A short-baseline single-epoch positioning method based on the Beidou-3 quad-frequency signal

Abstract

The present invention discloses a short-baseline single-epoch positioning method based on the four-frequency signals of Beidou-3. In view of the characteristic that Beidou-3 can broadcast four-frequency signals, and taking advantage of the characteristics of multi-frequency combined observations, such as long wavelength, weak ionospheric influence, and low noise, first, the (-1, 0, 1, 0) and (0, 1, 0, -1) ultra-wide-lane ambiguities are solved by using the four-frequency carrier and pseudorange observation data of Beidou-3; secondly, the (0, -3, 1, 2) wide-lane ambiguity is solved based on the geometric model; then the (0, -1, 1, 0) and (0, 0, 1, -1) wide-lane ambiguities are calculated; finally, the narrow-lane ambiguity is solved and fixed based on the least squares principle, and then substituted back into the observation equation to solve the three-dimensional coordinate parameters in a single epoch. By using the positioning method proposed by the present invention, short-baseline single-epoch positioning can be achieved, effectively improving the timeliness of GNSS positioning, and having good application prospects in the fields of deformation monitoring and dynamic positioning, etc.

Description

Technical Field

[0001] The present invention belongs to the technical field of Beidou satellite navigation system positioning, and particularly relates to a short-baseline single-epoch positioning method based on the four-frequency signals of Beidou-3. Background Art

[0002] The Beidou satellite navigation system has evolved from the experimental satellite navigation system (BDS-1) to a regional satellite navigation system (BDS-2), and finally entered the global satellite navigation system (BDS-3) stage. BDS-3 consists of 3 GEO satellites, 3 IGSO satellites and 24 MEO satellites, and was officially launched on July 31, 2020, aiming to provide navigation, positioning and timing services for global users. In order to achieve compatibility with BDS-2, BDS-3 inherits the B1I and B3I frequency points. In addition, BDS-3 also broadcasts three frequency point signals, namely B1C, B2a and B2b, to achieve compatible interoperability with the GPS system and the Galileo system. Compared with three-frequency or dual-frequency signals, the four-frequency signals can form more combined observations with excellent characteristics such as long wavelength, weak ionospheric influence and low noise. These advantages are of great significance for improving the efficiency of ambiguity resolution, cycle slip detection and repair, and high-precision positioning.

[0003] The fixation of integer ambiguities is the key and core to achieve high-precision real-time positioning. GNSS multi-frequency ambiguity resolution can generally be divided into two types: geometric models and non-geometric models. Geometric-related models are resolution models that use the carrier and pseudorange observations of multiple satellites to estimate the integer ambiguities and geometric terms as unknown parameters simultaneously, such as the LAMBDA method. In non-geometric models, the ambiguity of each satellite is solved independently, and the resolution model directly solves the ambiguity only using the observations of a single satellite, such as the TCAR method and the CIR method. The current multi-frequency positioning methods mainly target dual-frequency or triple-frequency data. However, with the broadcast of four-frequency and above data by Beidou-3, it provides favorable conditions for four-frequency ambiguity resolution and four-frequency single-epoch positioning. Summary of the Invention

[0004] The purpose of the present invention is to: aiming at the deficiency that the ambiguity of traditional single-frequency short-baseline positioning requires a certain time to be fixed, a short-baseline single-epoch positioning method based on the four-frequency signals of Beidou-3 is proposed, which can realize short-baseline single-epoch positioning and effectively improve the efficiency of ambiguity resolution and the timeliness of GNSS positioning.

[0005] To achieve the above purpose, the present invention provides the following technical solution: a short-baseline single-epoch positioning method based on the four-frequency signals of Beidou-3. Based on the four-frequency carrier and pseudorange observation data of Beidou-3, the following steps are executed to obtain the three-dimensional coordinate parameters in the carrier double-difference observation equation, and complete the short-baseline single-epoch positioning of the four-frequency signals of Beidou-3;

[0006] Step S1: Using the four-frequency carrier and pseudorange observation data of Beidou-3, calculate the ultra-wide-lane ambiguities of the carrier combinations (-1, 0, 1, 0) and (0, 1, 0, -1) respectively based on the geometry-free model for a single epoch, and then round them to obtain the rounded and fixed ultra-wide-lane ambiguities Δ▽N (-1,0,1,0) and Δ▽N (0,1,0,-1) ;

[0007] Step S2: Take the rounded and fixed ultra-wide-lane ambiguities as high-precision pseudorange observations, substitute them into the observation equation, and solve for the wide-lane ambiguity Δ▽N (0,-3,1,2) ;

[0008] Step S3: According to the rounded and fixed ultra-wide-lane ambiguity Δ▽N (0,1,0,-1) obtained in Step S1, and the wide-lane ambiguity Δ▽N (0,-3,1,2) obtained in Step S2, calculate the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) through linear combination;

[0009] Step S4: Take the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) obtained in Step S3 as high-precision pseudorange observations, and based on the least squares principle, calculate the narrow-lane ambiguity of the carrier combination (0, 0, 1, 0), and obtain the floating-point solution and variance-covariance matrix of the narrow-lane ambiguity of the carrier combination (0, 0, 1, 0). For the narrow-lane ambiguity Δ▽N (0,0,1,0) use the least squares de-correlation method to search for and fix the ambiguity, and then according to the fixed narrow-lane ambiguity, substitute it into the carrier double-difference observation equation to solve for the three-dimensional coordinate parameters for a single epoch.

[0010] Further, the aforementioned Step S1 includes the following sub-steps:

[0011] Step S1.1: Using the four-frequency carrier and pseudorange observation data of Beidou-3, calculate the ultra-wide-lane ambiguity of the carrier combination (-1, 0, 1, 0) based on the geometry-free model for a single epoch, and then round and fix the calculated ultra-wide-lane ambiguity of the carrier combination (-1, 0, 1, 0) as follows:

[0012]

[0013] where Δ▽ represents the double-difference operator, Δ▽N (-1,0,1,0) represents the ultra-wide-lane ambiguity of the (-1, 0, 1, 0) carrier combination, [·] represents the rounding operator, Δ▽φ (-1,0,1,0) represents the (-1, 0, 1, 0) carrier combination observation value in meters, Δ▽P (1,1,0,0) represents the pseudorange combination observation value of the carrier combination (1, 1, 0, 0) in meters, and λ(-1,0,1,0) Denote the wavelength of the carrier combination (-1, 0, 1, 0) observation;

[0014] Step S1.2: Using the four-frequency carrier and pseudorange observation data of Beidou-3, calculate the ultra-wide lane ambiguity of the carrier combination (0, 1, 0, -1) based on the geometry-free model for a single epoch, and then round and fix the calculated ultra-wide lane ambiguity of the carrier combination (0, 1, 0, -1) as follows:

[0015]

[0016] In equation (2), Δ▽ represents the double-difference operator, Δ▽N (0,1,0,-1) represents the ultra-wide lane ambiguity of (0, 1, 0, -1), [·] represents the rounding operator, Δ▽φ (0,1,0,-1) represents the carrier combination (0, 1, 0, -1) observation value in meters, Δ▽P (0,1,0,1) represents the carrier combination (0, 1, 0, 1) pseudorange combination observation value in meters, λ (0,1,0,-1) represents the wavelength of the carrier combination (0, 1, 0, -1) observation.

[0017] Furthermore, the aforementioned step S2 is specifically: Based on the rounded and fixed ultra-wide lane ambiguity Δ▽N obtained in step S1 (-1,0,1,0) 、Δ▽N (0,1,0,-1) , and used as high-precision pseudorange observation values, adopt the geometric correlation model to perform least-squares joint solution for the wide lane ambiguity Δ▽N (0,-3,1,2) , as follows:

[0018]

[0019] Among them, l (0,-3,1,2) =Δ▽φ (0,-3,1,2) -Δ▽ρ,

[0020]

[0021] In equation (3), a, b, c, and d represent the combination coefficients of the carrier observation values, v (a,b,c,d) represents the residual between the carrier observation quantity and the calculated quantity, X represents the three-dimensional coordinate parameter, B represents the linearized coefficient matrix of the baseline vector X, I represents the identity matrix, l (a,b,c,d) represents the constant term of the double-difference observation equation, Δ▽ represents the double-difference operator, represents the observation value in meters, λ (a,b,c,d) represents the wavelength of the carrier combination observation value, ρ represents the distance between the satellite and the receiver, Δ▽N (0,-3,1,2) represents the wide lane ambiguity of the carrier combination (0, -3, 1, 2).

[0022] Further, the foregoing step S3 is specifically as follows: According to the rounded and fixed ultra-wide lane ambiguity Δ▽N obtained in step S1 (0,1,0,-1) and the wide lane ambiguity Δ▽N obtained in step S2 (0,-3,1,2) , linearly combine Δ▽N (0,1,0,-1) and Δ▽N (0,-3,1,2) to obtain the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) wide lane ambiguities; as shown in the following formula:

[0023]

[0024] In formula (4), Δ▽ represents the double-difference operator, Δ▽N (0,-1,1,0) represents the carrier combination (0, -1, 1, 0) wide lane ambiguity, Δ▽N (0,0,1,-1) represents the carrier combination (0, 0, 1, -1) wide lane ambiguity, Δ▽N (0,1,0,-1) represents the carrier combination (0, 1, 0, -1) ultra-wide lane ambiguity, Δ▽N (0,-3,1,2) represents the carrier combination (0, -3, 1, 2) wide lane ambiguity.

[0025] Further, the foregoing step S4 is specifically as follows: Use the wide lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) obtained in step S3 as high-precision pseudorange observations, and solve the B1C narrow lane ambiguity based on the geometric model, as shown in the following formula:

[0026]

[0027] In formula (5): X = [x y z] T , l (0,0,1,0) = Δ▽φ (0,0,1,0) - Δ▽ρ,

[0028]

[0029] In the formula, a, b, c, and d represent the combination coefficients of the carrier observations, v (a,b,c,d) represents the residual between the carrier observation and the calculated value, X represents the three-dimensional coordinate parameter, B represents the linearized coefficient matrix of the baseline vector X, l (a,b,c,d) represents the constant term of the double-difference observation equation, Δ▽ represents the double-difference operator, represents the observation value in meters, I represents the identity matrix, λ (a,b,c,d) represents the wavelength of the carrier combination observation value, ρ represents the distance between the satellite and the receiver, Δ▽N (0,0,1,0) represents the B1C narrow lane ambiguity.

[0030] Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects: In view of the deficiency that the ambiguity of the traditional single-frequency short baseline positioning needs a certain time to be fixed, the present invention proposes a short baseline single epoch positioning method based on the BeiDou-3 four-frequency signal. This method makes full use of the advantage that BeiDou-3 can broadcast four-frequency signals, combines the observed values of the four-frequency signals to obtain some combined observed values with excellent characteristics, generally having long wavelengths, weak ionospheric influence, and low noise. Then, a geometry-independent model is used to fix two ultra-wide lane ambiguities, a geometry-related model is used to fix one wide lane and one narrow lane ambiguity, and the least squares de-correlation method is used to search for and fix the narrow lane ambiguity. Finally, the narrow lane with the fixed ambiguity is substituted back into the carrier double-difference observation equation for single epoch positioning. The present invention can achieve short baseline single epoch positioning, effectively improving the ambiguity resolution efficiency and the timeliness of GNSS positioning, and has good application prospects in the fields of deformation monitoring and dynamic positioning. Description of the Drawings

[0031] Figure 1 It is a flow chart of the short baseline single epoch positioning method based on the BeiDou-3 four-frequency signal;

[0032] Figure 2 It is the solution deviation of the (-1, 0, 1, 0) ultra-wide lane ambiguity solved by the geometry-free model for each epoch of the baseline HC01-HC02 and the baseline HC03-HC04;

[0033] Figure 3 It is the solution deviation of the (0, 1, 0, -1) ultra-wide lane ambiguity solved by the geometry-free model for each epoch of the baseline HC01-HC02 and the baseline HC03-HC04;

[0034] Figure 4 It is the Ratio value of the (0, -3, 1, 2) wide lane ambiguity fixed for each epoch of the baseline HC01-HC02 and the baseline HC03-HC04;

[0035] Figure 5 It is the Ratio value of the narrow lane ambiguity fixed for each epoch of the baseline HC01-HC02 and the baseline HC03-HC04;

[0036] Figure 6 It is the positioning error of the baseline HC01-HC02 in the three directions of north (N), east (E), and up (U);

[0037] Figure 7 It is the positioning error of the baseline HC03-HC04 in the three directions of north (N), east (E), and up (U). Detailed Embodiment

[0038] To better understand the technical content of the present invention, specific embodiments are hereby given and described in conjunction with the accompanying drawings as follows. In the present invention, various aspects of the present invention are described with reference to the drawings, and many illustrative embodiments are shown in the drawings. The embodiments of the present invention are not limited to those described in the drawings. It should be understood that the present invention can be implemented by any one of the various concepts and embodiments introduced above, as well as the concepts and embodiments described in detail below, because the concepts and embodiments disclosed in the present invention are not limited to any embodiment. In addition, some aspects disclosed in the present invention can be used alone, or in any suitable combination with other aspects disclosed in the present invention.

[0039] As Figure 1 shown, a short-baseline single-epoch positioning method based on the Beidou-3 four-frequency signal disclosed in an embodiment of the present invention first uses the Beidou-3 four-frequency carrier and pseudorange observation data to solve the carrier combinations (-1, 0, 1, 0) and (0, 1, 0, -1) ultra-wide-lane ambiguities and round them; secondly, taking the two ultra-wide-lane ambiguities as constraint conditions, based on a geometric model to solve the wide-lane ambiguity Δ▽N (0,-3,1,2) ; then using the ultra-wide-lane ambiguity Δ▽N (0,1,0,-1) and the wide-lane ambiguity Δ▽N (0,-3,1,2) , through linear combination calculation to obtain the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1); the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) are used as high-precision pseudorange observation values, and based on the least squares principle, calculate the narrow-lane ambiguity of the carrier combination (0, 0, 1, 0), and obtain the floating-point solution and variance-covariance matrix of the narrow-lane ambiguity of the carrier combination (0, 0, 1, 0). For the narrow-lane ambiguity Δ▽N (0,0,1,0) , use the least squares de-correlation method to search for and fix the ambiguity. After that, according to the fixed narrow-lane ambiguity, substitute it into the carrier double-difference observation equation, and solve for the three-dimensional coordinate parameters in a single epoch. The method includes the following specific steps:

[0040] Using the Beidou-3 four-frequency carrier and pseudorange observation data, based on a non-geometric model, calculate the ultra-wide-lane ambiguity of the carrier combination (-1, 0, 1, 0) in a single epoch, and then round and fix the calculated ultra-wide-lane ambiguity of the carrier combination (-1, 0, 1, 0), as shown in the following formula:

[0041]

[0042] In formula (1), Δ▽ represents the double-difference operator, Δ▽N (-1,0,1,0) represents the ultra-wide-lane ambiguity of the (-1, 0, 1, 0) carrier combination, [·] represents the rounding operator, Δ▽φ (-1,0,1,0) represents the (-1, 0, 1, 0) carrier combination observation value in meters, Δ▽P (1,1,0,0)denotes the carrier combination (1, 1, 0, 0) pseudorange combination observation value in meters, λ (-1,0,1,0) denotes the wavelength of the carrier combination (-1, 0, 1, 0) observation;

[0043] Using the Beidou-3 four-frequency carrier and pseudorange observation data, based on the geometry-free model, the ultra-wide lane ambiguity of the carrier combination (0, 1, 0, -1) is calculated for a single epoch. Then, the calculated ultra-wide lane ambiguity of the carrier combination (0, 1, 0, -1) is rounded and fixed as follows:

[0044]

[0045] In equation (2), Δ▽ represents the double-difference operator, Δ▽N (0,1,0,-1) denotes the (0, 1, 0, -1) ultra-wide lane ambiguity, [·] represents the rounding operator, Δ▽φ (0,1,0,-1) denotes the carrier combination (0, 1, 0, -1) observation value in meters, Δ▽P (0,1,0,1) denotes the carrier combination (0, 1, 0, 1) pseudorange combination observation value in meters, λ (0,1,0,-1) denotes the wavelength of the carrier combination (0, 1, 0, -1) observation.

[0046] After two ultra-wide lane ambiguities are fixed, substituting them back into the observation equation can be used as high-precision pseudorange observation values, and the wide lane ambiguity Δ▽N is solved using the geometric model constraint. The specific steps are as follows: (0,-3,1,2) Specific steps are as follows:

[0047] Based on the obtained rounded and fixed ultra-wide lane ambiguity Δ▽N (-1,0,1,0) 、Δ▽N (0,1,0,-1) As high-precision pseudorange observation values, the geometric correlation model is used for least-squares joint solution of the wide lane ambiguity Δ▽N (0,-3,1,2) as follows:

[0048]

[0049] In equation (3),

[0050] l (0,-3,1,2) =Δ▽φ (0,-3,1,2) -Δ▽ρ,

[0051] where a, b, c, and d represent the combination coefficients of the carrier observations, v (a,b,c,d) denotes the residual between the carrier observation and the calculated value, X represents the three-dimensional coordinate parameters, B represents the linearized coefficient matrix of the baseline vector X, I represents the identity matrix, l (a,b,c,d) denotes the constant term of the double-difference observation equation, Δ▽ represents the double-difference operator, denotes the observation value in meters, λ (a,b,c,d) denotes the wavelength of the carrier combined observation value, ρ denotes the distance between the satellite and the receiver, Δ▽N (0,-3,1,2) denotes the wide-lane ambiguity of the carrier combination (0, -3, 1, 2).

[0052] According to the rounded and fixed ultra-wide-lane ambiguity Δ▽N (0,1,0,-1) and the wide-lane ambiguity Δ▽N (0,-3,1,2) , the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) are calculated through linear combination, as shown in the following formula:

[0053]

[0054] In formula (4), Δ▽ represents the double-difference operator, Δ▽N (0,-1,1,0) denotes the wide-lane ambiguity of the carrier combination (0, -1, 1, 0), Δ▽N (0,0,1,-1) denotes the wide-lane ambiguity of the carrier combination (0, 0, 1, -1), Δ▽N (0,1,0,-1) denotes the ultra-wide-lane ambiguity of the carrier combination (0, 1, 0, -1), Δ▽N (0,-3,1,2) denotes the wide-lane ambiguity of the carrier combination (0, -3, 1, 2).

[0055] Finally, the obtained wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) are used as high-precision pseudorange observation values, and the B1C narrow-lane ambiguity is solved based on the geometric model, as shown in the following formula:

[0056]

[0057] In formula (5): X = [x y z] T , l (0,0,1,0) = Δ▽φ (0,0,1,0) - Δ▽ρ,

[0058] In the formula, a, b, c, and d represent the combination coefficients of the carrier observation values, v (a,b,c,d) denotes the residual between the carrier observation value and the calculated value, X represents the three-dimensional coordinate parameter, B represents the linearized coefficient matrix of the baseline vector X, l (a,b,c,d) denotes the constant term of the double-difference observation equation, Δ▽ represents the double-difference operator, denotes the observation value in meters, I represents the identity matrix, λ (a,b,c,d) denotes the wavelength of the carrier combined observation value, ρ denotes the distance between the satellite and the receiver, Δ▽N (0,0,1,0) denotes the B1C narrow-lane ambiguity.

[0059] The accuracy verification of the method of the present invention is as follows: Two groups of measured Beidou-3 four-frequency short baseline data are used for verification. The data sampling time of baseline HC01-HC02 is December 17, 2021 (24 hours), the baseline length is 4.1 km, the sampling interval is 30 s, and the number of epochs is 2,880. The data sampling time of baseline HC03-HC04 is January 10, 2022 (24 hours), the baseline length is 9.0 km, the sampling interval is 30 s, and the number of epochs is 2,880. The two groups of short baseline data are respectively processed by the method of the present invention. The reliability of the integer ambiguity fixed by searching using the LAMBDA algorithm is reflected by comparing the Ratio value, and the positioning accuracy is analyzed by comparing the positioning result with the accurate coordinates of the station.

[0060] Figure 2 and Figure 3 are the solution biases of the ultra-wide lane ambiguities of each epoch (-1, 0, 1, 0) and (0, 1, 0, -1) for baseline HC01-HC02 and baseline HC03-HC04. It can be seen from the figure that the single-epoch ambiguity biases of the two ultra-wide lane combinations (-1, 0, 1, 0) and (0, 1, 0, -1) are both within ±0.5 cycles, the corresponding RMS statistical values are both less than 0.06 cycles, and the proportion within 0.3 cycles is 100%. This indicates that the two ultra-wide lane ambiguities can be reliably fixed by using the rounding method.

[0061] Figure 4 are the Ratio values of the fixed wide lane ambiguities of each epoch (0, -3, 1, 2) for baseline HC01-HC02 and baseline HC03-HC04. The Ratio value is the ratio of the variances of the optimal fixed solution and the sub-optimal fixed solution of the ambiguity, which can be used to evaluate the ambiguity resolution effect. Generally, it is set to 2-3, and 2 is used as the evaluation threshold in this method. It can be seen from the figure that most epochs of baseline HC01-HC02 can pass the Ratio threshold test, and the wide lane ambiguity fixing rate can reach 99.90%. All epochs of baseline HC03-HC04 can pass the Ratio threshold test, and the wide lane ambiguity fixing rate can reach 100%.

[0062] Figure 5 are the Ratio values of the fixed narrow lane ambiguities of each epoch for baseline HC01-HC02 and baseline HC03-HC04. It can be seen from the figure that most epochs of baseline HC01-HC02 can pass the Ratio threshold test, and the narrow lane ambiguity fixing rate can reach 99.93%. All epochs of baseline HC03-HC04 can pass the Ratio threshold test, and the narrow lane ambiguity fixing rate can reach 100%.

[0063] Figure 6The positioning errors of baseline HC01-HC02 in the three directions of north (N), east (E), and up (U). As can be seen from the figure, the positioning errors of baseline HC01-HC02 in the plane direction fluctuate within the range of -2 to 2 cm, and the positioning errors in the elevation direction fluctuate within the range of -5 to 5 cm. The RMS values of the positioning accuracy statistics in the N / E / U three directions are 0.33 cm, 0.35 cm, and 0.86 cm respectively, and single-epoch millimeter-level positioning can be achieved.

[0064] Figure 7 The positioning errors of baseline HC03-HC04 in the three directions of north (N), east (E), and up (U). As can be seen from the figure, the positioning errors of baseline HC03-HC04 in the plane direction fluctuate within the range of -3 to 3 cm, and the positioning errors in the elevation direction fluctuate within the range of -5 to 5 cm. The RMS values of the positioning accuracy statistics in the N / E / U three directions are 0.90 cm, 0.51 cm, and 1.26 cm respectively, and single-epoch centimeter-level positioning can be achieved.

[0065] It should be noted that the description of the above embodiments is only used to help understand the method of the present application and its core idea. For those of ordinary skill in the art of this technology, without departing from the principle of the present application, several improvements and modifications can still be made to the present application, and these improvements and modifications are also within the protection scope of the claims of the present application.

[0066] Although the present invention has been described above with preferred embodiments, it is not intended to limit the present invention. Those with ordinary knowledge in the technical field to which the present invention pertains can make various changes and modifications without departing from the spirit and scope of the present invention. Therefore, the protection scope of the present invention shall be determined by the scope defined in the claims.

Claims

1. A short-baseline single-epoch positioning method based on the Beidou-3 four-frequency signal, characterized in that, based on the Beidou-3 four-frequency carrier and pseudorange observation data, the following steps are performed to obtain the three-dimensional coordinate parameters in the carrier double-difference observation equation, and complete the short-baseline single-epoch positioning of the Beidou-3 four-frequency signal; Step S1: Using the Beidou-3 four-frequency carrier and pseudorange observation data, calculate the ultra-wide-lane ambiguities of the carrier combinations (-1, 0, 1, 0) and (0, 1, 0, -1) respectively based on the geometry-free model for a single epoch, and then round them to obtain the rounded and fixed ultra-wide-lane ambiguities Δ▽N (-1,0,1,0) and Δ▽N (0,1,0,-1) ; Step S2: Use the rounded and fixed ultra-wide lane ambiguity as a high-precision pseudorange observation value, substitute it into the observation equation, and solve for the wide lane ambiguity Δ▽N based on geometric model constraints (0,-3,1,2) ; Step S3. Based on the rounded and fixed ultra-wide lane ambiguity Δ▽N obtained in Step S1 (0,1,0,-1) and the wide lane ambiguity Δ▽N obtained in Step S2 (0,-3,1,2) , calculate the wide lane ambiguities of carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) through linear combination; Step S4: Use the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) obtained in step S3 as high-precision pseudorange observations, and based on the least squares principle, calculate the narrow-lane ambiguity of the carrier combination (0, 0, 1, 0), and obtain the floating-point solution and variance-covariance matrix of the narrow-lane ambiguity of the carrier combination (0, 0, 1, 0). For the narrow-lane ambiguity Δ▽N (0,0,1,0) Use the least squares de-correlation method to search for and fix the ambiguity. Then, substitute the fixed narrow-lane ambiguity into the carrier double-difference observation equation to solve for the three-dimensional coordinate parameters in a single epoch; wherein, step S1 includes the following sub-steps: Step S1.1: Using the Beidou-3 four-frequency carrier and pseudorange observation data, calculate the ultra-wide-lane ambiguity of the carrier combination (-1, 0, 1, 0) based on the geometry-free model for a single epoch, and then round and fix the calculated ultra-wide-lane ambiguity of the carrier combination (-1, 0, 1, 0), as shown in the following formula: (1) In the formula, represents the double-difference operator, represents the (-1, 0, 1, 0) carrier-phase combination ultra-wide-lane ambiguity, and [·] represents the rounding operator, represents the (-1, 0, 1, 0) carrier-phase combination observation value in meters, represents the carrier-phase combination (1, 1, 0, 0) pseudorange combination observation value in meters, and λ (-1,0,1,0) represents the wavelength of the (-1, 0, 1, 0) carrier-phase combination observation value; Step S1.2: Using the Beidou-3 four-frequency carrier and pseudorange observation data, calculate the ultra-wide-lane ambiguity of the carrier combination (0, 1, 0, -1) based on the geometry-free model for a single epoch, and then round and fix the calculated ultra-wide-lane ambiguity of the carrier combination (0, 1, 0, -1), as shown in the following formula: (2) In the formula, represents the double-difference operator, represents the (0, 1, 0, -1) ultra-wide-lane ambiguity, and [·] represents the rounding operator, represents the carrier combination (0, 1, 0, -1) observation value in meters, represents the carrier combination (0, 1, 0, 1) pseudorange combination observation value in meters, λ (0,1,0,-1) represents the wavelength of the carrier combination (0, 1, 0, -1) observation value; Step S2 specifically is: Based on the rounded and fixed ultra-wide lane ambiguity obtained in step S1 and using it as a high-precision pseudo-range observation value, a least squares joint solution of the wide lane ambiguity is carried out by adopting a geometric correlation model as follows: (3) In the formula, where a, b, c, and d represent the combination coefficients of the carrier observations, and v (a,b,c,d) represents the residual between the carrier observation and the calculated value, X represents the three-dimensional coordinate parameters, B represents the linearized coefficient matrix of the baseline vector X, I represents the identity matrix, and l (a,b,c,d) represents the constant term of the double-difference observation equation, represents the double-difference operator, represents the observation value in meters, and λ (a,b,c,d) represents the wavelength of the carrier combined observation, ρ represents the distance between the satellite and the receiver, and Δ▽N (0,-3,1,2) represents the carrier combination (0, -3, 1, 2) wide-lane ambiguity; The specific content of step S3 is as follows: according to the rounded and fixed ultra-wide lane ambiguity obtained in step S1 and the wide lane ambiguity obtained in step S2 perform a linear combination and to obtain the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) wide lane ambiguities; as shown in the following formula: In equation (4), represents the double-difference operator, represents the carrier combination (0, -1, 1, 0) wide-lane ambiguity, represents the carrier combination (0, 0, 1, -1) wide-lane ambiguity, represents the carrier combination (0, 1, 0, -1) ultra-wide-lane ambiguity, represents the carrier combination (0, -3, 1, 2) wide-lane ambiguity; Step S4 is specifically: taking the wide-lane ambiguities of the carrier combinations (0, -1, 1, 0) and (0, 0, 1, -1) obtained in step S3 as high-precision pseudorange observation values, and solving the B1C narrow-lane ambiguity based on the geometry model, as shown in the following formula: where: X = [x y z] T , In the formula, a, b, c, and d represent the combination coefficients of carrier observations, and v (a,b,c,d) represents the residual between the carrier observation and the calculated quantity, X represents the three-dimensional coordinate parameter, B represents the linearization coefficient matrix of the baseline vector X, and l (a,b,c,d) represents the constant term of the double-difference observation equation, represents the double-difference operator, represents the observation value in meters, I represents the identity matrix, and λ (a,b,c,d) represents the wavelength of the carrier combined observation value, ρ represents the distance between the satellite and the receiver, represents the B1C narrow-lane ambiguity.

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