguity vector Floating point solution ADOP and scaling factors K The relationship between: (11) In the formula, is the partial ambiguity vector The dimension of is the partial ambiguity vector The corresponding number of observation satellites, According to the partial ambiguity vector Floating point solution The variance-covariance matrix of Calculated partial ambiguity vector Floating point solution The ambiguity dilution of precision ADOP takes into account And formula (3), scaling factor K It can be written as: (12) Scaling Factor K It has the following two properties: (1) According to Weyl's theorem and positive definite matrix ( = or ) and a positive definite or semi-positive definite matrix Relationship , relational Established, that is, the scaling factor K has contraction; (2) according to “with compared to, The improvement in accuracy is only In equation (11), the scaling factor K Only the standard deviation of the undifferenced pseudorange observation can be The shrinkage factor, i.e. the scaling factor K With the pseudorange accuracy attribute, the single-frequency single-epoch single-system GNSS P-ADOP approximate formula is obtained.

[0031] Single-frequency single-epoch single-system partial ambiguity vector Floating point solution The P-ADOP formula is expressed as: (13) in, According to the partial ambiguity vector Floating point solution The variance-covariance matrix of Calculated partial ambiguity vector Floating point solution The ambiguity dilution of precision ADOP is , scaling factor K is a positive number less than 1 and has pseudorange accuracy attribute; Scaling Factor K The standard deviation of the undifferenced pseudorange observations The coefficient, shrinkage factor Used to describe the standard deviation of undifferenced pseudorange observations , , then the partial ambiguity vector of the single-frequency single-epoch single-system is Floating point solution P-ADOP approximate expression and shrinkage factor k The analytical formula is: (14) in,k is a positive shrinkage factor, is the standard deviation of the undifferenced pseudorange observations, is the standard deviation of the undifferenced carrier observation, and is the same as the partial ambiguity vector The corresponding coefficient matrix and cofactor matrix are, for The coefficient matrix of order , is the cofactor matrix, is the partial ambiguity vector The dimension of is the partial ambiguity vector The corresponding number of observed satellites.

[0032] Therefore, with the partial ambiguity vector Floating point solution In comparison, (1) the partial ambiguity vector Floating point solution has a smaller ADOP value, that is, its ambiguity fixation success rate is higher; (2) in improving the partial ambiguity vector Floating point solution To improve the accuracy or ADOP value, increase the pseudo-range observation and improve the original pseudo-range observation Accuracy, this property further reveals the influencing mechanism of the floating-point solution accuracy of some ambiguity vectors.

[0033] 3.3 P-ADOP double-difference reference satellite correlation analysis Let the baseline vector and the variance-covariance matrix of the double-difference ambiguity vector when the first observed satellite is used as the reference satellite be and , let the baseline vector and the variance-covariance matrix of the double-difference ambiguity vector when the second observation satellite is used as the reference satellite be and , and Established, that is , It is independent of the double-difference reference satellite as P-ADOP. To facilitate calculation and improve calculation efficiency, it is stipulated that the double-difference function model and the double-difference random model are constructed with the first observed satellite as the reference satellite.

[0034] ADOP value is independent of reference satellite, that is, it is independent of the choice of reference satellite. As an extended formula of ADOP, P-ADOP should be consistent with ADOP in this property. Therefore, by analyzing the shrinkage factor k Relationship with reference satellites Demonstrate the relevance of P-ADOP to reference satellites.

[0035] If the first observation satellite is used as the reference satellite to form a double difference observation equation, then the equations (3) and (4) are and Can be expressed as and ,Right now and ,in, , is composed of the undifferenced unit direction vectors between the receiver and the satellite Order coefficient matrix; , , The elements are all 1 Column vector, for The unit matrix, is a diagonal matrix. Similarly, let the second observation satellite be the reference star and They are and ,but: (15) In the formula, and They are the double difference coefficient matrix and the observation cofactor matrix respectively when the second satellite is used as the reference satellite; is a reversible matrix with determinant 1.

[0036] 3.4 Shrinkage Factor k The inverse transformation formula of Constructing the scaling factor when taking the first observed satellite as the reference satellite K middle The analytical formula for the inverse transformation; according to The de-inverse transform weighting coefficient matrix is ​​determined by the de-inverse transform analytical formula, and the shrinkage factor representing the theoretical relationship between P-ADOP and ADOP is established. k The analytical expression for the inverse transformation of .

[0037] Assuming that both equations (1) and (2) are models with the first observed satellite as the reference satellite, when constructing the model with the first observed satellite as the reference satellite The inverse transformation formula is as follows: (16) Among them, the inverse matrix and the adjoint matrix The functional relationship between them is: (17) The analytical formula is: (18) Among them, diag( ) is the vector " ” is a diagonal matrix with the main diagonal elements.

[0038] Let the double difference coefficient matrix and double difference cofactor matrix when the first observed satellite is used as the reference satellite be: and , the double difference coefficient matrix and double difference cofactor matrix when the second observation satellite is used as the reference satellite are and , the relationship between the double difference coefficient matrix and the double difference cofactor matrix is ​​as follows: (19) in, is a reversible matrix with determinant 1, Established, It is independent of double-difference reference satellite.

[0039] The shrinkage factor when the first observed satellite is used as the reference satellite k middle The analytical formula for the inverse transformation is: (20) in, and are the double difference coefficient matrix and double difference cofactor matrix when the first observed satellite is used as the reference satellite, ω is the weight of the observation satellites other than the reference satellite. The weight of the reference satellite is .

[0040] according to The analytical formula for the inverse transformation is the contraction factor of the single-frequency single-epoch single-system GNSS when the first observed satellite is used as the reference satellite. k The analytical formula for the inverse transformation is as follows: (twenty one) in, and They are oriented to the partial fuzzy vectors and the overall ambiguity vector The de-inverse transform weighted coefficient moment.

[0041] De-inverse transformation shrinkage factor k In and Specifically: (twenty two) in, , is the imaginary unit of the complex number, , is the partial ambiguity vector The corresponding weighted double difference coefficient matrix, is the overall blur vector The corresponding weighted double difference coefficient matrix. Equations (14) and (21) are only applicable to the estimation of P-ADOP values ​​of single-frequency, single-epoch and single-system.

[0042] 3.5 General approximate formula for single-frequency multi-system or multi-frequency single-epoch GNSS non-inverting transformation P-ADOP Combined single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The analytical formula for the inverse transformation is used to obtain the approximate formula for the single-frequency, single-epoch, single-system GNSS non-inverse transformation P-ADOP. The approximate formula for the single-frequency, single-epoch, single-system GNSS non-inverse transformation P-ADOP is derived by analogy to obtain the general approximate formula for the single-frequency, multi-system or multi-frequency, single-epoch GNSS non-inverse transformation P-ADOP.

[0043] The single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula is as follows: (twenty three) When the pseudorange observations and carrier observations are single-frequency multi-system or multi-frequency single-epoch GNSS observations, adjust the weighting coefficients and ambiguity dimensions in the single-frequency single-epoch single-system GNSS non-inverse transform P-ADOP approximate formula, multiply the SMRW factors of each frequency, and average the wavelength, undifferenced pseudorange standard deviation, and undifferenced carrier standard deviation of each frequency to obtain the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transform P-ADOP general approximate formula; the single-frequency multi-system or multi-frequency single-epoch single baseline non-inverse transform P-ADOP general approximate formula is: (twenty four) in, is the partial ambiguity vector Middle j The ratio of the weighted sum of the frequencies to the weighted product, N is the partial ambiguity vector The dimension of and They are respectively oriented to the partial ambiguity vector and the overall ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix, and are the partial ambiguity vectors middle t The average value of the pseudorange and carrier undifference standard deviation for each frequency, is the partial ambiguity vector middle t The average carrier wavelength of the frequency.

[0044] The average value of carrier wavelength in the general approximate formula of single-frequency multi-system or multi-frequency single-epoch GNSS non-inverting transformation P-ADOP , carrier non-difference standard deviation average , the average value of pseudorange non-difference standard deviation , partial ambiguity vector Middle j The ratio of the sum of the frequency weights to the product of the weights , partial ambiguity vector The dimension N, oriented to the partial ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix and the overall ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix Specifically: (25) in, , , is the partial ambiguity vector The dimension of is the partial ambiguity vector Middle j The number of observed satellites corresponding to the frequency ambiguity vector; and are the partial ambiguity vectors middle t The average value of the pseudorange and carrier non-difference standard deviation of the frequency is the same as the value in equation (6): and The meaning is the same, and ; and Respectively j The undifferenced standard deviation of the frequency pseudorange and carrier, and Corresponding to j Frequency and , , , and Respectively j The undifferenced standard deviation of the frequency pseudorange and carrier, For the j The carrier wavelength of the frequency, and the meanings of other parameters are consistent with those in formula (6).

[0045] The above-mentioned embodiments only express several implementation methods of the present invention, and the description is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention patent. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for determining the PAR ambiguity precision factor for single-epoch GNSS, characterized in that: include: Construct a single epoch GNSS double-difference mathematical model and transform the pseudo-range observations in the model and carrier observations Divided into two groups ( , )and( , ), and the single-epoch GNSS double-difference mathematical model after the observations are split is obtained, and the overall ambiguity vector Divide into two groups accordingly ; Using the least squares method, we construct , Or Observable , and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of With the observed quantity and The partial ambiguity vectors calculated by the single epoch GNSS double difference mathematical model after the observations are split Floating point solution The variance-covariance matrix of The functional relationship between them; using the determinant reduction theorem and the partial fuzzy vector in the functional relationship Floating point solution The variance-covariance matrix of , construct the partial ambiguity vector Floating point solution The single-frequency single-epoch single-system P-ADOP expression; Constructing the scaling factor when taking the first observed satellite as the reference satellite K middle The analytical formula for the inverse transformation; according to The de-inverse transform weighting coefficient matrix is ​​determined by the de-inverse transform analytical formula, and the shrinkage factor representing the theoretical relationship between P-ADOP and ADOP is established. k The analytical expression of the inverse transformation of ; Combined single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The de-inverse transform analytical expression is used to determine the PAR ambiguity precision factor P-ADOP.

2. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 1, characterized in that: The single-epoch GNSS double-difference mathematical model after the observations are split is specifically: ； in, , " ” are , , B、 or ; , , and Respectively represent The expectation and variance of is the pseudorange observation, is the carrier observation quantity, and are the baseline vector and the overall ambiguity vector respectively, , is the carrier wavelength, for The coefficient matrix of order , It is a cooperative factor array.

3. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 1, characterized in that: The partial ambiguity vector is constructed Floating point solution The variance-covariance matrix of and the partial ambiguity vector Floating point solution The variance-covariance matrix of The functional relationship between them is as follows: ； in, and The observed quantities are , , , Or Observable , , The calculated partial ambiguity vector Floating point solution and the baseline vector b Floating point solution The variance-covariance matrix of is a positive definite or semi-positive definite matrix, , , For only and The calculated baseline vector b Floating point solution The variance-covariance matrix of is the standard deviation of the undifferenced pseudorange observations, is the standard deviation of the undifferenced carrier observation; If the partial ambiguity vector and the overall ambiguity vector Corresponding to t and The carrier observations of frequencies, then the partial ambiguity vector The corresponding observation double difference covariance matrix is , is the partial ambiguity vector Middle j The double-difference covariance matrix of the observations corresponding to the frequency ambiguity vector.

4. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 1, characterized in that: The partial ambiguity vector is constructed Floating point solution The single-frequency single-epoch single-system P-ADOP expression includes: According to the definition of ambiguity precision dilution ADOP, the single-frequency single-epoch single-system partial ambiguity vector Floating point solution The P-ADOP formula is expressed as: ； in, According to the partial ambiguity vector Floating point solution The variance-covariance matrix of Calculated partial ambiguity vector Floating point solution The ambiguity dilution of precision ADOP is , scaling factor K is a positive number less than 1 and has pseudorange accuracy properties; the single-frequency single-epoch single-system P-ADOP expression is used to characterize the partial ambiguity vector Floating point solution ADOP and scaling factors K the relationship between; Scaling Factor K The standard deviation of the undifferenced pseudorange observations The coefficient, shrinkage factor k Used to describe the standard deviation of undifferenced pseudorange observations , , then the partial ambiguity vector of the single-frequency single-epoch single-system is Floating point solution P-ADOP approximate expression and shrinkage factor k The analytical formula is: ； in, k is a positive shrinkage factor, is the standard deviation of the undifferenced pseudorange observations, is the standard deviation of the undifferenced carrier observation, and is the same as the partial ambiguity vector The corresponding coefficient matrix and cofactor matrix, for The coefficient matrix of order , is the cofactor matrix, is the partial ambiguity vector The dimension of is the partial ambiguity vector The corresponding number of observed satellites.

5. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 1, characterized in that: The shrinkage factor is constructed by taking the first observed satellite as the reference satellite. k middle The analytical formula for the inverse transformation includes: Let the double difference coefficient matrix and double difference cofactor matrix when the first observed satellite is used as the reference satellite be: and , the double difference coefficient matrix and double difference cofactor matrix when the second observation satellite is used as the reference satellite are and , the relationship between the double difference coefficient matrix and the double difference cofactor matrix is ​​as follows: ； in, is a reversible matrix with determinant 1, Established, It has double difference reference satellite independence; The shrinkage factor when the first observed satellite is used as the reference satellite k middle The analytical formula for the inverse transformation is: ； in, and are the double difference coefficient matrix and double difference cofactor matrix when the first observed satellite is used as the reference satellite, is the weight of the observation satellites other than the reference satellite. The weight of the reference satellite is ; according to To inverse transform analytical formula, the shrinkage factor is taken as the reference satellite when the first observed satellite is used k The analytical formula for the inverse transformation is as follows: ； in, and They are oriented to the partial fuzzy vectors and the overall ambiguity vector The inverse transform weighting coefficient matrix of .

6. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 5, characterized in that: The construction takes the first observed satellite as the reference satellite The inverse transformation formula is as follows: ； Inverse Matrix and the adjoint matrix The functional relationship between them is: ； The analytical formula is: ； Among them, diag( ) is a vector" ” is a diagonal matrix with the main diagonal elements.

7. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 5, characterized in that: When the pseudorange observations and carrier observations are single-frequency single-epoch single-system GNSS observations, the de-inverse transformation shrinkage factor k In and Specifically: ； in, , is the imaginary unit of the complex number, , is the partial ambiguity vector The corresponding weighted double difference coefficient matrix, is the overall blur vector The corresponding weighted double difference coefficient matrix.

8. The method for determining the PAR ambiguity precision factor for single-epoch GNSS according to claim 1, characterized in that: The simultaneous single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The de-inverse transformation analytical formula is used to determine the PAR ambiguity precision factor P-ADOP, which includes: Combined single-frequency single-epoch single-system P-ADOP expression and shrinkage factor k The analytical formula for the inverse transformation is used to obtain the single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula; the single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula is analogically derived to obtain the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP general approximate formula; and the PAR ambiguity precision factor P-ADOP is determined by the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transformation P-ADOP general approximate formula; The single-frequency single-epoch single-system GNSS non-inverse transformation P-ADOP approximate formula is specifically: ； When the pseudorange observations and carrier observations are single-frequency multi-system or multi-frequency single-epoch GNSS observations, adjust the weighting coefficients and ambiguity dimensions in the single-frequency single-epoch single-system GNSS non-inverse transform P-ADOP approximate formula, multiply the SMRW factors of each frequency, and average the wavelength, undifferenced pseudorange standard deviation, and undifferenced carrier standard deviation of each frequency to obtain the single-frequency multi-system or multi-frequency single-epoch GNSS non-inverse transform P-ADOP general approximate formula; The general approximate formula of single-epoch single-baseline non-inverse transformation P-ADOP of single-frequency multi-system or multi-frequency is as follows: ； in, is the partial ambiguity vector Middle j The ratio of the weighted sum of the frequencies to the weighted product, N is the partial ambiguity vector The dimension of and They are respectively oriented to the partial ambiguity vector and the overall ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix, and are the partial ambiguity vectors middle t The average value of the pseudorange and carrier undifference standard deviation for each frequency, is the partial ambiguity vector middle t The average value of the carrier wavelength at each frequency; The average value of carrier wavelength in the general approximate formula of single-frequency multi-system or multi-frequency single-epoch GNSS non-inverting transformation P-ADOP , carrier non-difference standard deviation average , the average value of pseudorange non-difference standard deviation , partial ambiguity vector Middle j The ratio of the sum of the frequency weights to the product of the weights , partial ambiguity vector The dimension N, oriented to the partial ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix and the overall ambiguity vector The multi-frequency de-inverse transform weighting coefficient matrix Specifically: ； in, and Corresponding to j Frequency and , , , and Respectively j The undifferenced standard deviation of the frequency pseudorange and carrier, For the j The carrier wavelength of the frequency.

Images