Baseline constraint and quality weighting double-dynamic positioning partial ambiguity fixing method

Abstract

The invention provides a dual-dynamic positioning partial ambiguity fixing method based on baseline constraint and quality weighting, and relates to the technical field of satellite navigation positioning. According to the method, parameters of an existing RTK relative positioning function model are adjusted, error correction is introduced by adding a difference process to reduce positioning errors caused by unknown accurate position information of a reference station, and a double-dynamic-carrier relative positioning function resolving model is established; removing the ambiguity parameter with the maximum deviation through baseline constraint, and reconstructing a double-difference partial ambiguity parameter; high weights are given to ambiguity parameters of high-quality frequency point observation data, the weights of ambiguity parameters of low-quality or discontinuous frequency point data are reduced, and re-optimized partial ambiguity is obtained; ambiguity fixing and checking are achieved on the optimized partial ambiguity through an improved model driving and data driving fixing strategy, then a high-precision position solution is obtained, and a positioning result with higher precision and better robustness is provided for relative positioning of the double-dynamic carrier.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite navigation and positioning, and particularly relates to a dual-dynamic positioning partial ambiguity fixing method with baseline constraint and quality weighting. Background Art

[0002] In recent years, with the rapid development of the Beidou navigation system, its advantages in positioning accuracy and coverage in the field have gradually emerged. In the high-precision applications of the Global Navigation Satellite System (GNSS), the carrier-phase double-difference technology with a static reference station is widely used in engineering surveying and setting out, petroleum geophysical prospecting surveying, precision approach of aircraft, etc.; the carrier-phase differential technology can achieve centimeter-level relative positioning accuracy, but it requires that the reference station serving as the reference source of differential information is fixed, so that the system coverage and application are restricted. In some fields such as carrier landing of shipborne aircraft, in-air refueling of aircraft, formation flight of aircraft, satellite-to-satellite orbit determination, relative positioning of moving vehicles, deformation monitoring of large mobile carriers, and space docking of aircraft, it is necessary to accurately determine the relative position between two moving carriers. At this time, it is difficult to establish a fixed reference station, and the traditional Real-Time Kinematic (RTK) method using a fixed reference station no longer meets the positioning requirements. The mathematical model of the fixed reference station positioning mode will cause serious errors to the results, so the traditional RTK cannot meet the needs of dynamic users. Therefore, in the scenario of dual-dynamic carriers where both the mobile station and the reference station are dynamic, it is necessary to improve the positioning function solution model and reduce the positioning error caused by the unknown accurate position information of the reference station. At the same time, RTK relative positioning is restricted by the fixing of the carrier-phase integer ambiguity. Correct ambiguity fixing can achieve high-precision positioning, while incorrect ambiguity fixing may lead to large errors in the estimation results.

[0003] Currently, the research on ambiguity fixing mainly focuses on starting from reducing bad observation data to improve the ambiguity fixing effect and positioning accuracy. It is difficult to reduce the complexity of ambiguity resolution by processing rapidly changing ambiguities at the observation data level, and it is difficult to fix all high-dimensional integer ambiguity parameters. In this case, the Partial Ambiguity Resolution (PAR) strategy using data-driven and model-driven strategies can select some ambiguities with excellent quality from high-dimensional integer ambiguities for fixing, reducing the calculation dimension. Among them, the model-driven only considers the theoretical accuracy of the observed values, that is, only uses the prior model to select some ambiguities, lacking the consideration of real data, while the data-driven cannot provide an evaluation of the strength of the observed model. The above methods have all carried out certain innovative work in related aspects of ambiguity fixing, but they do not consider baseline data.

[0004] Therefore, based on baseline constraint and quality weight determination, the present invention proposes a method for fixing partial ambiguities driven by data plus model for dual-dynamic carriers, which eliminates the ambiguity parameters with the largest deviation through baseline constraint and reconstructs the double-difference partial ambiguity parameters. At the same time, higher weights are assigned to the ambiguity parameters of high-quality frequency-point observation data, and the weights of the ambiguity parameters of lower-quality or discontinuous frequency-point data are reduced to obtain re-optimized partial ambiguities. Then, through the improved model-driven and data-driven fixing strategy, the selected partial ambiguities are fixed and verified, and then a high-precision position solution is obtained, providing a more accurate and robust positioning result for the relative positioning of dual-dynamic carriers. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a method for fixing partial ambiguities in dual-dynamic positioning with baseline constraint and quality weight determination aiming at the deficiencies of the above-mentioned prior art, improving the accuracy and reliability of ambiguity fixing, and further improving the positioning accuracy and stability, so as to provide guarantee for realizing high-precision relative positioning of dual-dynamic carriers.

[0006] To solve the above technical problem, the technical solution adopted by the present invention is: a method for fixing partial ambiguities in dual-dynamic positioning with baseline constraint and quality weight determination, which eliminates the ambiguity parameters with the largest deviation through baseline constraint and reconstructs the double-difference partial ambiguity parameters; assigns higher weights to the ambiguity parameters of high-quality frequency-point observation data, and reduces the weights of the ambiguity parameters of lower-quality or discontinuous frequency-point data to obtain re-optimized partial ambiguities; then, through the improved model-driven and data-driven fixing strategy, the selected partial ambiguities are fixed and verified, and then a high-precision position solution is obtained, providing a more accurate and robust positioning result for the relative positioning of dual-dynamic carriers; including the following steps:

[0007] Step 1: Adjust the parameters of the existing RTK relative positioning function model, introduce error correction through adding the differential process to reduce the positioning error caused by the unknown accurate position information of the reference station, and establish a relative positioning function solution model for dual-dynamic carriers;

[0008] Establish GNSS undifferenced observation equations, single-difference observation equations between the mobile station and the reference station, and double-difference observation equations between the mobile station and the reference station for the satellite;

[0009] During the double-difference process, the receiver clock error is further eliminated, and at the same time, the baseline deviation of each positioning is obtained by taking the difference between two baseline vectors and ;

[0010]

[0011] wherein, are the distance vector values from satellite s to mobile station receiver terminal r and reference station receiver terminal b and subtracting to obtain the baseline vector; are the distance vector values from satellite k to mobile station receiver terminal r and reference station receiver terminal b and the baseline vector obtained by subtraction; is the carrier phase observation of receiver terminal r for satellite s at frequency i; λ i is the wavelength of the i-th frequency of the satellite; is the carrier phase observation of reference station receiver terminal b for satellite s at frequency i;

[0012] Optimize the RTK relative positioning function model into a double-dynamic carrier relative positioning function model with mutual differencing between two terminals, and at the same time obtain the baseline deviation after mutual differencing between mobile station receiver terminal r and reference station receiver terminal b, as follows:

[0013]

[0014] where, is the baseline deviation of mobile station receiver terminal r at frequency i after double-differencing, calculated with reference station receiver terminal b as the reference; and is the baseline vector calculated from satellites s and k at frequency i with reference station receiver terminal b as the reference; is the baseline deviation of reference station receiver terminal b at frequency i after double-differencing, calculated with mobile station receiver terminal r as the reference; and is the baseline vector calculated from satellites s and k at frequency i with mobile station receiver terminal r as the reference;

[0015] For the baseline deviation obtained after mutual differencing between mobile station receiver terminal r and reference station receiver terminal b, take its average value as the baseline deviation of the current epoch to further reduce the influence of positioning error, then the baseline deviation value of this epoch is:

[0016]

[0017] Step 2: Obtain the original observation data of the receiver terminal, and use the double-dynamic carrier relative positioning function model to perform preliminary solution on the original observation data to obtain the mutual double-difference result between two dynamic carriers;

[0018] Step 3: Apply baseline constraints to the current epoch to preferentially select single-difference partial ambiguities, that is, constrain the baseline vector by baseline deviation, screen out the maximum baseline deviation value for each epoch, and then find the corresponding baseline vector. Finally, eliminate the ambiguity parameters and satellites participating in the solution for the corresponding epoch to realize the recombination of double-difference partial ambiguities. At the same time, adjust the weights of the observables of high-quality data corresponding to the GNSS frequency points through the weighting of the observation data, increase the weight of high-quality data, obtain new double-difference ambiguity parameters, and realize data-driven selection of partial ambiguities;

[0019] Step 3.1: Preferentially select single-difference partial ambiguities through baseline constraints to obtain single-difference partial ambiguities without the maximum deviation, that is, eliminate the maximum single-difference value and its corresponding satellite, and then recombine the double-difference partial ambiguities to reduce the maximum deviation of the baseline solution;

[0020] Step 3.2: Assign weights to the data of different frequency points according to the observation quality to obtain re-optimized double-difference partial ambiguities;

[0021] Step 3.2.1: Establish an observation weighting scheme combining elevation and carrier-to-noise ratio (CNR) value;

[0022] Step 3.2.2: Based on Step 3.2.1, establish a Hopular-based weighting scheme through the Hopular method. This weighting scheme includes the observation variances of NLOS errors in pseudorange and carrier phase measurements, and also uses the carrier-to-noise ratio value and the loss-of-lock indicator (LLI) to provide additional constraints to calculate the GNSS observation variances;

[0023] Step 4: Perform Kalman filtering on the preliminary solution results obtained by processing the original observation data acquired in Step 2 to obtain the floating-point solutions of the position and ambiguity parameters and their corresponding variance-covariance matrices, perform improved model-driven, and then combine the ratio test of the reliability of the ambiguity fixed solution in data-driven to realize the fixation of partial ambiguities.

[0024] Step 4.1: Fix the re-optimized partial ambiguities through the LAMBDA algorithm; among them, add the SRC index method in the model-driven part, conduct quantitative evaluation through statistical tests to construct the success rate, verify whether the fixation success rate of the candidate partial ambiguities meets the threshold requirements, and thus decide whether to accept the fixed solution of the partial ambiguities to improve the reliability of the solution results;

[0025] Step 4.2: In the data-driven part, the ratio test for judging the reliability ratio of the ambiguity fixed solution is further carried out by combining the actual measurement data of the mobile station and the reference station receivers to verify the fixing rate of the ambiguity and the positioning accuracy; during the fixing process, the satellites for which the ambiguity is fixed in the next epoch are appropriately adjusted according to the magnitude of the ratio detection value between epochs and the ambiguity fixing status, and the gross positioning errors are eliminated.

[0026] Step 4.2.1: After the integer bootstrap success rate, the ratio test is carried out on the partial ambiguity solution results calculated by the model-driven part by combining the actual measurement data.

[0027] During the ambiguity search process, the quadratic form s[0] of the sub-optimal solution residual and the quadratic form s[1] of the optimal solution residual in the partial ambiguity fixed solutions are obtained, as well as the ambiguity fixing success rate; when s[0] / s[1] is greater than or equal to the threshold g of the ratio test, it indicates that the current ambiguity fixing meets the accuracy requirements; otherwise, the ambiguity parameters are eliminated in the order of conditional variance, and the success rate and the quadratic form s[0] of the sub-optimal solution residual and the quadratic form s[1] of the optimal solution residual in the fixed solution are recalculated until s[0] / s[1] is greater than or equal to g.

[0028] Step 4.2.2: If the result of the partial ambiguity solution in the current epoch fails the ratio test, the partial ambiguities with small variances are selected and the gross positioning errors are eliminated.

[0029] Step 4.2.3: If the ratio value of the partial ambiguity solution result in the current epoch is ratio1 and the ratio value of the previous epoch is pre_ratio, when pre_ratio is greater than or equal to g and the ratio value ratio1 of the current epoch is less than g, but the ambiguity in the current epoch cannot be fixed; or pre_ratio is greater than twice ratio1, in these two states, the satellites newly added in the current epoch compared with the previous epoch are eliminated, and the preferred partial ambiguity parameters are newly constructed.

[0030] Suppose there are n visible satellites after the initial screening in a certain epoch, which are (S 1 , S 2 , …, S n ), and the reference star is set as S n , then n - 1 single-difference ambiguities can be formed, which are (T 1 , T 2 , …, T n-1 ); if the number of ambiguities with single-difference ambiguity variances less than the threshold is less than the set value, the algorithm exits without ambiguity fixing, otherwise all the ambiguities are fixed after preprocessing.

[0031] Screen each of the n - 1 satellites except the reference satellite one by one. After removing the newly added satellite, n - 2 partial ambiguity groups are formed respectively, namely (T 1 , T 2 , …, T n-2 ); perform partial ambiguity fixing on these n - 2 partial ambiguity groups, and calculate the ratio values (R 1 , R 2 , …, R n-2 ) and the integer bootstrap success rates (P 1 , P 2 , …, P n-2 ) corresponding to the partial ambiguity groups (T IB，1 , T IB，2 , …, T IB,n-2 ). Sort the ratio values of each partial ambiguity group; if the newly added satellite has stable observation values for 20 consecutive epochs, it participates in the ambiguity fixing of the next process; subsequently, perform model - driven partial ambiguity fixing again to obtain a new ratio value ratio2. When ratio2 is greater than or equal to g, the partial fixed solution is obtained, otherwise, the ambiguity float solution will continue to be used for positioning calculation;

[0032] Step 4.2.4: Check the ratio value and success rate of the partial ambiguity group with the largest ratio value. If the test conditions are not met, re - execute Step 4.1 until the test can pass. If the conditions are met, fix the partial ambiguity at this time;

[0033] Step 4.2.5: Apply variance constraints to the fixed partial or all ambiguity fixed solutions to re - estimate other ambiguities and obtain their variance - covariance matrix. Re - execute Steps 4.2.1 - 4.2.4 until there are ambiguities that cannot be fixed among the remaining ambiguities or the number of ambiguities fixed as integers is less than the set value, then end;

[0034] After the solution is completed, the double - difference partial ambiguities at this time will be brought back to the single - difference ambiguities, and then the integer solution of the cycle ambiguity is obtained.

[0035] The beneficial effects of adopting the above technical solutions are as follows: The double - dynamic positioning partial ambiguity fixing method with baseline constraint and quality - weighted variance provided by the present invention is based on the ambiguity fixing technology, relying on the global satellite navigation system, combined with the LAMBDA (Least Square Ambiguity Decorrelation Adjustment) algorithm. By constructing a partial ambiguity parameter subset through baseline constraint and data quality - weighted variance, and optimizing the fixed strategies of model - driven and data - driven, it improves the accuracy and reliability of ambiguity fixing, and further improves the positioning accuracy and stability, providing a guarantee for realizing high - precision relative positioning of double - dynamic carriers. Description of the Drawings

[0036] Figure 1 It is a schematic diagram of single-difference carrier phase provided by an embodiment of the present invention;

[0037] Figure 2 It is a schematic diagram of double-difference carrier phase provided by an embodiment of the present invention;

[0038] Figure 3 It is a flowchart of a partial ambiguity fixing strategy driven by data plus model of baseline constraint and data weight determination. Detailed Embodiment

[0039] The following combines the drawings and embodiments to further describe in detail the specific implementation manners of the present invention. The following embodiments are used to illustrate the present invention, but are not used to limit the scope of the present invention.

[0040] In this embodiment, a double-dynamic positioning partial ambiguity fixing method with baseline constraint and quality weight determination includes the following steps:

[0041] Step 1: Adjust the existing RTK relative positioning model parameters, and reduce the positioning error caused by the unknown accurate position information of the reference station by introducing error correction in the differential process, and establish a double-dynamic carrier relative positioning function solution model;

[0042] Step 1.1: Establish a GNSS undifferenced observation equation;

[0043] The GNSS undifferenced observation equation describes the functional relationship between the original GNSS receiver observations and each unknown parameter; at a certain moment, the observation of satellite s by mobile station receiver terminal r at frequency i is expressed as:

[0044]

[0045] Wherein, is the pseudorange observation of receiver terminal r relative to satellite s at frequency i, is the carrier phase observation of receiver terminal r for satellite s at frequency i; λ i is the wavelength of the i-th frequency of the satellite; is the geometric distance between satellite s and receiver terminal r; c is the speed of light; dt r and dt s are the clock biases of receiver terminal r and satellite s respectively; is the ionospheric delay between satellite s and receiver terminal r, and its magnitude is related to frequency i; is the tropospheric delay between satellite s and receiver terminal r; N r,iis the carrier phase integer ambiguity of the receiver terminal r at frequency i; ε and ξ are the pseudorange and carrier phase measurement errors respectively.

[0046] Step 1.2: Establish the single-difference observation equation between the mobile station and the reference station;

[0047] Suppose the receiver terminal r of the mobile station and the receiver terminal b of the reference station observe the same satellite s simultaneously, and then perform a single-difference operation on the observations of satellite s by the two receiver terminals. The single-difference (SD) operation is defined by defined as is the single-difference operator, and the single-difference schematic diagram is as shown in Figure 1 shown. The distance vector values and from satellite s to the receiver terminal r of the mobile station and the receiver terminal b of the reference station are subtracted to obtain the baseline vector i.e., the distance vector between the receiver terminal r of the mobile station and the receiver terminal b of the reference station. is the carrier phase observation of the reference station receiver terminal b for satellite s at frequency i; the observation equation of the single-difference between stations is:

[0048]

[0049] where is the pseudorange single-difference observation of satellite s at frequency i observed by the receiver terminal r and the receiver terminal b of the reference station, is the carrier phase single-difference observation of satellite s at frequency i observed by the receiver terminal r and the receiver terminal b of the reference station, is the geometric distance difference between the receiver terminal r of the mobile station, the receiver terminal b of the reference station and satellite s; is the clock difference after the single-difference operation of the receiver terminal r of the mobile station and the receiver terminal b of the reference station; is the ionospheric delay error between the receiver terminal r of the mobile station, the receiver terminal b of the reference station and satellite s; is the tropospheric delay error between the receiver terminal r of the mobile station, the receiver terminal b of the reference station and satellite s; is the single-difference carrier phase integer ambiguity between the receiver terminal r of the mobile station and the receiver terminal b of the reference station at frequency i; and are the noise errors of the pseudorange observation and the carrier phase observation after the single-difference operation respectively.

[0050] After the single-difference operation, the influence of the satellite clock difference can be eliminated. In the short baseline range, the related errors of the ionospheric delay I and the tropospheric delay T will be effectively eliminated after the single-difference operation, and then the single-difference observation equation between stations is simplified to:

[0051]

[0052] Step 1.3: Establish the station-satellite double difference observation equation between the mobile station and the reference station;

[0053] On the basis of the inter-station single difference, another common-view satellite k is introduced and regarded as a reference satellite. The mobile station receiver terminal r and the reference station receiver terminal b simultaneously observe satellites s and k, and make an inter-satellite single difference between the two satellites to form a station-satellite double difference (DD) observation value. The double difference process is: Definition, where is a double difference operator, and its geometric relationship is as follows Figure 2 As shown. The double difference observation equation is:

[0054]

[0055] in, is the pseudo-range station-satellite double difference observation of satellite s and satellite k at frequency i observed by mobile station receiver terminal r and reference station receiver terminal b; is the carrier phase station-satellite double difference observation of satellite s and satellite k at frequency i observed by mobile station receiver terminal r and reference station receiver terminal b; is the geometric distance difference between the mobile station receiver terminal r and the reference station receiver terminal b and the satellite s and the satellite k; is the carrier phase station-satellite double difference integer ambiguity of the mobile station receiver terminal r and the reference station receiver terminal b on frequency i; and They are the noise errors of the pseudorange observation and the carrier phase observation after the double difference process.

[0056] The receiver clock error is further eliminated in the double difference process. and Subtract and get the baseline deviation of each positioning

[0057]

[0058] in, is the distance vector from satellite k to mobile station receiver terminal r and reference station receiver terminal b and Subtract and get the baseline vector Baseline vector and double difference ambiguity It is an unknown quantity and can be obtained by initially solving the mobile station coordinates through the least squares method or filtering.

[0059] Step 1.4: Establish a relative positioning function model for dual dynamic carriers;

[0060] When the relevant position information of the reference station receiver terminal b is known and used as a reference for differential processing, the baseline deviation is mainly affected by the single-point positioning error of the mobile station receiver terminal r. In the scenario of dual dynamic carriers, the true position information of the reference station receiver terminal b is unknown, and the single-point positioning result of each epoch is temporarily used to approximate the true value. At this time, the baseline deviation will be affected by the single-point positioning error of the mobile station receiver terminal r and the single-point positioning error of the reference station receiver terminal b. Therefore, it is necessary to optimize the RTK relative positioning function model (the double-difference observation equation in Step 1.3) into a relative positioning function model for dual dynamic carriers with mutual differential of the two terminals, and at the same time obtain the baseline deviation after mutual differential of the mobile station receiver terminal r and the reference station receiver terminal b, as shown in the following formula:

[0061]

[0062] where, is based on the reference station receiver terminal b as a reference, and calculates the baseline deviation of the mobile station receiver terminal r after double-difference processing at frequency i; and are the baseline vectors calculated from satellites s and k at frequency i based on the reference station receiver terminal b as a reference; is based on the mobile station receiver terminal r as a reference, and calculates the baseline deviation of the reference station receiver terminal b after double-difference processing at frequency i; and are the baseline vectors calculated from satellites s and k at frequency i based on the mobile station receiver terminal r as a reference;

[0063] For the baseline deviation obtained after mutual differential of the mobile station receiver terminal r and the reference station receiver terminal b, take its average value as the baseline deviation of the current epoch to further reduce the influence of positioning error. Then the baseline deviation value of this epoch is:

[0064]

[0065] Through this optimized relative positioning function model for dual dynamic carriers, the dual dynamic carriers can synchronously obtain the relevant information of the carriers, and reduce the unnecessary errors caused by the unknown information of the reference station.

[0066] Step 2: Obtain the original observation data of the receiver terminal;

[0067] Using two Beidou navigation receiver terminals to collect the observed navigation messages in a moving state as the original observed data, and combining with the double-dynamic carrier relative positioning function model in Step 1, the original observed data is quickly and preliminarily solved through Step 1 to obtain the mutual double-difference results between the two dynamic carriers, preparing for further solution.

[0068] Step 3: Optimize the single-difference partial ambiguity for the current epoch by applying baseline constraints, that is, through the baseline deviation given in Step 1.3 constrain the baseline vector to screen out the maximum baseline deviation value for each epoch, and then find the corresponding baseline vector. Finally, eliminate the ambiguity parameters and satellites participating in the solution for the corresponding epoch to realize the recombination of the double-difference partial ambiguity. At the same time, through the weight determination of the observed data, adjust the weights of the observables of the high-quality data (data with high elevation angle, high carrier-to-noise ratio or high continuity) corresponding to the GNSS frequency points, improve the weights of the high-quality data, and obtain new double-difference ambiguity parameters to realize data-driven selection of partial ambiguity;

[0069] Step 3.1: Optimize the single-difference partial ambiguity through baseline constraints to obtain the single-difference partial ambiguity without the maximum deviation, that is, eliminate the maximum single-difference value and its corresponding satellite, and then recombine the double-difference partial ambiguity to reduce the maximum deviation of the baseline solution;

[0070] The baseline deviation reflects to a certain extent the deviation of the single-difference baseline , that is, the deviation of the preliminary positioning solution. If the baseline deviation is too large, it means that the deviation of the positioning solution of the corresponding satellite is too large, that is, the accuracy of the single-difference ambiguity parameter is too low, resulting in difficulty in fixing the ambiguity parameter of this satellite. Therefore, the method of eliminating this single-difference ambiguity parameter from the ambiguity parameter set and reconstructing the double-difference ambiguity parameter can be adopted for optimization;

[0071] Step 3.2: Assign weights to the data of different frequency points according to the quality of the observed values to obtain the re-optimized double-difference partial ambiguity;

[0072] Assign higher weights to the ambiguity parameters of the high-quality frequency point observed data, and reduce the weights of the ambiguity parameters of the lower-quality or discontinuous frequency point data to obtain the re-optimized partial ambiguity. The optimized partial ambiguity can effectively fix the floating-point partial ambiguity as an integer solution with higher certainty in the subsequent processing, and then converge the state estimation of the baseline coordinates to a higher accuracy through Kalman filtering. The specific steps for the selection and assignment of weights are as follows:

[0073] Step 3.2.1: Establish an observation weighting scheme combining elevation and carrier-to-noise density ratio (CNR) value;

[0074] Traditional observation value weighting schemes are established using the elevation or carrier-to-noise ratio of satellites. The deviation values of the elevation-based weighting scheme are as follows:

[0075]

[0076] Wherein, And Are the standard deviations of the pseudorange observation value and the carrier phase observation value weighted by elevation respectively; α and β are error factors, which are assigned empirical values of 0.003 in the present invention; γ is the code / phase error ratio, and elev is the elevation angle of the satellite to the receiver.

[0077] The deviation values of the carrier-to-noise ratio-based weighting scheme are as follows:

[0078]

[0079] Wherein, And Are the standard deviations of the pseudorange observation value and the carrier phase observation value weighted by the carrier-to-noise ratio respectively; C is a factor composed of the carrier phase noise bandwidth and the conversion term from cycle 2 to square millimeter. In the present invention, C is set to the empirical value 1. CNR is the carrier-to-noise ratio of the GNSS signal, in units of dB-Hz.

[0080] The error factor for the carrier phase observation value combining elevation and carrier-to-noise ratio is:

[0081]

[0082] Wherein, And Are the standard deviations of the pseudorange observation value and the carrier phase observation value weighted by the carrier-to-noise ratio, which are established by combining elevation and carrier-to-noise ratio respectively; K is an adjustment factor for the signal type, which is set to different values according to whether it is a line-of-sight signal; γ is the code / phase error ratio, elev is the elevation angle of the satellite to the receiver; CNR is the carrier-to-noise ratio of the GNSS signal.

[0083] The calculation formula of the error factor for the carrier phase observation value combining elevation and carrier-to-noise ratio describes the weighting model considering both elevation and carrier-to-noise ratio. It can be seen that the variance of the observation value depends on elevation and carrier-to-noise ratio.

[0084] Compared with the elevation-based method only, the elevation and carrier-to-noise ratio combined method also incorporates the carrier-to-noise ratio in the weight determination. In the case of high altitude and low carrier-to-noise ratio, this method will provide a greater observation variance than the elevation-based method only. Similarly, this method utilizes the elevation of the satellite to outperform the carrier-to-noise ratio-only weighting scheme and can provide a smaller observation variance than the carrier-to-noise ratio-only method in the case of high altitude and low carrier-to-noise ratio. For line-of-sight (LOS) signals, the K value is 1, while for non-line-of-sight (NLOS) signals, the K value is represented by other values. The value of γ is set to the empirical value of the code / phase error ratio, which is 0.01.

[0085] Step 3.2.2: Based on Step 3.2.1, establish a Hopular-based weighting scheme through the Hopular method. Different from the above traditional methods, this scheme incorporates the observation variances of NLOS errors in pseudorange and carrier phase measurements and also utilizes the carrier-to-noise ratio value and the loss of lock indicator (LLI) to provide additional constraints to calculate the GNSS observation variance as shown in the following formula:

[0086]

[0087] Where, and are the variances of the pseudorange observation value and the carrier phase observation value respectively; and are the observation variances of the NLOS errors of the pseudorange observation value and the carrier phase observation value respectively; and are the standard deviations established by weighting the pseudorange observation value and the carrier phase observation value through elevation respectively;

[0088] Since the elevation-based weighting model can achieve good performance in open areas, its error can be regarded as the LOS error. The calculation of the observation variances of the NLOS errors of the pseudorange observation value and the carrier phase observation value is as follows:

[0089]

[0090] Where, ε P and ε L are the NLOS errors of the pseudorange observation value and the carrier phase observation value respectively, with the unit of m 2 , which is set to 1m in this embodiment 2 ; e is the Euler number; E is the adaptively adjusted exponential factor, and P NLOS is the predicted probability of the NLOS signal. To prevent over-weighting of the observation value, the Euler number e is selected to control the growth rate of the exponential function. The predicted probability P of the NLOS signal NLOSObtained by the GNSS signal classifier of the Hopular method. At the same time, the value of the exponentially adjusted exponential factor E in the above formula can linearly affect the exponential function. Therefore, accurately solving the value of the exponential factor can ensure the overall quality of the variance calculation.

[0091] The value of the exponential factor is further adjusted by the LLI constraint, as shown in the following formula:

[0092]

[0093] In this embodiment, when the CNR value of the GNSS signal is higher than 45 dB-Hz, the observation value can be regarded as passing the LOS threshold. Therefore, by setting the exponential factor E to 0, the NLOS error can be excluded in the weighting scheme. When the CNR value drops below 35 dB-Hz or the LLI indicates a cycle slip, the exponential factor E is increased to 9.5 to reduce the weight of the measurement value. By default, the exponential factor will be 1.1 for predicting the variance of the NLOS probability calculation.

[0094] Through the above process, the weight of the low-quality observation signal in the solution process can be reduced, the influence of the related error can be minimized, and the data quality of the partial ambiguity parameters corresponding to the carrier phase observation value at this frequency can be further guaranteed, thus ensuring the correct solution of the ambiguity parameters in the next step.

[0095] Step 4: After performing Kalman filtering on the preliminary solution results obtained by processing the original observation data acquired in Step 2, the floating-point solutions of the position and ambiguity parameters and their corresponding variance-covariance matrices are obtained. Then, an improved model-driven approach is carried out, and combined with the ratio test of the reliability of the ambiguity fixed solution in the data-driven method, partial ambiguity fixing is achieved. The specific solution process is as Figure 3 shown.

[0096] Step 4.1: Fixing the partially optimized ambiguities through the LAMBDA algorithm; among them, the SRC index method is added to the model-driven part, and the success rate is constructed through statistical tests for quantitative evaluation to verify whether the success rate of fixing the candidate partially optimized ambiguities meets the threshold requirements, so as to determine whether to accept the fixed solution of the partially optimized ambiguities to improve the reliability of the solution results. The main calculation process is as follows:

[0097] The GNSS double-difference observation equation is rewritten as a linear observation equation, as shown in the following formula:

[0098] y = Bb + Aa + ε

[0099] Among them, y is the residual vector of double-difference carrier phase measurement; b is the vector containing the baseline coordinate increment; a represents the double-difference ambiguity (abbreviated as DD ambiguity) constrained by the baseline; B is the design matrix of baseline coordinates; A is the design matrix corresponding to the double-difference ambiguity; ε is the vector of measurement noise.

[0100] The preliminary solution obtained by processing the original observation data acquired in step 2 is processed by Kalman filtering to initially obtain the floating-point solutions of the position and ambiguity parameters, i.e., the baseline coordinates and the floating-point solutions of some of the double-difference ambiguity floating-point solutions constrained by the baseline as well as the variance-covariance (VC) combination matrix of the floating-point solutions of some of the double-difference ambiguity floating-point solutions:

[0101]

[0102] Among them, is the variance matrix of is and the covariance matrix of, used to statistically analyze the correlation between the two; is and the covariance matrix between, and satisfies is the variance matrix of

[0103] Due to the integer nature of the ambiguity, discrete search must be performed on the integers. The Z-transform (integer Gauss transform) in LAMBDA is used to remove the correlation between the ambiguities to reduce the size of the search space. At the same time, the conditional variance sorting method is used to transform the variance-covariance matrix of some of the double-difference ambiguity floating-point solutions to obtain the floating-point solution, variance-covariance matrix, and conditional variance after reducing the correlation;

[0104] The Z-transform starts from the LDL decomposition of the covariance matrix of the double-difference ambiguity floating-point solution, as shown in the following formula

[0105]

[0106] In the formula, is the covariance matrix of the double-difference ambiguity floating-point solution after the Z-transform, and are both symmetric positive definite matrices, L is a lower triangular matrix, D is a positive diagonal matrix, from the symmetric positive definite covariance It is decomposed; the matrix D can be used as a metric for the variance of the floating-point ambiguity after decorrelation. The Z-transform matrix Z is an integer approximation of L. All elements in the Z matrix are integers, and the absolute value of the determinant is equal to 1. Then Z is applied to the n-dimensional partial double-difference ambiguity floating-point solution partial ambiguity for decorrelation, as shown in the following formula:

[0107]

[0108] where is the double-difference partial ambiguity after Z-transform, is the fixed double-difference partial ambiguity, is the original fixed double-difference partial ambiguity. Next, for the integer bootstrap technique is used for recursive conditional rounding

[0109]

[0110] where [·] represents the rounding operator, the subscript m represents the m-th ambiguity in the Z-transform partial ambiguity, and I = 1, 2, …, m - 1 is the number of previously rounded partial ambiguities in the above formula; represents the constraint of the latter ambiguity by the previous fixed ambiguity parameter ; represents the variance of the m-th ambiguity parameter; σ m,j The terms are the elements of matrices L and D generated by LDL decomposition. The specific results of the matrices are:

[0111]

[0112] Then an integer search is performed in the decorrelated space to minimize the objective function of the optimal ambiguity solution :

[0113]

[0114] When the best candidate ambiguity can no longer be improved, a fixed success rate test is performed. Only when passing the SRC index test, the candidate ambiguity is fixed as an integer:

[0115]

[0116] In the formula, P ILS is the fixation rate of the LAMBDA algorithm; P IB is the integer bootstrap success rate, generally taken as 0.995; Φ(·) is the cumulative distribution function of the standard Gaussian normal distribution; d i′ represents the i'-th diagonal element of matrix D.

[0117] In the initial partial floating-point double-difference partial ambiguity, the more ambiguity parameters are included, the lower the success rate. Since the calculation of the success rate does not involve the true value, but the prior information of the initial variance.

[0118] Step 4.2: Since the model-driven approach lacks consideration of real data, in the data-driven part, the ratio test that combines the actual measurement data of the rover and reference station receivers to judge the reliability ratio of the ambiguity fixed solution further verifies the fixation rate of the ambiguity and the accuracy of positioning; during the fixation process, the satellites for which the ambiguity is fixed in the next epoch are appropriately adjusted in combination with the magnitude of the ratio detection value between epochs and the ambiguity fixed state, and the gross positioning errors are eliminated. The specific processing process is as Figure 3 shown in the data-driven part.

[0119] Step 4.2.1: After the integer bootstrap success rate, the ratio test is performed on the partial ambiguity solution results calculated in the model-driven part in combination with the actual measurement data. The definition of the ratio test is as follows:

[0120]

[0121] where, is the sub-optimal solution in the partial ambiguity fixed solution, is the optimal solution in the partial ambiguity fixed solution. The ratio test uses the ratio of the residual quadratic forms of the sub-optimal solution s[0] and the optimal solution s[1] of the fixed solution as the test statistic. The larger the ratio value, the higher the accuracy of the obtained fixed solution. The threshold of the ratio test is g, and generally the value of g is 3.

[0122] During the ambiguity search process, the residual quadratic form s[0] of the sub-optimal solution, the residual quadratic form s[1] of the optimal solution, and the ambiguity fixation success rate in the partial ambiguity fixed solution are obtained. When s[0] / s[1] is greater than or equal to g, it indicates that the current ambiguity fixation meets the accuracy requirements. Otherwise, the ambiguity parameters are eliminated in the order of the conditional variance, and the success rate and the residual quadratic form s[0] of the sub-optimal solution and the residual quadratic form s[1] of the optimal solution in the fixed solution are recalculated until s[0] / s[1] is greater than or equal to g.

[0123] Step 4.2.2: If the result of the partial ambiguity solution in the current epoch fails the ratio test, the partial ambiguities with small variances are screened, and the gross positioning errors are eliminated, that is, the mean value of the variances corresponding to the floating-point solutions of the baseline coordinates is calculated. When the mean value is greater than the threshold of 0.1, it indicates that the current positioning error is large and it is eliminated.

[0124] Step 4.2.3: If the ratio value of the partial ambiguity resolution result of the current epoch is ratio1, and the ratio value of the previous epoch is pre_ratio, when pre_ratio is greater than or equal to g and the ratio value ratio1 of the current epoch is less than g, but the ambiguities of the current epoch cannot be fixed; or pre_ratio is greater than twice ratio1. In these two states, the satellites newly added in the current epoch compared to the previous epoch (the satellites and corresponding frequency points that reached the fixed state in the previous epoch) are excluded, and a new set of optimized partial ambiguity parameters is constructed.

[0125] Suppose there are n visible satellites after preliminary screening in a certain epoch, which are (S 1 , S 2 , …, S n ). If the reference satellite is set as S n , then n - 1 single-difference ambiguities can be formed, which are (T 1 , T 2 , …, T n-1 ). If the number of ambiguities with single-difference ambiguity variance less than the threshold is less than 4, the algorithm exits without fixing the ambiguities; otherwise, all the ambiguities after preprocessing are fixed.

[0126] Screen each of the n - 1 satellites except the reference satellite one by one. After excluding the newly added satellites, n - 2 sets of partial ambiguities are formed respectively, which are (T 1 , T 2 , …, T n-2 ). Perform partial ambiguity fixing on these n - 2 sets of partial ambiguities, and calculate the corresponding ratio values (R 1 , R 2 , …, R n-2 ) and integer bootstrap success rates (P 1 , P 2 , …, P n-2 ) for the partial ambiguity groups (T IB，1 , T IB，2 , …, T IB,n-2 ), and sort the ratio values of each partial ambiguity group. If the newly added satellites have stable observation values for 20 consecutive epochs, they can participate in the ambiguity fixing in the next process. Subsequently, perform model-driven partial ambiguity fixing again to obtain a new ratio value ratio2. When ratio2 is greater than or equal to g, the partial fixed solution is obtained; otherwise, the floating-point ambiguity solution will continue to be used for positioning calculation.

[0127] Step 4.2.4: Check the ratio value and success rate for the partial ambiguity group with the largest Ratio value. If the test conditions are not met, repeat Step 4.1 until the test can pass. If the conditions are met, fix the partial ambiguities at this time.

[0128] Step 4.2.5: Re-estimate other ambiguities by applying variance constraints to the fixed solution of part or all of the ambiguities, and obtain their variance-covariance matrix. Re-execute Steps 4.2.1 - 4.2.4 until there are ambiguities that cannot be fixed among the remaining ambiguities or the number of ambiguities fixed as integers is less than 4, then end.

[0129] By this method, it is possible to use the Ratio test factor to eliminate satellites as few as possible to retain as many ambiguities as possible, and effectively process the ambiguity data through the limitation of the variance threshold, reducing the participation of poor-quality data in the positioning solution process.

[0130] After the solution is completed, the double-difference partial ambiguities at this time will be brought back to the single-difference ambiguities, and then the integer solution of the cycle ambiguities will be obtained, which will be used as a known constant in the subsequent processing.

[0131] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some or all of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope defined by the claims of the present invention.

Claims

1. A method for fixing partial ambiguities in dual dynamic positioning with baseline constraints and quality weighting, characterized by: The following steps are involved: Step 1: Adjust the parameters of the existing RTK relative positioning function model, introduce error correction by adding a differential process to reduce the positioning error caused by the unknown accurate position information of the reference station, and establish a dual dynamic carrier relative positioning function solution model; Step 2: Obtain the original observation data of the receiver terminal, use the dual dynamic carrier relative positioning function model to perform preliminary calculation on the original observation data, and obtain the mutual double difference result between the two dynamic carriers; Step 3: Apply baseline constraints to the current epoch to select the single-difference partial ambiguity, that is, constrain the baseline vector through the baseline deviation, screen out the maximum baseline deviation value of each epoch, and then find the corresponding baseline vector, and finally eliminate the ambiguity parameters and satellites involved in the solution of the corresponding epoch to achieve the reorganization of the double-difference partial ambiguity. At the same time, adjust the weight of the observation quantity of high-quality data corresponding to the GNSS frequency point through the weighting of the observation data, improve the weight of high-quality data, and obtain new double-difference ambiguity parameters to achieve data-driven partial ambiguity selection; Step 4: Perform Kalman filtering on the initial solution results of the original observation data obtained in step 2 to obtain the floating-point solutions of the position and ambiguity parameters and their corresponding variance-covariance matrices, perform improved model driving, and then combine the proportional test of the reliability of the ambiguity fixed solution in the data drive to achieve partial ambiguity fixation.

2. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraints and quality weighting according to claim 1 is characterized in that: The step 1 comprises: Establish GNSS non-difference observation equations, single-difference observation equations between mobile stations and reference stations, and station-satellite double-difference observation equations between mobile stations and reference stations; The receiver clock error is further eliminated in the double difference process. and Subtract and get the baseline deviation of each positioning in, is the distance vector from satellite s to mobile station receiver terminal r and reference station receiver terminal b and Subtract and get the baseline vector; is the distance vector from satellite k to mobile station receiver terminal r and reference station receiver terminal b and The baseline vector obtained by subtraction; is the carrier phase observation of satellite s at frequency i by receiver terminal r; i is the wavelength of the satellite’s i-th frequency; is the carrier phase observation of satellite s at frequency i by the reference station receiver terminal b; The RTK relative positioning function model is optimized to a dual dynamic carrier relative positioning function model with two terminals differentially positioned. At the same time, the baseline deviation of the mobile station receiver terminal r and the reference station receiver terminal b after differentially positioned is obtained as follows: in, The reference station receiver terminal b is used as the reference to calculate the baseline deviation of the mobile station receiver terminal r at frequency i after double difference processing; and is the baseline vector calculated from satellites s and k at frequency i with reference to the reference station receiver terminal b; The baseline deviation of the reference station receiver terminal b at frequency i after double difference processing is calculated with the mobile station receiver terminal r as the reference; and is the baseline vector calculated from satellites s and k at frequency i with reference to mobile station receiver terminal r; The baseline deviation obtained by the difference between the mobile station receiver terminal r and the reference station receiver terminal b is taken as the baseline deviation of the current epoch to further reduce the influence of the positioning error. The baseline deviation value of this epoch is for:

3. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraint and quality weighting according to claim 2 is characterized in that: The step 3 comprises: Step 3.1: Optimize the single difference partial ambiguity through baseline constraints to obtain the single difference partial ambiguity without maximum deviation, that is, remove the maximum single difference value and its corresponding satellite, and then reorganize the double difference partial ambiguity to reduce the maximum deviation of the baseline solution; Step 3.2: Assign weights to the data at different frequencies according to the quality of the observations to obtain the re-optimized double-difference partial ambiguity.

4. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraint and quality weighting according to claim 3 is characterized in that: The step 3.2 comprises: Step 3.2.1: Establish an observation weighting scheme that combines elevation and carrier-to-noise ratio (CNR) values; Step 3.2.2: Based on step 3.2.1, a Hopular-based weighting scheme is established through the Hopular method. The weighting scheme includes the observed variance of the NLOS error in the pseudorange and carrier phase measurements. The carrier-to-noise ratio value and the loss of lock indicator LLI are used to provide additional constraints to calculate the GNSS observation variance.

5. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraint and quality weighting according to claim 4, characterized in that: The step 4 comprises: Step 4.1: Fix the reoptimized partial ambiguity through the LAMBDA algorithm; in which, the SRC index method is added to the model-driven part to verify whether the fixation success rate of the candidate partial ambiguity meets the threshold requirement, so as to decide whether to accept the fixation solution of the partial ambiguity; Step 4.2: In the data-driven part, the ratio test Ratio-test is used to judge the reliability of the ambiguity fixation solution by combining the actual measurement data of the mobile station and the reference station receiver to further verify the ambiguity fixation rate and positioning accuracy; in the fixation process, the satellites for ambiguity fixation in the next epoch are appropriately adjusted based on the size of the ratio detection value between epochs and the ambiguity fixation status, and the gross positioning errors are eliminated; After the solution is completed, the double-difference partial ambiguity at this time will be brought back to the single-difference ambiguity, and then the integer solution of the integer ambiguity will be obtained.

6. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraint and quality weighting according to claim 5, characterized in that: The step 4.2.2 includes: Step 4.2.1: After the success rate of integer bootstrapping is obtained, the partial ambiguity resolution results calculated by the model-driven part are ratio-checked in combination with the actual measurement data; Step 4.2.2: If the result of partial ambiguity resolution at the current epoch fails the ratio test, select partial ambiguities with small variances to eliminate gross positioning errors; Step 4.2.3: If the ratio value of the partial ambiguity resolution result of the current epoch is ratio1, and the ratio value of the previous epoch is pre_ratio, when pre_ratio is greater than or equal to g and the ratio value ratio1 of the current epoch is less than g, but the ambiguity of the current epoch cannot be fixed; or pre_ratio is greater than twice ratio1, in these two states, the satellites newly added in the current epoch compared to the previous epoch are eliminated, and the preferred partial ambiguity parameters are newly constructed; Step 4.2.4: Check the ratio value and success rate of the partial ambiguity group with the largest ratio value. If the test condition is not met, re-execute step 4.1 until it can pass the test. If the condition is met, fix the partial ambiguity at this time; Step 4.2.5: Fix some or all of the ambiguities and impose variance constraints to re-estimate other ambiguities and obtain their variance-covariance matrices. Re-execute steps 4.2.1 to 4.2.4 until there are ambiguities in the remaining ambiguities that cannot be fixed or the number of ambiguities fixed to integers is less than the set value.

7. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraint and quality weighting according to claim 6, characterized in that: The step 4.2.1 includes: During the ambiguity search process, the residual quadratic form s[0] of the suboptimal solution and the residual quadratic form s[1] of the optimal solution in the partial ambiguity fixing solution as well as the ambiguity fixing success rate are obtained; when s[0] / s[1] is greater than or equal to the ratio test threshold g, it indicates that the current ambiguity fixing meets the accuracy requirements; otherwise, the ambiguity parameters will be eliminated in the order of conditional variance, and the success rate as well as the residual quadratic form s[0] of the suboptimal solution and the residual quadratic form s[1] of the optimal solution in the fixed solution will be recalculated until s[0] / s[1] is greater than or equal to g.

8. The method for fixing partial ambiguities of dual dynamic positioning with baseline constraint and quality weighting according to claim 7, characterized in that: The step 4.2.3 includes: Suppose that after initial screening at a certain epoch, there are n visible satellites, namely (S1, S2, ..., S n ), set the reference star as S n , then n-1 single-difference ambiguities can be formed, namely (T1, T2, ..., T n-1 ); if the number of ambiguities whose single difference ambiguity variance is less than the threshold is less than the set value, the algorithm is exited without ambiguity fixation, otherwise all ambiguities are fixed after preprocessing; The n-1 satellites except the reference satellite are screened one by one, and after removing the newly added satellites, n-2 partial ambiguity groups are formed, namely (T1, T2, ..., T n-2 ); fix the partial ambiguity of the n-2 partial ambiguity groups and calculate the partial ambiguity groups (T1, T2, ..., T n-2 ) corresponding to the ratio value (R1, R2, ..., R n-2 ) and integer bootstrap success rate (P IB，1 , P IB，2 ,…,P IB,n-2 ), sort the ratio values ​​of each partial ambiguity group; if the newly added satellite has stable observation values ​​for 20 consecutive epochs, the ambiguity participating in the next process is fixed; then, the model-driven partial ambiguity fixation is performed again to obtain a new ratio value ratio2. When ratio2 is greater than or equal to g, the partial fixed solution is obtained, otherwise the ambiguity floating point solution will continue to be used for positioning solution.

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