Overall adjustment method for relative corrections of network RTK (Real-Time Kinematic) master and reference stations

Abstract

The invention relates to an overall adjustment method for relative corrections of a network RTK (Real-Time Kinematic) main reference station, which comprises the following steps of: 1, reading data, constructing a triangulation network, calculating a closing error of a triangulation network baseline error improvement number, judging whether a gross error exists in the closing error or not, and if so, entering the next step; if not, outputting an adjustment result; 2, according to an indirect adjustment principle, a baseline vector adjustment method is adopted to solve a correction number about a certain specified master station; establishing a baseline vector error equation according to a relationship between double differences and baseline transmission; on the basis of a triangular relation formed by the main station and the auxiliary station, constraint conditions are obtained, and overall adjustment calculation of a relative error correction number is carried out; and 3, positioning and repairing the gross error based on the overall adjustment calculation result, and outputting an adjustment result. According to the method, the vector relation of the error correction of each baseline, the closing error of the triangulation network and the interpolation relation between the stations are comprehensively considered, and one-time overall generation of the relative correction of the main reference station in the network RTK is realized.

Description

Technical Field

[0001] The invention relates to the field of satellite positioning technology, and in particular to an overall adjustment method for relative correction numbers of a network RTK main reference station. Background Art

[0002] The global navigation satellite system (GNSS) has the advantages of being global, all-weather, and high-precision, and has been widely used in geodesy, precision agriculture, public transportation, and other fields. Existing dynamic positioning technologies mainly include real-time precision point positioning (PPP) and network real-time kinematic positioning (RTK). Precision point positioning only requires a single receiver and precision products such as satellite precise orbits and clock errors to achieve centimeter-level high-precision positioning on a global scale. It has the advantages of easy operation and flexibility, and has gradually become one of the research hotspots of GNSS. However, the real-time PPP technology has a long initialization time, and real-time processing requires additional Beidou / GNSSSR corrections. It has high requirements for Internet communication and cannot meet the needs of high-precision positioning users in terms of positioning timeliness, accuracy, and reliability.

[0003] In order to meet the needs of high-precision dynamic navigation and positioning services and realize centimeter-level, evenly distributed, and highly reliable real-time dynamic positioning applications within the region, GNSS regional augmentation technology based on a regional continuously operating GNSS reference station network has emerged. The GNSS regional augmentation system that uses phase observations to calculate error correction information and broadcasts it to users is usually called a network RTK system, which can provide users with real-time centimeter-level positioning services. However, RTK technology is limited by the distance between base stations and mobile stations. When the distance between stations exceeds 15km, the spatial correlation of the atmospheric error of the satellite signal on the propagation path will be weakened, making it difficult to fix the carrier phase ambiguity and unable to provide reliable centimeter-level positioning results. Therefore, scholars have proposed a network RTK technology with multiple reference stations. Multiple (3 or more) Beidou / GNSS reference stations are established in the target area to form a mesh coverage of the entire area. On this basis, a benchmark is established to calculate and broadcast Beidou / GNSS correction information, thereby performing real-time correction positioning for mobile station users in the area. This is called Beidou / GNSS network RTK, also known as multi-reference station RTK. Network RTK usually uses the Delaunay triangulation method to construct the network, solve the double-difference ambiguity of each triangle edge in the network, establish a precise error estimation model based on the systematic or random relationship between the mobile station position and the reference station of various distance-related error sources, and calculate the error correction information of the mobile station position.

[0004] The existing main error correction calculation models include linear interpolation model, low-order trend surface model, distance-related interpolation model, linear combination model and least squares configuration model. However, the result obtained by the above error correction calculation method is the error correction between the baselines in the base station network. However, the information required by some mobile station users is the error correction relative to a specified master base station. The methods mentioned above cannot meet this requirement. Therefore, it is necessary to use some method to calculate the error correction of the specified master base station relative to all auxiliary base stations and broadcast it to users as the final product. At present, the commonly used method is the shortest path transmission method, but this method has problems such as the inability to verify the unique path and poor fault tolerance during use. Summary of the invention

[0005] The present invention provides an overall adjustment method for relative correction numbers of a network RTK main reference station to solve the above technical problems.

[0006] In order to solve the above technical problems, the present invention provides an overall adjustment method for relative correction numbers of a network RTK master reference station, comprising the following steps:

[0007] Step 1: read the data and construct a triangulated network, calculate the closure error of the triangulated network baseline error improvement number, determine whether the closure error has a gross error, and in response to the presence of a gross error, proceed to the next step; in response to the absence of a gross error, output the adjustment result;

[0008] Step 2: According to the indirect adjustment principle, the baseline vector adjustment method is used to solve the correction number for a specified master station; according to the relationship between double difference and baseline transfer, the baseline vector error equation is established; based on the triangle relationship formed by the master station and the auxiliary station, the constraint conditions are obtained, and the overall adjustment solution of the relative error correction number is performed;

[0009] Step 3: Based on the overall adjustment solution results obtained in the second step, locate and repair the gross errors and output the adjustment results.

[0010] Preferably, the baseline vector error equation is:

[0011]

[0012] Among them, L1 is the error correction number of each baseline in the base station triangulation network, It is the estimated value of the double difference relative error correction from the main station to other auxiliary stations. B1 is the coefficient matrix describing the linear relationship between the error correction of each baseline in the triangulation network and the relative error correction of the main station. V1 is the residual of the error correction.

[0013] Preferably, the weight matrix P1 of the error correction number in the observation equation is set as a diagonal matrix, and each diagonal element is determined based on the closure error test result in the first step.

[0014] Preferably, the constraints include:

[0015] If the master station is located in the triangle formed by the auxiliary stations, the linear interpolation method is used to obtain the corresponding interpolation coefficients and to construct the error correction number interpolation equation;

[0016] If the master station is not located in the triangle formed by the auxiliary stations, the three auxiliary stations closest to the master station are selected, and the interpolation coefficients are obtained using the linear interpolation method to construct the error correction number interpolation equation.

[0017] Preferably, the constraints also include:

[0018] Determine in turn whether each auxiliary station is located within the triangle formed by the main station and the remaining auxiliary stations.

[0019] If it is established, the error correction interpolation equation is obtained by interpolating the main station and the two auxiliary stations forming a triangle;

[0020] Otherwise, two or three auxiliary stations closest to the auxiliary station are used to perform interpolation together with the main station to obtain the interpolation equation of the error correction number.

[0021] Preferably, in the second step, the overall adjustment solution method of the relative error correction number is: using the least squares method to calculate the estimated value of the relative error correction number relative to the master station after adjustment and its verified unit weighted mean error.

[0022] Preferably, the unit weighted mean error for:

[0023]

[0024] Among them, V and P are the baseline vector error equation and weight matrix respectively, n is the number of observation equations, and t is the number of parameters to be determined.

[0025] Preferably, if n>t and If it is greater than the first threshold, a second adjustment is performed; otherwise, the current adjustment result is used as the final estimate of the unknown baseline correction number.

[0026] Preferably, the first threshold is 2 mm.

[0027] Preferably, when performing the overall adjustment solution of the relative error correction number, the ionospheric correction number and the geometric correction number are calculated separately.

[0028] Compared with the prior art, the overall adjustment method of the relative correction number of the network RTK master reference station provided by the present invention has the following advantages:

[0029] 1. The present invention proposes a multi-baseline relative error correction number overall adjustment method centered on the master station, which can not only obtain high-precision error correction numbers about the master reference station, but also ensure the consistency and reliability of the error correction numbers of the entire network through closure error inspection and adjustment calculation;

[0030] 2. The present invention comprehensively considers the vector relationship of each baseline error correction number, the baseline closure error of the Delaunay triangulation network and the interpolation relationship between stations, and realizes the one-time overall generation of the relative correction number of the main reference station in the network RTK. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flow chart of an overall adjustment method of relative correction numbers of a network RTK master reference station in a specific implementation mode of the present invention;

[0032] Figure 2 This is a schematic diagram of the base station network;

[0033] Figure 3 This is the distribution map of the base station and mobile station R2;

[0034] Figure 4 It is an error sequence diagram of positioning results of two methods (shortest path transfer method and the method provided by the present invention);

[0035] Figure 5 The figure is a sequence diagram of positioning satellites of two methods (the shortest path transmission method and the method provided by the present invention). DETAILED DESCRIPTION

[0036] In order to describe the technical solution of the above invention in more detail, specific embodiments are listed below to demonstrate the technical effects; it should be emphasized that these embodiments are used to illustrate the present invention but not to limit the scope of the present invention.

[0037] The overall adjustment method of the relative correction number of the network RTK master reference station provided by the present invention is as follows: Figure 1 As shown, the following steps are included:

[0038] Step 1: Read the data and construct a triangulated network, calculate the closure error of the triangulated network baseline error improvement number, determine whether the closure error has a gross error, and in response to the existence of a gross error, proceed to the next step; in response to the absence of a gross error, output the adjustment result. The closure error of the baseline error correction number of each side in the same triangle must theoretically be 0. Taking into account the existence of observation errors, the closure error should be within a certain minimum threshold range. Therefore, if the closure error of the triangulated network exceeds the limit, then the error correction number of at least one baseline in the triangulated network must be wrong.

[0039] Step 2: According to the basic principle of indirect adjustment, the baseline vector adjustment method is used to solve the correction number for a specified master station; according to the relationship between double difference and baseline transfer, the baseline vector error equation is established; based on the triangular relationship formed by the master station and the auxiliary station, the constraint conditions are obtained, and the overall adjustment solution of the relative error correction number is performed.

[0040] Step 3: Based on the overall adjustment solution results obtained in the second step, locate and repair the gross errors and output the adjustment results.

[0041] The present invention proposes a multi-baseline relative error correction number overall adjustment method centered on the master station. This method comprehensively considers the vector relationship of each baseline error correction number, the baseline closure error of the Delaunay triangulation network, and the interpolation relationship between stations, and realizes the one-time overall generation of the relative correction number of the master reference station in the network RTK.

[0042] In some embodiments, the baseline vector error equation is:

[0043]

[0044] Among them, L1 is the error correction number of each baseline in the base station triangulation network, It is the estimated value of the double difference relative error correction from the main station to other auxiliary stations. B1 is the coefficient matrix describing the linear relationship between the error correction of each baseline in the triangulation network and the relative error correction of the main station. V1 is the residual of the error correction.

[0045] by Figure 2 Taking the reference station network shown in the figure as an example, assuming that the designated master station is 1, for the current epoch k, reference satellite i and non-reference satellite j, the main matrices in the observation equation can be specifically expressed as follows:

[0046]

[0047] In some embodiments, the weight matrix P1 of the error correction number in the observation equation is set to a diagonal matrix, and each diagonal element is determined based on the closure error test result in the first step. Specifically, if a triangulated network passes the closure error test, the weights of the error correction numbers of each side in the triangle are set to 1.0; if a triangulated network fails the closure error test, the weights of the error correction numbers of all other sides except the common sides that pass the closure error test (if any) are set to 0.1; if a triangulated network does not undergo closure error test, the weights of the error correction numbers of all other sides except the common sides (if any) in the above two cases are set to 0.5.

[0048] In some embodiments, in order to further improve the accuracy of subsequent error correction, the present invention adds constraints. The constraints include:

[0049] If the master station is located in the triangle formed by the auxiliary stations, the linear interpolation method is used to obtain the corresponding interpolation coefficients and construct the error correction number interpolation equation, which is then used as the constraint equation and solved together with the above baseline vector relationship equation.

[0050] Specifically, for Figure 2 The base station network is first determined to be located in the triangle formed by auxiliary stations 2, 3, 5 and auxiliary stations 2, 3, 4. Based on the principle that the sum of the distances from the main station to each vertex of the triangle is the smallest, the triangle 2-3-5 is determined to be the triangle with the minimum sum of distances containing the main station 1. The interpolation equation is as follows:

[0051]

[0052] Where α is the coefficient of linear interpolation, and the first number before the comma in the subscript represents the station number to be interpolated. The weight of the interpolation equation is set to 0.1. Further, the error correction numbers in formula (3) are linearly transformed, and the constraint equations of the relative error correction numbers relative to the main reference station can be obtained through polynomial arrangement, as shown below:

[0053]

[0054] If the master station is not located in the triangle formed by the auxiliary stations, the three auxiliary stations closest to the master station are selected, and the interpolation coefficients are obtained by linear interpolation method to form the error correction interpolation equation, with the weight set to 0.01. It is assumed here that the three auxiliary stations have the same weight.

[0055] In some embodiments, the constraints further include:

[0056] Determine in turn whether each auxiliary station is located within the triangle formed by the main station and the remaining auxiliary stations.

[0057] If it is established, the error correction interpolation equation is obtained by interpolation between the main station and the two auxiliary stations forming a triangle, and the weight is set to 0.1;

[0058] Otherwise, two or three auxiliary stations closest to the auxiliary station are used to perform interpolation together with the main station 1, with a weight of 0.01, to obtain the interpolation equation of the error correction number.

[0059] according to Figure 2 The following constraint equation can be obtained for the base station network:

[0060]

[0061] In formula (5), the weights of each equation are 0.01, 0.01, 0.01, 0.1, and 0.01. Adding formulas (4) and (5) to formula (1), the final error equation and weight matrix are:

[0062]

[0063] P=diag(P1,0.1,0.01,0.01,0.01,0.1,0.01) (7)

[0064] By using the least square method to solve equation (6), we can obtain the estimated value of the relative error correction number relative to the master station after adjustment and its unit weighted mean error after verification, which are expressed as follows:

[0065]

[0066] Wherein, V and P are the baseline vector error equation and weight matrix respectively, n is the number of observation equations, and t is the number of parameters to be determined. In this embodiment, n=17, t=5.

[0067] In some embodiments, if n>t and If the error is greater than the first threshold value, in this embodiment, the first threshold value is 2 mm, the adjustment result is considered to be unreliable and a second adjustment is required; otherwise, the current adjustment result is considered to be reliable and the current adjustment result can be used as the final estimate of the unknown baseline correction number. The second adjustment process is iterated until the minimum unit weighted error of the ionospheric correction number is obtained. In some embodiments, when performing the overall adjustment solution of the relative error correction number, the ionospheric correction number and the geometric item correction number are calculated separately. The use of the adjustment method can ensure the consistency of the correction number of the entire network. At the same time, based on the observation value residual obtained by the adjustment, a baseline with poor or erroneous correction numbers can be found. By adjusting the observation vector for a second adjustment, a more reliable correction number is obtained, thereby assisting the ambiguity resolution of the baseline and correcting the erroneous ambiguity.

[0068] In order to test the performance of the overall adjustment method proposed in this application in calculating the correction of the main reference station, a large number of comparative analyses were conducted between this application and the traditional shortest path transfer method.

[0069] This application compares the performance differences of the two methods from multiple angles. First, the Bernese software is used to calculate the reference station coordinates, inter-reference station ambiguity, and mobile station coordinate error corrections in the example, which are used as reference standards. At the same time, GPS and BDS satellites with elevation angles above 15 degrees are selected for statistics. Select the designated main reference station, and generate the main reference station correction number according to the shortest path search method and the overall adjustment method. This application respectively counts the success rate of the two methods in generating network RTK error correction numbers and the error rate after successfully generating the correction number. Then, in order to further verify the impact of the generated correction number on the RTK positioning accuracy of the mobile station, a mobile station was selected in the example for RTK positioning solution. And the performance of the two methods is compared in terms of the average number of available satellites, the Ratio value of the ambiguity fixation, the plane positioning accuracy and the elevation positioning accuracy.

[0070] The test case uses data from 8 evenly distributed base stations and 1 mobile station. The station distribution is as follows: Figure 3 This application selected 24-hour data from the base station and the mobile station for analysis. The data time is from 0:00 on November 11, 2021 to 0:00 on November 12, 2021. The average station spacing between the base stations is 48.2 km.

[0071] During the experiment, the receiver and antenna type used are shown in Table 1 below:

[0072] Table 1 Receiver and antenna type information

[0073]

[0074] When processing the baseline of the base station network, the success rate of resolving the FSNS-GTCH baseline ambiguity is low. Figure 3 It is marked with a red baseline. When FSNS is selected as the main station, the correction numbers of all stations relative to FSNS can be obtained. The calculated baseline correction numbers are used to generate the correction numbers of the main reference station according to the shortest path search method and the overall adjustment method (this application), and the ambiguity between the reference station coordinates and the base station is calculated based on the Bernese software post-processing to calculate the corresponding correction numbers as a reference, and GPS and BDS satellites with altitude angles above 15 degrees are selected for statistics. The success rate of correction number generation of the two methods, as well as the error rate after the correction number is successfully generated, are statistically analyzed, and the statistical results are shown in Table 2 below:

[0075] Table 2 Success rate of different master reference station generation methods and error rate after generating corrections (FSNS as master station)

[0076]

[0077] From the success rate and error rate results in Table 2, it can be seen that when the shortest path search method is used to calculate the SDGT station correction, the success rate is low and the error rate is high. The reason is that when calculating the SDGT station correction, the path obtained by the shortest path transfer method is SDGT-GTCH-FSNS. The correction of the SDGT station can only be successfully calculated when the SDGT-GTCH baseline and the GTCH-FSNS baseline are successfully solved at the same time. The ambiguity of the SDGT-GTCH baseline has many periods of unsuccessful fixation and fixation errors, resulting in a low success rate and high error rate for the relative error correction of SDGT relative to the FSNS station. However, there are many other correct paths between SDGT and FSNS, such as SDGT-GMGT-SSGT-FSNS, SDGT-GTCH-SSGT-FSNS, etc. The overall adjustment method uses these baselines with successful ambiguity fixation, so the success rate and error rate of SDGT have not dropped significantly, and the success rate and error rate are 95.2% and 0.009% respectively. In summary, the average success rate and error rate of the shortest path transfer method are 90.9% and 1.01%, respectively, while the overall adjustment method further improves to 97.83% and 0.00%.

[0078] In order to further evaluate the effect of the overall adjustment method on the accuracy improvement of network RTK corrections, this application uses the error corrections generated by two methods to Figure 3 The mobile station R2 in the base station network coverage area is used for positioning calculation to verify the positioning accuracy of the algorithm at the mobile station. According to the precise reference coordinates of the mobile station R2, the positioning error sequences of the mobile station in the three directions of north N, east E, and sky U are obtained, such as Figure 4 shown.

[0079] from Figure 4 It can be seen that the positioning results calculated by the overall adjustment method have position errors in the N and E directions within 5 cm, and the U direction error within 10 cm. However, the positioning results of the shortest path transfer method have large deviations, and the error sequence has a large amplitude of jitter. The overall adjustment law shows a strong detection and repair capability, the error sequence change trend is relatively stable, and the reliability is higher.

[0080] This example also counts the number of visible positioning satellites of the Beidou system for the mobile station R2 during the entire observation period. The results of the visible satellite number sequence for RTK positioning using the two methods are as follows: Figure 5 shown.

[0081] from Figure 5It can be seen that during the experimental data observation time, the number of satellites in the overall adjustment method is greater than 13 in most periods, and a maximum of 19 Beidou satellites can be observed, and a minimum of 10 Beidou satellites can be observed. The number of satellites in the shortest path method is greater than 11 in most periods, and a maximum of 16 satellites can be observed, and a minimum of 8 satellites can be observed. The average number of positioning satellites in the overall adjustment method is significantly greater than that in the shortest path method, and the positioning solution result is more reliable.

[0082] Finally, the accuracy of the positioning results is statistically analyzed, as shown in Table 3.

[0083] Table 3. Error statistics of the mobile station R2 positioning results

[0084]

[0085] As can be seen from Table 3, the overall adjustment method has more average available satellites, and the ratio mean is greater than the shortest path transfer method, and the positioning accuracy and ambiguity fixation reliability are good. The positioning errors of the shortest path transfer method and the overall adjustment method are 3.54cm and 2.91cm respectively, and the positioning accuracy of the overall adjustment method is improved by about 17.8%. Therefore, the positioning performance of the overall adjustment method provided by the present invention is significantly better than the shortest path transfer method.

[0086] In summary, the overall adjustment method of the relative correction number of the network RTK master reference station provided by the present invention can obtain high-precision error correction numbers about the master reference station on the one hand, and on the other hand, through closure error inspection and adjustment calculation, the consistency and reliability of the error correction numbers of the whole network are guaranteed. Measured data are adopted to analyze and verify, and the result shows that, relative to the traditional shortest path search method, the overall adjustment calculation method proposed by the present invention has a success rate of more than 95% and an error rate of less than 0.01%, which is better than the shortest path search method as a whole, and particularly when the partial baseline solution is wrong or not successfully solved, the success rate is improved by more than 20%, and the error rate decreases by 5%. Through dynamic positioning test and analysis, it is shown that the positioning accuracy of the present invention is improved by about 17% compared with the shortest path transfer method, and has better stability and reliability.

[0087] Obviously, those skilled in the art can make various changes and modifications to the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the invention fall within the scope of the claims of the invention and their equivalents, the invention is also intended to include these modifications and variations.

Claims

1. A method for adjusting relative corrections of a network RTK master reference station, characterized in that: The steps include: Step 1: read the data and construct a triangulated network, calculate the closure error of the triangulated network baseline error improvement number, determine whether the closure error has a gross error, and in response to the presence of a gross error, proceed to the next step; in response to the absence of a gross error, output the adjustment result; Step 2: According to the indirect adjustment principle, the baseline vector adjustment method is used to solve the correction number for a specified master station; according to the relationship between double difference and baseline transfer, the baseline vector error equation is established; based on the triangle relationship formed by the master station and the auxiliary station, the constraint conditions are obtained, and the overall adjustment solution of the relative error correction number is performed; Step 3: Based on the overall adjustment solution results obtained in the second step, locate and repair the gross errors and output the adjustment results.

2. the overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 1, is characterized in that, The baseline vector error equation is: Among them, L1 is the error correction number of each baseline in the base station triangulation network, It is the estimated value of the double difference relative error correction from the main station to other auxiliary stations. B1 is the coefficient matrix describing the linear relationship between the error correction of each baseline in the triangulation network and the relative error correction of the main station. V1 is the residual of the error correction.

3. the overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 2, is characterized in that, The weight matrix P1 of the error correction number in the observation equation is set as a diagonal matrix, and each diagonal element is determined based on the closure error test result in the first step.

4. the overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 1, is characterized in that, The constraints include: If the master station is located in the triangle formed by the auxiliary stations, the linear interpolation method is used to obtain the corresponding interpolation coefficients and to construct the error correction number interpolation equation; If the master station is not located in the triangle formed by the auxiliary stations, the three auxiliary stations closest to the master station are selected, and the interpolation coefficients are obtained using the linear interpolation method to construct the error correction number interpolation equation.

5. The overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 4 is characterized in that, The constraints also include: Determine in turn whether each auxiliary station is located within the triangle formed by the main station and the remaining auxiliary stations. If it is established, the error correction interpolation equation is obtained by interpolating the main station and the two auxiliary stations forming a triangle; Otherwise, two or three auxiliary stations closest to the auxiliary station are used to perform interpolation together with the main station to obtain the interpolation equation of the error correction number.

6. The overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 5, characterized in that, In the second step, the overall adjustment solution method of the relative error correction number is: use the least squares method to calculate the estimated value of the relative error correction number relative to the master station after adjustment and its unit weighted mean error after verification.

7. The overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 6, characterized in that, The unit weight error for: Among them, V and P are the baseline vector error equation and weight matrix respectively, n is the number of observation equations, and t is the number of parameters to be determined.

8. The overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 7, characterized in that, If n>t and If it is greater than the first threshold, a second adjustment is performed; otherwise, the current adjustment result is used as the final estimate of the unknown baseline correction number.

9. The overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 8, characterized in that, The first threshold is 2 mm.

10. The overall adjustment method of the relative correction number of the network RTK master reference station as claimed in claim 1, characterized in that: When performing the overall adjustment solution of relative error corrections, the ionospheric corrections and geometric corrections are calculated separately.

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