A method and system for obtaining integer ambiguity based on dual-frequency carrier signals

Abstract

This invention discloses a method and system for obtaining integer ambiguity based on dual-frequency carrier signals. The method includes: combining dual-frequency carrier signals into a wide-lane configuration to establish a wide-lane carrier dual-difference positioning model; introducing a regularization method into the wide-lane carrier dual-difference positioning model to solve for the floating-point solution and variance-covariance matrix of the wide-lane integer ambiguity; using the LAMBDA method to perform decorrelation processing on the wide-lane integer ambiguity, and searching for the wide-lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide-lane integer ambiguity as the center to obtain the integer solution of the wide-lane integer ambiguity; substituting the obtained integer solution of the wide-lane integer ambiguity into the wide-lane carrier dual-difference positioning model and initially solving for the coordinates of the measurement point; verifying the initially solved coordinates of the measurement point using a double verification standard, and resolving the coordinates of the measurement point if the double verification is met; and verifying the effectiveness of the integer ambiguity verification and correction method proposed in this invention through experiments.

Description

Technical Field

[0001] This invention relates to a method for obtaining integer ambiguity based on dual-frequency carrier signals, belonging to the field of satellite navigation and positioning technology. Background Technology

[0002] With the development of Global Navigation Satellite Systems (GNSS), their applications are becoming increasingly widespread. However, the positioning error of traditional single-point positioning methods in satellite navigation systems ranges from a few meters to tens of meters, which cannot meet the high-precision measurement requirements of engineering surveying and other applications. Real-Time Kinematic (RTK) technology utilizes the difference between real-time carrier phase observations from two stations to calculate coordinates, which can greatly improve the accuracy of satellite positioning. The carrier phase contains unknown integer cycles, i.e., integer ambiguity. Correctly resolving integer ambiguity is a prerequisite for achieving centimeter-level positioning.

[0003] The resolution of integer ambiguity involves two steps: search and verification. The Least Square Ambiguity Decorrelation Adjustment (LAMBDA) algorithm improves ambiguity search efficiency by reducing the correlation between ambiguity parameters. It is considered the most theoretically rigorous and effective ambiguity resolution method and is widely used. However, LAMBDA suffers from low fault tolerance and lacks feedback, failing to guarantee a high success rate in integer ambiguity resolution. Statistical difference testing is a commonly used method for integer ambiguity verification. This method determines the correctness of the integer ambiguity resolution by judging whether there is a significant difference between the optimal and suboptimal solutions in the integer ambiguity combinations. However, its threshold setting has a certain degree of randomness; a higher threshold reduces the fixation rate of integer ambiguity, while a lower threshold affects the reliability of the integer ambiguity verification. Summary of the Invention

[0004] This invention provides a method and system for obtaining integer ambiguity based on dual-frequency carrier signals. By combining regularization and LAMBDA and further introducing corrections, a new method and system for obtaining integer ambiguity based on dual-frequency carrier signals is constructed.

[0005] The technical solution of the present invention is as follows: According to one aspect of the present invention, a method for obtaining integer ambiguity based on dual-frequency carrier signals is provided, comprising:

[0006] Step 1: Combine the dual-frequency carrier signals in a wide-lane configuration to obtain the wide-lane carrier wavelength and wide-lane integer ambiguity; based on the wide-lane carrier wavelength and wide-lane integer ambiguity, establish a wide-lane carrier dual-difference positioning model;

[0007] Step 2: Introduce a regularization method into the wide-lane carrier double-difference positioning model to solve the wide-lane integer ambiguity floating-point solution and variance-covariance matrix;

[0008] Step 3: Use the LAMBDA method to reduce the correlation of the wide lane integer ambiguity, and search for the wide lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide lane integer ambiguity as the center to obtain the integer solution of the wide lane integer ambiguity.

[0009] Step 4: Substitute the obtained integer solution of wide-lane integer ambiguity into the wide-lane carrier double-difference positioning model, and calculate the coordinates of the measurement point for the first time; verify the coordinates of the measurement point for the first calculation using a double verification standard, and calculate the coordinates of the measurement point again if the double verification is met.

[0010] The wide lane combination is as follows:

[0011]

[0012] In the formula, f1 and f2 are the carrier frequencies of L1 and L2, respectively, and λ1 and λ2 are the carrier wavelengths of L1 and L2, respectively. w , λ w and N w N1 and N2 are the wide-lane carrier frequency, wavelength, and wide-lane integer ambiguity, respectively; N1 and N2 are the integer ambiguities at L1 and L2 carrier frequencies, respectively.

[0013] Simultaneously observe k+1 satellites, using one of them as the reference satellite, obtain the carrier double-difference observation equations for k wide-lane combinations, and construct a wide-lane carrier double-difference positioning model; wherein, the carrier double-difference observation equations for the wide-lane combinations are: Where, A=[C Dλ w X is the 3D baseline correction vector, C represents the coefficient matrix corresponding to the coordinate correction, and D represents the coefficient matrix corresponding to the integer ambiguity; L 宽 This represents the difference vector between the observed and calculated values ​​of the wide-lane carrier double-difference value.

[0014] Step 4 specifically involves: substituting the calculated integer solution of the wide-lane integer ambiguity into the wide-lane carrier double-difference positioning model, and initially calculating the coordinates of the measurement point; then substituting the calculated coordinates into the double-difference observation equations of the two frequency carriers to separate the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency; and determining whether the coordinates of the measurement point can pass the double verification criteria.

[0015] When any one of the test criteria fails, the wide lane integer ambiguity is searched again to obtain the coordinates of the measurement point under the new wide lane integer ambiguity ambiguity integer solution. The double test criteria judgment is repeated until both tests pass or the maximum number of iterations is reached.

[0016] When both test criteria are passed, the carrier signal double-difference observation equations at the two frequencies obtained based on the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency are added together to obtain the carrier double-difference observation equation for the narrow lane combination. Based on the carrier double-difference observation equation for the narrow lane combination, the narrow lane carrier double-difference positioning model is constructed, and the coordinates of the measurement point are calculated again.

[0017] The dual verification criteria include coordinate accuracy and TEC verification; coordinate accuracy is used as the first verification and TEC verification is used as the second verification.

[0018] According to another aspect of the present invention, a system for obtaining integer ambiguity based on a dual-frequency carrier signal is provided, comprising:

[0019] A module is established to combine dual-frequency carrier signals in a wide-lane configuration to obtain the wide-lane carrier wavelength and wide-lane integer ambiguity; based on the wide-lane carrier wavelength and wide-lane integer ambiguity, a wide-lane carrier dual-difference positioning model is established.

[0020] The first solution module is used to introduce a regularization method in the wide-lane carrier double-difference positioning model to solve the wide-lane integer ambiguity floating-point solution and variance-covariance matrix.

[0021] The module is used to perform downcorrelation processing on the wide lane integer ambiguity using the LAMBDA method, and to search for the wide lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide lane integer ambiguity as the center, so as to obtain the integer solution of the wide lane integer ambiguity.

[0022] The second solution module is used to substitute the integer solution of the wide lane integer ambiguity into the wide lane carrier double-difference positioning model and initially solve the coordinates of the measurement point. The coordinates of the measurement point initially solved are verified by a double verification standard. If the double verification is met, the coordinates of the measurement point are solved again.

[0023] The beneficial effects of this invention are:

[0024] 1. Wide-lane combination in the observation domain results in a longer carrier wavelength, which is beneficial for searching for integer ambiguity. At the same time, incorrect solution values ​​will cause more obvious errors, which is beneficial for verifying integer ambiguity. Narrow-lane combination in the observation domain has less noise, which is beneficial for improving positioning accuracy.

[0025] 2. The coordinate accuracy check of the measurement points involves subtracting the calculated coordinate values ​​from the prior coordinates. When the deviation exceeds the prior accuracy range, the integer ambiguity is determined to be incorrect. This process checks the independence of each calculation unit. The TEC check utilizes the continuous and slow nature of ionospheric changes. If the integer ambiguity is fixed correctly, the value of the double-difference ionospheric delay will change small and smoothly; otherwise, if the ambiguity is incorrectly fixed, a large jump will occur. Using both the coordinate accuracy of the measurement points and the TEC check to perform a dual check on the calculated integer ambiguity can detect most epochs with incorrect integer ambiguity calculations, improving the reliability of the integer ambiguity check.

[0026] 3. This invention proposes to use an intelligent search algorithm to find the optimal integer solution globally when the test result is invalid, which solves the problems of lack of feedback and low fault tolerance of the LAMBDA algorithm and improves the accuracy of integer ambiguity. Attached Figure Description

[0027] Figure 1 This is a flowchart of the present invention;

[0028] Figure 2 A graph showing the coordinate deviation of the measurement points obtained by the LAMBDA method;

[0029] Figure 3 A graph showing the coordinate deviation of the measurement points obtained by the Tihkonov+LAMBDA method;

[0030] Figure 4 A double-difference ionospheric delay residual plot for the satellite;

[0031] Figure 5 This is a diagram showing the coordinate deviation of the measurement points obtained from the solution of the modified narrow-lane carrier double-difference positioning model. Detailed Implementation

[0032] The invention will be further described below with reference to the accompanying drawings and embodiments, but the scope of the invention is not limited to the description.

[0033] Example 1: As Figure 1-5As shown, according to one aspect of the present invention, a method for obtaining integer ambiguity based on dual-frequency carrier signals is provided, comprising: Step 1: combining the dual-frequency carrier signals in a wide-lane configuration to obtain the wide-lane carrier wavelength and wide-lane integer ambiguity; establishing a wide-lane carrier dual-difference positioning model based on the wide-lane carrier wavelength and wide-lane integer ambiguity; Step 2: introducing a regularization method into the wide-lane carrier dual-difference positioning model to solve the floating-point solution of the wide-lane integer ambiguity and the variance-covariance matrix; Step 3: using the LAMBDA method to perform decorrelation processing on the wide-lane integer ambiguity, and searching for the wide-lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide-lane integer ambiguity as the center to obtain the integer solution of the wide-lane integer ambiguity; Step 4: substituting the obtained integer solution of the wide-lane integer ambiguity into the wide-lane carrier dual-difference positioning model, and initially solving the coordinates of the measurement point; verifying the initially solved coordinates of the measurement point using a double verification standard, and resolving the coordinates of the measurement point if the double verification is met.

[0034] Furthermore, the double-difference observation equation for two frequency carriers can be expressed as:

[0035]

[0036] In the formula, X is the three-dimensional baseline correction vector, C represents the coefficient matrix corresponding to the coordinate correction, N1 and N2 are the integer ambiguities at L1 and L2 carrier frequencies, respectively, λ1 and λ2 are the L1 and L2 carrier wavelengths, respectively, D represents the coefficient matrix corresponding to the integer ambiguities, and ρ1 and ρ2 are the calculated receiver-to-satellite distances corresponding to the double-difference observation equations at L1 and L2 carrier frequencies, respectively. These are the carrier observation values ​​corresponding to the double-difference observation equations at carrier frequencies L1 and L2, respectively.

[0037] The wide lane combination is:

[0038]

[0039] In the formula, f1 and f2 are the carrier frequencies of L1 and L2, respectively, and λ1 and λ2 are the carrier wavelengths of L1 and L2, respectively. w , λ w and N w These represent the wide-lane carrier frequency, wavelength, and wide-lane integer ambiguity, respectively. Compared to the wide-lane wavelength of 86.2 cm constructed by combining an L1 carrier with a wavelength of 19 cm and an L2 carrier with a wavelength of 24 cm, this is highly advantageous for solving the integer ambiguity.

[0040] Simultaneously observe k+1 satellites, using one of them as the reference satellite, obtain the carrier double-difference observation equations for k wide-lane combinations, and construct a wide-lane carrier double-difference positioning model; wherein, the carrier double-difference observation equations for each wide-lane combination are: A=[C Dλ wSpecifically, the carrier double-difference observation equation for the wide-lane combination is obtained by subtracting the double-difference observation equations of the two frequency carriers (i.e., by subtracting from Equation 1). This represents the difference vector between the observed and calculated values ​​of the wide-lane carrier double-difference observation. For example, if three satellites are observed simultaneously, two wide-lane combination carrier double-difference observation equations can be established. Assuming that satellite 1 is the reference satellite, satellites 1 and 2 form a set to construct wide-lane combination carrier double-difference observation equation 1, and satellites 1 and 3 form a set to construct wide-lane combination carrier double-difference observation equation 2.

[0041] Furthermore, in step 2: the Tikhonov regularization method is introduced into the wide-lane carrier double-difference positioning model to solve the wide-lane integer ambiguity floating-point solution and variance-covariance matrix;

[0042]

[0043] In the formula, for abbreviation for Q; Y =(A T PA+αR) -1 Let be the variance-covariance matrix, α be the regularization parameter, P be the unit weight matrix, and R be the regularization matrix.

[0044] Further, in step 3: using the LAMBDA method, the wide lane integer ambiguity is decorrelated, and the wide lane integer ambiguity is searched in the ambiguity domain with the floating-point solution of the wide lane integer ambiguity as the center;

[0045]

[0046] In the formula, N, These correspond to the integer solutions, floating-point solutions, and variance-covariance matrix of the wide-lane integer ambiguity in the original search space, respectively. These correspond to the integer solutions, floating-point solutions, and variance-covariance matrix of the wide-lane integer ambiguity in the new search space, respectively, where z is the integer transformation matrix.

[0047] Further, in step 4: the integer solution of the wide-lane integer ambiguity is substituted into the wide-lane carrier double-difference positioning model, and the coordinates of the measurement point are initially calculated. The coordinates calculated in step 4 are substituted into formula (1) to separate the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency; it is then determined whether the coordinates of the measurement point can pass the coordinate accuracy and TEC test.

[0048] When any one of the verification methods fails, the GWO algorithm is used to search for the wide lane integer ambiguity again to obtain the coordinates of the measurement point under the new wide lane integer ambiguity solution. The double verification standard judgment is repeated until both verifications pass or the maximum number of iterations is reached.

[0049] When both verification criteria are passed, the carrier signal double-difference observation equations obtained at the two frequencies based on the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency are added together to obtain the carrier double-difference observation equation for the narrow lane combination. The narrow lane carrier double-difference positioning model constructed based on the carrier double-difference observation equation for the narrow lane combination is used to solve the coordinates of the measurement point again. The correctness of the integer ambiguity is verified based on the coordinates of the measurement point obtained from the second solution.

[0050] The narrow alley combination is as follows:

[0051]

[0052] In the formula, f1 and f2 are the carrier frequencies of L1 and L2, respectively, and λ1 and λ2 are the carrier wavelengths of L1 and L2, respectively. n , λ n and N n These represent the narrow-lane carrier frequency, wavelength, and narrow-lane integer ambiguity, respectively. Compared to the narrow-lane wavelength constructed by combining the wavelengths of L1 carrier 19cm and L2 carrier 24cm, which is 10.7cm, the noise is lower and more accurate positioning results can be obtained.

[0053] Specifically, a narrow-lane carrier double-difference positioning model is constructed based on the carrier double-difference observation equations for k narrow-lane combinations; wherein, the carrier double-difference observation equations for each narrow-lane combination are: The carrier double-difference observation equation for the narrow-lane combination is obtained by adding the double-difference observation equations of the two frequency carriers (i.e., by adding Equation 1). This represents the difference vector between the observed and calculated values ​​of the narrow-lane carrier double-difference value.

[0054] The TEC test uses the double-difference ionospheric residual as an indicator, and its expression is:

[0055]

[0056] Furthermore, the threshold value range of the TEC test is (T1, T2); T1 represents the maximum value of the double-difference ionospheric delay residual in adjacent epochs when the integer ambiguity solution is correct; T2 represents the minimum value of the double-difference ionospheric delay residual in adjacent epochs when the integer ambiguity solution is incorrect.

[0057] Furthermore, the following is a description of optional specific embodiments of the present invention:

[0058] Based on the distribution of control points within the campus, a baseline with a length of 975m was selected for data acquisition. Carrier signals from five satellites with common visibility were selected at the time of acquisition, with a sampling interval of 5 seconds, for a total sampling duration of 30 minutes. 165 consecutive sample values ​​were selected for processing, and every 6 sample values ​​were grouped into one epoch for position calculation, resulting in 160 epochs. A comparative experiment was conducted between this invention and the standalone LAMBDA method:

[0059] The coordinate deviation corresponding to the integer ambiguity solved by the LAMBDA method alone is as follows: Figure 2 As shown. The coordinate deviation corresponding to the integer ambiguity calculated by the present invention using the regularization + LAMBDA method is as follows: Figure 3 As shown, the LAMBDA method alone has a large deviation in solving integer ambiguity. This is due to the severe ill-conditioned nature of the double-difference localization model before regularization. The regularization + LAMBDA method reduces the ill-conditioned nature of the double-difference localization model and improves the success rate of integer ambiguity solving, but there are still some cases of integer ambiguity solving errors in some epochs.

[0060] The double-difference ionospheric delay residuals corresponding to integer ambiguities solved by the regularization + LAMBDA method are as follows: Figure 4 As shown in the figure, the epochs in which the double-difference ionospheric delay residual jumps correspond to... Figure 3 In epochs where integer ambiguity resolution is incorrect, the double-difference ionospheric delay residuals of adjacent epochs are very small, within 1 cm; when integer ambiguity resolution is correct, the double-difference ionospheric delay residuals of adjacent epochs are large, greater than 3 cm. Therefore, the threshold for the TEC test is set to 2 cm. It can be seen that... Figure 3 Errors in integer ambiguity resolution typically result in coordinate deviations at the meter level due to the longer carrier waves in wide-lane combinations. Since the initial coordinates of the station can be obtained with decimeter-level positioning accuracy using methods such as pseudorange finite difference, a threshold of 1 meter is set during coordinate accuracy verification. If the deviation between the measured point coordinates and the initial coordinates is less than 1 meter, the coordinate accuracy verification passes. This verification process can detect the vast majority of erroneous integer ambiguity solutions, improving the reliability of integer ambiguity verification.

[0061] To improve the accuracy of integer ambiguity resolution, upon detecting erroneous integer ambiguity resolution at an epoch, the GWO algorithm is first used to re-search for integer ambiguities until the searched integer ambiguities pass the coordinate accuracy and TEC checks. To avoid this process getting stuck in an infinite loop, the maximum number of iterations is set to 60. This process solves the problems of low fault tolerance and lack of feedback in the LAMBDA method, thus improving the success rate of integer ambiguity resolution. Finally, to obtain more accurate measurement point coordinates, the double-difference observation equations of the dual-frequency carrier signal are combined in a narrow-lane configuration to solve for the measurement point coordinates. The solution results are as follows: Figure 5 As shown, the calculated coordinates of the measurement point have a deviation of less than 2.5 cm in all three directions, which is much higher than the decimeter-level positioning accuracy obtained by methods such as pseudorange difference, thus verifying the effectiveness of the integer ambiguity testing method proposed in this invention.

[0062] According to another aspect of the present invention, a system for obtaining integer ambiguity based on dual-frequency carrier signals is provided, comprising: an establishment module for combining dual-frequency carrier signals in a wide-lane configuration to obtain the wide-lane carrier wavelength and wide-lane integer ambiguity; establishing a wide-lane carrier dual-difference positioning model based on the wide-lane carrier wavelength and wide-lane integer ambiguity; a first solution module for introducing a regularization method into the wide-lane carrier dual-difference positioning model to solve the floating-point solution of the wide-lane integer ambiguity and the variance-covariance matrix; an acquisition module for using the LAMBDA method to perform decorrelation processing on the wide-lane integer ambiguity, and searching for the wide-lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide-lane integer ambiguity as the center to obtain the integer solution of the wide-lane integer ambiguity; a second solution module for substituting the obtained integer solution of the wide-lane integer ambiguity into the wide-lane carrier dual-difference positioning model and initially solving the coordinates of the measurement point; verifying the initially solved coordinates of the measurement point using a double verification standard, and resolving the coordinates of the measurement point if the double verification is met. For any parts of the modules not described in detail above, please refer to the relevant descriptions in the embodiments.

[0063] The specific embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for obtaining integer ambiguity based on dual-frequency carrier signals, characterized in that, include: Step 1: Combine the dual-frequency carrier signals in a wide-lane configuration to obtain the wide-lane carrier wavelength and wide-lane integer ambiguity; based on the wide-lane carrier wavelength and wide-lane integer ambiguity, establish a wide-lane carrier dual-difference positioning model; Step 2: Introduce a regularization method into the wide-lane carrier double-difference positioning model to solve the wide-lane integer ambiguity floating-point solution and variance-covariance matrix; Step 3: Use the LAMBDA method to reduce the correlation of the wide lane integer ambiguity, and search for the wide lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide lane integer ambiguity as the center to obtain the integer solution of the wide lane integer ambiguity. Step 4: Substitute the obtained integer solution of wide-lane integer ambiguity into the wide-lane carrier double-difference positioning model, and calculate the coordinates of the measurement point for the first time; verify the coordinates of the measurement point calculated for the first time using a double verification standard, and calculate the coordinates of the measurement point again if the double verification is met. Step 4 specifically involves: substituting the calculated integer solution of the wide-lane integer ambiguity into the wide-lane carrier double-difference positioning model, and initially calculating the coordinates of the measurement point; then substituting the calculated coordinates into the double-difference observation equations of the two frequency carriers to separate the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency; and determining whether the coordinates of the measurement point can pass the double verification criteria. When any one of the test criteria fails, the GWO algorithm is used to search the wide lane integer ambiguity again to obtain the coordinates of the measurement point under the new wide lane integer ambiguity solution. The double test criteria judgment is repeated until both tests pass or the maximum number of iterations is reached. When both test criteria are passed, the carrier signal double-difference observation equations at the two frequencies obtained based on the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency are added together to obtain the carrier double-difference observation equation for the narrow lane combination. The narrow lane carrier double-difference positioning model constructed based on the carrier double-difference observation equation for the narrow lane combination is used to solve the coordinates of the measurement point again. The dual verification criteria include coordinate accuracy and TEC verification; coordinate accuracy is used as the first verification and TEC verification as the second verification. The TEC test expression is as follows: ； in, , These are the carrier wavelengths of L1 and L2, respectively; These are the carrier wavelengths of L1 and L2, respectively; These are the carrier observation values ​​corresponding to the double-difference observation equations at carrier frequencies L1 and L2, respectively.

2. The method for obtaining integer ambiguity based on dual-frequency carrier signals according to claim 1, characterized in that, The wide lane combination is as follows: ； In the formula, , These are the L1 and L2 carrier frequencies, respectively. , and N1 and N2 are the wide-lane carrier frequency, wavelength, and wide-lane integer ambiguity, respectively; N1 and N2 are the integer ambiguities at L1 and L2 carrier frequencies, respectively. Simultaneously observe k+1 satellites, using one of them as the reference satellite, obtain the carrier double-difference observation equations for k wide-lane combinations, and construct a wide-lane carrier double-difference positioning model; wherein, the carrier double-difference observation equations for the wide-lane combinations are: ;in, = , Here, C represents the coefficient matrix corresponding to the coordinate correction, and D represents the coefficient matrix corresponding to the integer ambiguity. This represents the difference vector between the observed and calculated values ​​of the wide-lane carrier double-difference value.

3. A system for obtaining integer ambiguity based on dual-frequency carrier signals, characterized in that, include: A module is established to combine dual-frequency carrier signals in a wide-lane configuration to obtain the wide-lane carrier wavelength and wide-lane integer ambiguity. A wide-lane carrier dual-difference positioning model is established based on the wide-lane carrier wavelength and wide-lane integer ambiguity. The first solution module is used to introduce a regularization method in the wide-lane carrier double-difference positioning model to solve the wide-lane integer ambiguity floating-point solution and variance-covariance matrix. The module is used to perform downcorrelation processing on the wide lane integer ambiguity using the LAMBDA method, and to search for the wide lane integer ambiguity in the ambiguity domain with the floating-point solution of the wide lane integer ambiguity as the center, so as to obtain the integer solution of the wide lane integer ambiguity. The second solution module is used to substitute the integer solutions of the wide lane integer ambiguity into the wide lane carrier double-difference positioning model and initially solve the coordinates of the measurement points. The coordinates of the measurement points initially solved are verified by a double verification standard. If the double verification is met, the coordinates of the measurement points are solved again. Specifically, the process involves substituting the integer solutions of the wide-lane integer ambiguity into the wide-lane carrier double-difference positioning model, initially calculating the coordinates of the measurement point, and then substituting the calculated coordinates into the double-difference observation equations for the two frequency carriers to separate the integer ambiguity N1 at carrier frequency L1 and the integer ambiguity N2 at carrier frequency L2. Finally, it is determined whether the coordinates of the measurement point pass the dual verification criteria. When any one of the test criteria fails, the GWO algorithm is used to search the wide lane integer ambiguity again to obtain the coordinates of the measurement point under the new wide lane integer ambiguity solution. The double test criteria judgment is repeated until both tests pass or the maximum number of iterations is reached. When both test criteria are passed, the carrier signal double-difference observation equations at the two frequencies obtained based on the integer ambiguity N1 at the L1 carrier frequency and the integer ambiguity N2 at the L2 carrier frequency are added together to obtain the carrier double-difference observation equation for the narrow lane combination. The narrow lane carrier double-difference positioning model constructed based on the carrier double-difference observation equation for the narrow lane combination is used to solve the coordinates of the measurement point again. The dual verification criteria include coordinate accuracy and TEC verification; coordinate accuracy is used as the first verification and TEC verification as the second verification. The TEC test expression is as follows: ； in, , These are the carrier wavelengths of L1 and L2, respectively; These are the carrier wavelengths of L1 and L2, respectively; These are the carrier observation values ​​corresponding to the double-difference observation equations at carrier frequencies L1 and L2, respectively.

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