A method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting

Abstract

This invention provides a method for fixing partial ambiguities in dual-dynamic positioning based on baseline constraints and quality weighting, relating to the field of satellite navigation and positioning technology. This method adjusts the parameters of existing RTK relative positioning function models, introducing error correction through a differential process to reduce positioning errors caused by unknown reference station position information, and establishes a dual-dynamic carrier relative positioning function solution model. It eliminates the ambiguity parameters with the largest deviations through baseline constraints and reconstructs the dual-difference partial ambiguity parameters. It assigns higher weights to ambiguity parameters from high-quality frequency observation data and reduces the weights of ambiguity parameters from lower-quality or discontinuous frequency data, obtaining re-optimized partial ambiguities. Then, an improved model-driven and data-driven fixing strategy is used to fix and verify the optimized partial ambiguities, thereby obtaining a high-precision position solution, providing more accurate and robust positioning results for the relative positioning of dual-dynamic carriers.

Description

Technical Field

[0001] This invention relates to the field of satellite navigation and positioning technology, and in particular to a method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting. Background Technology

[0002] In recent years, with the rapid development of the BeiDou Navigation Satellite System, its advantages in positioning accuracy and coverage have become increasingly prominent. In high-precision applications of the Global Navigation Satellite System (GNSS), carrier phase differential technology with a static reference station is widely used in engineering surveying and setting out, oil geophysical exploration, and precision aircraft approach. While carrier phase differential technology can achieve centimeter-level relative positioning accuracy, it requires a fixed reference station as the differential information source, thus limiting the system's coverage and applications. However, in areas such as carrier-based aircraft landing, aerial refueling, aircraft formation flying, 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. In these cases, 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 using a fixed reference station positioning mode will produce serious errors in the results. Therefore, traditional RTK cannot meet the needs of dynamic users. Therefore, in scenarios involving dual dynamic carriers where both the rover and reference station are dynamic, it is necessary to improve the positioning function calculation model to reduce positioning errors caused by the unknown accurate location information of the reference station. Simultaneously, RTK relative positioning is limited by the fixed integer ambiguity of the carrier phase. Correct ambiguity fixing can achieve high-precision positioning, while incorrect ambiguity fixing may lead to significant errors in the estimation results.

[0003] Current research on ambiguity fixation mainly focuses on reducing poorly performing observation data to improve ambiguity fixation effectiveness and positioning accuracy. However, processing rapidly changing ambiguities at the observation data level makes it difficult to reduce the complexity of ambiguity resolution, and it's challenging to fix all parameters of high-dimensional integer ambiguities. In this context, partial ambiguity resolution (PAR) strategies using data-driven and model-driven approaches can select high-quality ambiguities from high-dimensional integer ambiguities for fixation, reducing computational dimensionality. Model-driven approaches only consider the theoretical accuracy of observations, using only prior models to select partial ambiguities, lacking consideration of real-world data. Data-driven approaches, on the other hand, cannot provide an assessment of the strength of the observed model. While these methods have made some innovative contributions to ambiguity fixation, they do not consider baseline data.

[0004] Therefore, this invention proposes a data-plus-model-driven partial ambiguity fixing method for dual-dynamic carriers, based on baseline constraints and quality weighting. By eliminating the ambiguity parameters with the largest deviations through baseline constraints, the double-difference partial ambiguity parameters are reconstructed. Simultaneously, higher weights are assigned to ambiguity parameters from high-quality frequency observation data, while the weights of ambiguity parameters from lower-quality or discontinuous frequency data are reduced, resulting in re-optimized partial ambiguities. An improved model-driven and data-driven fixing strategy is then used to fix and verify the selected partial ambiguities, thereby obtaining a high-precision positional solution. This provides more accurate and robust positioning results 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 address the shortcomings of the prior art by providing a method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting, thereby improving the accuracy and reliability of ambiguity fixing, and thus improving positioning accuracy and stability, providing a guarantee for achieving high-precision relative positioning of dual dynamic carriers.

[0006] To solve the above-mentioned technical problems, the technical solution adopted by this invention is: a dual-dynamic positioning partial ambiguity fixing method based on baseline constraints and quality weighting. This method removes the ambiguity parameters with the largest deviations through baseline constraints and reconstructs the dual-difference partial ambiguity parameters. It assigns higher weights to the ambiguity parameters of high-quality frequency point observation data and reduces the weights of ambiguity parameters of lower-quality or discontinuous frequency point data, resulting in re-optimized partial ambiguities. Then, an improved model-driven and data-driven fixing strategy is used to fix and verify the ambiguities of the optimized partial ambiguities, thereby obtaining a high-precision position solution. This provides more accurate and robust positioning results for the relative positioning of dual-dynamic carriers. The method includes the following steps:

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

[0008] Establish GNSS non-differential observation equations, inter-station single-difference observation equations between the rover and the reference station, and inter-station double-difference observation equations between the rover and the reference station.

[0009] The receiver clock error is further eliminated during the double-difference process, while two baseline vectors are used. and The baseline deviation for each positioning is obtained by subtraction.

[0010]

[0011] in, Let be the distance vector values ​​from satellite s to rover receiver terminal r and reference station receiver terminal b. and The baseline vector is obtained by subtraction; Let K be the distance vector value from satellite k to the rover receiver terminal r and the reference station receiver terminal b. and The baseline vector obtained by subtraction; For receiver terminal r, the carrier phase observation of satellite s at frequency i is given; λ i Let be the wavelength of the i-th frequency of the satellite; For the reference station receiver terminal b, the carrier phase observation of satellite s at frequency i is...

[0012] The RTK relative positioning function model is optimized into a dual dynamic carrier relative positioning function model with mutual differentiation between the two terminals. Simultaneously, the baseline deviation between the mobile station receiver terminal r and the reference station receiver terminal b after mutual differentiation is obtained, as shown in the following equation:

[0013]

[0014] in, The baseline deviation of the mobile station receiver terminal r at frequency i is calculated using the reference station receiver terminal b as a reference. and It is the baseline vector calculated by 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 is calculated using the mobile station receiver terminal r as a reference and after double difference processing. and It is the baseline vector calculated from satellites s and k at frequency i with reference to the mobile station receiver terminal r;

[0015] The baseline deviations obtained by differential analysis between the rover receiver terminal r and the reference station receiver terminal b are averaged and taken as the baseline deviation for the current epoch. This further reduces the impact of positioning errors. The baseline deviation value for this epoch is... for:

[0016]

[0017] Step 2: Obtain the raw observation data from the receiver terminal, and use the dual dynamic carrier relative positioning function model to perform preliminary calculations on the raw observation data to obtain the mutual double difference results between the two dynamic carriers;

[0018] Step 3: Apply baseline constraints to the current epoch to select the single-difference partial ambiguity. That is, constrain the baseline vector by the baseline deviation, select the largest baseline deviation value for each epoch, find the corresponding baseline vector, and finally remove the ambiguity parameters and satellites involved in the solution for the corresponding epoch to achieve the reorganization of the double-difference partial ambiguity. At the same time, adjust the weight of the observations of the high-quality data corresponding to the GNSS frequency point by weighting the observation data, increase the weight of the high-quality data, and obtain new double-difference ambiguity parameters to achieve data-driven partial ambiguity selection.

[0019] 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 reconstruct the double-difference partial ambiguity to reduce the maximum deviation of the baseline solution;

[0020] Step 3.2: Assign weights to data at different frequencies based on the quality of the observations to obtain the re-optimized double-difference partial ambiguity;

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

[0022] Step 3.2.2: Based on step 3.2.1, establish a weighted scheme based on the Hopular method. This weighted scheme includes the observation variance of NLOS error in pseudorange and carrier phase measurements, and also uses the carrier-to-noise ratio and the loss-of-lock indicator LLI to provide additional constraints to calculate the GNSS observation variance.

[0023] Step 4: After processing the preliminary solution results obtained from the raw observation data acquired in Step 2, Kalman filtering is performed to obtain the floating-point solutions of position and ambiguity parameters and their corresponding variance-covariance matrices. An improved model-driven approach is then adopted, and combined with the proportional test of the reliability of the fixed ambiguity solution in the data-driven approach, partial ambiguity fixation is achieved.

[0024] Step 4.1: Fixing the partial ambiguity through re-optimization using the LAMBDA algorithm; wherein, the SRC index method is added to the model-driven part, and the success rate is constructed by statistical test for quantitative evaluation, verifying whether the success rate of fixing the candidate partial ambiguity meets the threshold requirement, thereby deciding whether to accept the fixed solution of the partial ambiguity, so as to improve the reliability of the solution results.

[0025] Step 4.2: In the data-driven part, the reliability of the ambiguity fixation solution is judged by the ratio test, which combines the actual measurement data of the rover and reference station receivers, to further verify the ambiguity fixation rate and positioning accuracy. During the fixation process, the satellites for ambiguity fixation in the next epoch are appropriately adjusted based on the magnitude of the ratio detection value between epochs and the ambiguity fixation status, and positioning gross errors are eliminated.

[0026] Step 4.2.1: After obtaining the integer bootstrap success rate, perform a ratio test on the partial ambiguity resolution results calculated by the model-driven part, combined with actual measurement data;

[0027] During the ambiguity search process, the quadratic residual form s[0] of the suboptimal solution and the quadratic residual form s[1] of the optimal solution in the partial ambiguity fixed solution 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 will be eliminated in the order of conditional variance, and the success rate and the quadratic residual form s[0] of the suboptimal solution and the quadratic residual 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.

[0028] Step 4.2.2: If the result of partial ambiguity resolution in the current epoch does not pass the ratio test, then filter out the ambiguities with small variance and remove the gross errors in positioning.

[0029] Step 4.2.3: If the ratio value of the partial ambiguity resolution 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 of the current epoch is ratio1 less than g, but the ambiguity of the current epoch cannot be fixed; or when pre_ratio is greater than twice ratio1, in both of these states, satellites newly added in the current epoch compared to the previous epoch are removed, and a new preferred partial ambiguity parameter is constructed.

[0030] Suppose that after initial screening, there are n visible satellites at a certain epoch, namely (S1, S2, ..., S...). n The reference satellite is set as S. n Then, n-1 single-difference ambiguities can be formed, namely (T1, T2, ..., T... n-1 If the number of fuzzy variables whose variance is less than the threshold is less than the set value, the algorithm will exit and fuzzy variable fixing will not be performed; otherwise, all fuzzy variables after preprocessing will be fixed.

[0031] Each of the n-1 satellites excluding the reference satellite is screened, and newly added satellites are removed to form n-2 partial ambiguity groups, namely (T1, T2, ..., T...).n-2 For the n-2 partially ambiguity groups, partially ambiguity is fixed, and the partially ambiguity groups (T1, T2, ..., T...) are calculated. n-2 The corresponding ratio values ​​(R1, R2, ..., R) n-2 ) and integer bootstrapping success rate (P IB，1 P IB，2 , ..., P IB,n-2 The ratio values ​​of each ambiguity group are sorted. If a newly added satellite has stable observations for 20 consecutive epochs, it participates in the ambiguity fixation process in the next step. Subsequently, model-driven partial ambiguity fixation is performed again to obtain a new ratio value ratio2. When ratio2 is greater than or equal to g, a partial fixed solution is obtained; otherwise, the floating-point ambiguity solution will continue to be used for positioning calculation.

[0032] Step 4.2.4: Check the Ratio value and success rate of the ambiguity group with the largest Ratio value. If the test conditions are not met, repeat step 4.1 until the test can be passed. If the conditions are met, fix the ambiguity at this time.

[0033] Step 4.2.5: Apply variance constraints to the fixed solution with fixed partial or all ambiguities, re-estimate other ambiguities and obtain their variance-covariance matrix, and repeat steps 4.2.1-4.2.4 until there are ambiguities that cannot be fixed or the number of ambiguities fixed as integers is less than the set value, then the process ends.

[0034] After the solution is completed, the double-difference ambiguity will be brought back to the single-difference ambiguity, thus obtaining the integer solution of the integer ambiguity.

[0035] The beneficial effects of adopting the above technical solution are as follows: The baseline constraint and quality weighting dual dynamic positioning partial ambiguity fixing method provided by the present invention is based on ambiguity fixing technology, relies on the global satellite navigation system, and combines the LAMBDA (Least Square Ambiguity Decorrelation Adjustment) algorithm. It constructs a subset of partial ambiguity parameters through baseline constraints and data quality weighting, and optimizes the model-driven and data-driven fixing strategies to improve the accuracy and reliability of ambiguity fixing, thereby improving positioning accuracy and stability, and providing a guarantee for realizing high-precision relative positioning of dual dynamic carriers. Attached Figure Description

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

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

[0038] Figure 3 The flowchart illustrates the data plus model-driven partial ambiguity fixing strategy for baseline constraints and data weighting provided in this embodiment of the invention. Detailed Implementation

[0039] The specific embodiments of the present invention will be described in further detail below with reference to the accompanying drawings and examples. The following examples are for illustrative purposes only and are not intended to limit the scope of the invention.

[0040] In this embodiment, a method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting includes the following steps:

[0041] Step 1: Adjust the parameters of the existing RTK relative positioning 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;

[0042] Step 1.1: Establish the GNSS undifferentiated observation equation;

[0043] The GNSS non-differential observation equation describes the functional relationship between the raw observations of the GNSS receiver and the unknown parameters; at a certain moment, the observations of satellite s at frequency i observed by the mobile station receiver terminal r are expressed as:

[0044]

[0045] in, It is the pseudorange observation of the receiver terminal r relative to the satellite s at frequency i. For receiver terminal r, the carrier phase observation of satellite s at frequency i is given; λ i Let be the wavelength of the i-th frequency of the satellite; dt is the geometric distance between satellite s and receiver terminal r; c is the speed of light; r and dt s These are the clock differences between the receiver terminal r and the satellite s, respectively; The ionospheric delay between satellite s and receiver terminal r is related to frequency i. N is the tropospheric delay between satellite s and receiver terminal r; r,i Let denot r be the carrier phase integer ambiguity at frequency i; ε and ξ be the pseudorange and carrier phase measurement errors, respectively.

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

[0047] Set up a rover receiver terminal r and a reference station receiver terminal b to simultaneously observe the same satellite s. Then, perform inter-station single difference calculations on the observations of satellite s from both receiver terminals. The single difference (SD) calculation is performed by... definition, For a single difference operator, a single difference diagram is shown below. Figure 1 As shown. The distance vector values ​​from satellite s to the rover receiver terminal r and the reference station receiver terminal b. and The baseline vector is obtained by subtraction. That is, the distance vector between the rover receiver terminal r and the reference station receiver terminal b. For the carrier phase observation of satellite s at frequency i for reference station receiver terminal b; the inter-station single-difference observation equation is:

[0048]

[0049] in, For the pseudorange inter-station single-difference observations of satellite s at frequency i observed by receiver terminal r and reference station receiver terminal b, For the inter-station single-difference observations of the carrier phase of satellite s at frequency i observed by receiver terminal r and reference station receiver terminal b, The difference in geometric distance between the rover receiver terminal r and the reference station receiver terminal b and the satellite s; The clock difference between the mobile station receiver terminal r and the reference station receiver terminal b after single-difference calculation; The ionospheric delay error between the rover receiver terminal r and the reference station receiver terminal b and the satellite s; The tropospheric delay error between the rover receiver terminal r and the reference station receiver terminal b and the satellite s; Let i be the inter-station single-difference carrier phase integer ambiguity between mobile station receiver terminal r and reference station receiver terminal b at frequency i. and These are the noise errors of the pseudorange observation and the carrier phase observation, respectively, after single-difference calculation.

[0050] The influence of satellite clock bias can be eliminated through single-difference calculation. Within the short baseline range, the correlation errors of ionospheric delay I and tropospheric delay T will be effectively eliminated after single-difference calculation, thus simplifying the inter-station single-difference observation equation to:

[0051]

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

[0053] Based on the inter-station single difference, another common-view satellite k is introduced and regarded as the reference satellite. The rover receiver terminal r and the reference station receiver terminal b simultaneously observe satellites s and k, and inter-satellite single difference is performed between the two satellites, thus forming station-satellite double difference (DD) observations. The double difference process is as follows: Definition, where For a double difference operator, its geometric relation is as follows: Figure 2 As shown. The double-difference observation equation is:

[0054]

[0055] in, For pseudorange station-satellite double difference observations of satellites s and k at frequency i observed by rover receiver terminal r and reference station receiver terminal b; For the carrier phase station-satellite double difference observations of satellites s and k at frequency i observed by the mobile station receiver terminal r and the reference station receiver terminal b; The geometric distance difference between the rover receiver terminal r and the reference station receiver terminal b and satellites s and k; The carrier phase station-satellite double-difference integer ambiguity of mobile station receiver terminal r and reference station receiver terminal b at frequency i; and These are the noise errors of the pseudorange observation and the carrier phase observation after the double-difference process, respectively.

[0056] The receiver clock error is further eliminated during the double-difference process, while two baseline vectors are used. and The baseline deviation for each positioning is obtained by subtraction.

[0057]

[0058] in, Let K be the distance vector value from satellite k to the rover receiver terminal r and the reference station receiver terminal b. and The baseline vector is obtained by subtraction. Baseline vector and double difference ambiguity It is an unknown quantity, which can be obtained by initially solving for the coordinates of the mobile station using the least squares method or filtering.

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

[0060] When the relevant location information of the reference station receiver terminal b is known and used as a reference for differential processing, the baseline deviation... The magnitude of the baseline deviation is mainly affected by the single-point positioning error of the mobile station receiver terminal r. However, 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 used as an approximation of the true value. At this time, the baseline deviation... The magnitude of the error will be affected by both 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, the RTK relative positioning function model (the double-difference observation equation in step 1.3) needs to be optimized into a dual dynamic carrier relative positioning function model with mutual difference between the two terminals. At the same time, the baseline deviation after mutual difference between the mobile station receiver terminal r and the reference station receiver terminal b is obtained, as shown in the following formula:

[0061]

[0062] in, The baseline deviation of the mobile station receiver terminal r at frequency i is calculated using the reference station receiver terminal b as a reference. and It is the baseline vector calculated by 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 is calculated using the mobile station receiver terminal r as a reference and after double difference processing. and It is the baseline vector calculated from satellites s and k at frequency i with reference to the mobile station receiver terminal r;

[0063] The baseline deviations obtained by differential analysis between the rover receiver terminal r and the reference station receiver terminal b are averaged and taken as the baseline deviation for the current epoch. This further reduces the impact of positioning errors. The baseline deviation value for this epoch is... for:

[0064]

[0065] This optimized dual-dynamic carrier relative positioning function model enables the dual dynamic carriers to synchronously obtain carrier-related information, reducing unnecessary errors caused by unknown station information.

[0066] Step 2: Acquire the raw observation data from the receiver terminal;

[0067] Using navigation messages collected and observed by two Beidou navigation receiver terminals in motion as raw observation data, and combined with the dual dynamic carrier relative positioning function model in step 1, the raw observation data is rapidly preliminarily solved in step 1 to obtain the mutual double difference results between the two dynamic carriers, which prepares for further calculation.

[0068] Step 3: Apply baseline constraints to the current epoch to select the single-difference partial ambiguity, i.e., using the baseline deviation given in Step 1.3. For baseline vector Constraints are applied to filter out the largest baseline deviation value for each epoch, and then the corresponding baseline vector is found. Finally, the ambiguity parameters and satellites involved in the solution for the corresponding epoch are removed to achieve the reorganization of the double-difference partial ambiguity. At the same time, the weights of the high-quality data (data with high elevation angle and carrier-to-noise ratio or high continuity) corresponding to the GNSS frequency points are adjusted by weighting the observation data to increase the weight of high-quality data and obtain new double-difference ambiguity parameters, thus realizing data-driven partial ambiguity selection.

[0069] 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 reconstruct the double-difference partial ambiguity to reduce the maximum deviation of the baseline solution;

[0070] Baseline deviation To some extent, it reflects the single-difference baseline. The deviation, i.e. the deviation of the initial positioning solution, indicates that the deviation of the positioning solution of the corresponding satellite is too large. In other words, the accuracy of the single-difference ambiguity parameter is too low, making it difficult to fix the ambiguity parameter of the satellite. Therefore, the method of removing the 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 data at different frequencies based on the quality of the observations to obtain the re-optimized double-difference partial ambiguity;

[0072] Higher weights are assigned to the ambiguity parameters of high-quality frequency point observation data, while the weights of ambiguity parameters for lower-quality or discontinuous frequency point data are reduced, resulting in re-optimized partial ambiguity. This optimized partial ambiguity effectively fixes the floating-point ambiguity into a more deterministic integer solution in subsequent processing, and then Kalman filtering converges the baseline coordinate state estimation to a higher accuracy. The specific steps for selecting and allocating the weights are as follows:

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

[0074] Traditional observation weighting schemes are established using satellite elevation or carrier-to-noise ratio values. The bias values ​​for elevation-based weighting schemes are as follows:

[0075]

[0076] in, and These are the standard deviations of the pseudorange observations and carrier phase observations, respectively, weighted by elevation; α and β are error factors, which are assigned an empirical value of 0.003 in this invention; γ is the code / phase error ratio, and elev is the elevation angle from the satellite to the receiver.

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

[0078]

[0079] in, and These are the standard deviations of the pseudorange and carrier phase observations established using the carrier-to-noise ratio (CNR); C is a factor composed of the carrier phase noise bandwidth and a transformation term from a period of 2 to the square of a millimeter, which is set to an empirical value of 1 in this invention. CNR is the carrier-to-noise ratio of the GNSS signal, measured in dB-Hz.

[0080] The error factor for combining carrier phase observations with elevation and carrier-to-noise ratio is:

[0081]

[0082] in, and These are the standard deviations of pseudorange observations established by combining elevation and carrier-to-noise ratio, and carrier phase observations established by carrier-to-noise ratio; K is the signal type adjustment factor, which is set to different values ​​depending on whether it is a line-of-sight signal; γ is the code / phase error ratio; elev is the elevation angle from the satellite to the receiver; and CNR is the carrier-to-noise ratio of the GNSS signal.

[0083] The formula for calculating the error factor of carrier phase observations combined with elevation and carrier-to-noise ratio describes a weighted model that considers both elevation and carrier-to-noise ratio. It can be seen that the variance of the observations depends on both elevation and carrier-to-noise ratio.

[0084] Compared to methods based solely on elevation, the elevation-plus-carrier-to-noise ratio (CNR) combination method incorporates CNR into the weighting process. At high altitudes and low CNRs, this method provides a larger observation variance than elevation-only methods. Similarly, this method, utilizing satellite elevation to outperform CNR-only weighted schemes, can provide a smaller observation variance at high altitudes and low CNRs. For Line of Sight (LOS) signals, K is set to 1; for Non-Line of Sight (NLOS) signals, K is represented by other values. The value of γ is set to an empirical value of 0.01 for the code / phase error ratio.

[0085] Step 3.2.2: Based on Step 3.2.1, a Hopular-based weighted scheme is established. Unlike the traditional method described above, this scheme includes the observation variance of NLOS error in pseudorange and carrier phase measurements. It also utilizes the carrier-to-noise ratio (CNR) and the Loss of Lock Indicator (LLI) to provide additional constraints. The GNSS observation variance is calculated as shown in the following formula:

[0086]

[0087] in, and These are the variances of the pseudorange observations and the carrier phase observations, respectively. and These are the observation variances of the NLOS errors of the pseudorange observations and the carrier phase observations, respectively. and These are the standard deviations of the pseudorange observations and carrier phase observations, respectively, weighted by elevation.

[0088] Since the elevation-based weighted model performs well in open areas, its error can be considered as the LOS error. The observation variance of the NLOS error between pseudorange and carrier phase observations is calculated as follows:

[0089]

[0090] Where, ε P With ε L These are the NLOS errors of the pseudorange observations and the carrier phase observations, respectively, in meters. 2 In this embodiment, it is set to 1m 2 e is the Euler number; E is the adaptive adjustment exponential factor, P NLOS This is the predicted probability of the NLOS signal. To prevent overweighting of the observations, the Euler number e is chosen to control the growth rate of the exponential function. The predicted probability P of the NLOS signal... NLOS The variance is obtained from the GNSS signal classifier using the Hopular method. Furthermore, the value of the adaptively adjusted exponential factor E in the above equation linearly affects the exponential function. Therefore, accurately determining the value of the exponential factor ensures the overall quality of the variance calculation.

[0091] The value of the exponential factor can be further adjusted using LLI constraints, 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 can be considered to have passed the LOS threshold. Therefore, by setting the exponent factor E to 0, NLOS error can be excluded from the weighting scheme. When the CNR value drops below 35 dB-Hz or LLI shows a cycle slip, the exponent factor E is increased to 9.5 to reduce the weight of the measurement. By default, the exponent factor is 1.1, used to calculate the variance of the predicted NLOS probability.

[0094] The above process reduces the weight of low-quality observation signals in the solution process, reduces the impact of related errors, and further ensures the data quality of some ambiguity parameters corresponding to the carrier phase observation values ​​at this frequency, thereby ensuring the correct solution of ambiguity parameters in the next step.

[0095] Step 4: After processing the preliminary solution results obtained from the raw observation data acquired in Step 2, Kalman filtering is applied to obtain floating-point solutions for position and ambiguity parameters and their corresponding variance-covariance matrices. An improved model-driven approach is then implemented, and combined with the proportional reliability test of the ambiguity-fixed solution in the data-driven approach, partial ambiguity fixation is achieved. The specific solution process is as follows: Figure 3 As shown.

[0096] Step 4.1: Fixing the partial ambiguities through re-optimization using the LAMBDA algorithm; In this step, the SRC index method is added to the model-driven part, and the success rate is quantitatively evaluated through statistical testing to verify whether the success rate of fixing the candidate partial ambiguities meets the threshold requirement, thereby deciding whether to accept the fixed solution for that partial ambiguity, in order to improve the reliability of the solution results. The main calculation process is as follows:

[0097] The GNSS double-difference observation equations are rewritten as linear observation equations, as shown in the following formula:

[0098] y = Bb + Aa + ε

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

[0100] The preliminary solution obtained from the raw observation data acquired in step 2 is processed by Kalman filtering to obtain the preliminary floating-point solutions for the position and ambiguity parameters, i.e., the baseline coordinates. The floating-point solution of the partial ambiguity of the double-difference ambiguity with baseline constraints. And the variance-covariance (VC) combination matrix of the floating-point solutions of the double-difference ambiguity:

[0101]

[0102] in, for The variance matrix; for and The covariance matrix is ​​used to statistically determine the correlation between the two. for and The covariance matrix between them, and satisfying for The variance matrix.

[0103] Due to the integer nature of ambiguity, a discrete search must be performed on the integers. The Z-transform (integer Gaussian transform) in LAMBDA is used to remove the correlation between ambiguities, thereby reducing the size of the search space. Simultaneously, the conditional variance sorting method is used to transform the variance-covariance matrix of the floating-point solution of the double-difference ambiguity, obtaining the decorrelated floating-point solution, variance-covariance matrix, and conditional variance.

[0104] Z-transform solves the covariance matrix from double-difference floating-point ambiguities. The LDL decomposition begins as shown in the following formula.

[0105]

[0106] In the formula, Let be the covariance matrix of the double-difference ambiguity floating-point solution after Z-transform. and Both are symmetric positive definite matrices, L is a lower triangular matrix, and D is a diagonal matrix. The covariance is determined by the symmetric positive definiteness. The decomposition yields matrix D, which can be used to measure the variance of the decorrelated floating-point ambiguity. The Z-transform matrix Z is an integer approximation of L, where all elements are integers and the absolute value of the determinant is 1. Z is then applied to the n-dimensional partially double-difference ambiguity floating-point solution of the ambiguity. To perform decorrelation, as shown in the following formula:

[0107]

[0108] in, To determine the ambiguity of the double-difference portion after Z-transform. The ambiguity of the double difference component after fixing. This represents the original double-difference partial ambiguity after fixing. Next, regarding... Recursive conditional rounding using integer bootstrapping technique

[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 partial ambiguities previously rounded in the above formula; This indicates that the ambiguity parameter was previously fixed. Constrain the ambiguity after the constraint; σ represents the variance of the m-th ambiguity parameter; m,j The term is an element of matrices L and D generated by LDL decomposition. The specific result of the matrix is ​​as follows:

[0111]

[0112] Then, perform an integer search in the relevant space to find the objective function of the optimal fuzzy solution. Minimum value:

[0113]

[0114] When the optimal candidate ambiguity cannot be improved further, a fixed success rate test is performed. Only when the SRC metric test is passed is the candidate ambiguity fixed as an integer.

[0115]

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

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

[0118] Step 4.2: Since model-driven approaches lack consideration of real-world data, the data-driven part uses a ratio test (Ratio-test) to assess the reliability of the ambiguity fixation solution, combining actual measurement data from the rover and reference station receivers. This further verifies the ambiguity fixation rate and positioning accuracy. During the fixation process, the satellites for ambiguity fixation in the next epoch are appropriately adjusted based on the inter-epoch ratio detection value and the ambiguity fixation status. Gross positioning errors are also eliminated. The specific processing steps are as follows: Figure 3 The data-driven part is shown in the diagram.

[0119] Step 4.2.1: After obtaining the integer bootstrapping success rate, perform a ratio test on the partial ambiguity resolution results calculated by the model-driven part, combined with actual measurement data. The ratio test is defined as follows:

[0120]

[0121] in, This is a suboptimal solution among solutions with partially fixed ambiguity. For the optimal solution in the partially ambiguous fixed solution, the ratio test uses the ratio of the quadratic residual of the suboptimal solution s[0] and the optimal solution s[1] 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 g is generally taken as 3.

[0122] During the ambiguity search process, the quadratic residual form s[0] of the suboptimal solution and the quadratic residual form s[1] of the optimal solution in the partial ambiguity fixed solution are obtained, along with the ambiguity fixing success rate. When s[0] / s[1] is greater than or equal to g, it indicates that the current ambiguity fixing meets the accuracy requirements. Otherwise, the ambiguity parameters are eliminated according to the conditional variance, and the success rate and the quadratic residual forms s[0] and s[1] of the suboptimal solution and 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 partial ambiguity resolution in the current epoch fails the ratio test, then filter out the ambiguities with small variance and eliminate the gross positioning errors, i.e., calculate the baseline coordinates. The mean of the variance corresponding to the floating-point solution is used. When the mean is greater than the threshold of 0.1, it indicates that the current positioning error is large and the solution is removed.

[0124] Step 4.2.3: If the ratio value of the partial ambiguity resolution 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 of the current epoch is less than g, but the ambiguity of the current epoch cannot be fixed; or when pre_ratio is greater than twice ratio1, in both of these states, satellites newly added in the current epoch compared to the previous epoch (satellites that have reached a fixed state compared to the previous epoch and their corresponding frequency points) are removed, and a new preferred partial ambiguity parameter is constructed.

[0125] Suppose that after initial screening, there are n visible satellites at a certain epoch, namely (S1, S2, ..., S...). n The reference satellite is set as S. n Then, n-1 single-difference ambiguities can be formed, namely (T1, T2, ..., T... n-1If the number of ambiguities with a single-difference ambiguity variance less than the threshold is less than 4, the algorithm exits and ambiguity fixing is not performed; otherwise, all ambiguities after preprocessing are fixed.

[0126] Each of the n-1 satellites excluding the reference satellite is screened, and newly added satellites are removed to form n-2 partial ambiguity groups, namely (T1, T2, ..., T...). n-2 For the n-2 partially ambiguity groups, partially ambiguity is fixed, and the partially ambiguity groups (T1, T2, ..., T...) are calculated. n-2 The corresponding ratio values ​​(R1, R2, ..., R) n-2 ) and integer bootstrapping success rate (P IB，1 P IB，2 , ..., P IB,n-2 The ratio values ​​of each ambiguity group are sorted. If a newly added satellite has stable observations for 20 consecutive epochs, it can participate in the next ambiguity fixing process. Subsequently, model-driven partial ambiguity fixing is performed again to obtain a new ratio value, ratio2. When ratio2 is greater than or equal to g, a 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 of the ambiguity group with the largest Ratio value. If the test conditions are not met, repeat step 4.1 until the test can be passed. If the conditions are met, fix the ambiguity at this time.

[0128] Step 4.2.5: Apply variance constraints to the fixed solution with fixed partial or all ambiguities, re-estimate the other ambiguities and obtain their variance-covariance matrix, and repeat steps 4.2.1-4.2.4 until there are ambiguities that cannot be fixed or the number of ambiguities fixed as integers is less than 4, then the process ends.

[0129] This method can both use the Ratio test factor to remove as few satellites as possible to retain as much ambiguity as possible, and effectively process ambiguity data by limiting the variance threshold, thereby reducing the participation of poor-quality data in the positioning solution process.

[0130] After the solution is completed, the ambiguity of the double difference part is as follows. This will be brought back to the single-difference ambiguity, thus obtaining the integer ambiguity. The integer solutions will be used as known constants in 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 skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions 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 ambiguity in dual dynamic positioning based on baseline constraints and quality weighting, characterized in that: Includes the following steps: Step 1: Adjust the parameters of the existing RTK relative positioning function model, and reduce the positioning error caused by the unknown accurate position information of the reference station by introducing error correction through the addition of a differential process, and establish a dual dynamic carrier relative positioning function solution model; Step 2: Obtain the raw observation data from the receiver terminal, and use the dual dynamic carrier relative positioning function model to perform preliminary calculations on the raw observation data to obtain the mutual double difference results 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 by the baseline deviation, select the largest baseline deviation value for each epoch, find the corresponding baseline vector, and finally remove the ambiguity parameters and satellites involved in the solution for the corresponding epoch to achieve the reorganization of the double-difference partial ambiguity. At the same time, adjust the weight of the observations of the high-quality data corresponding to the GNSS frequency point by weighting the observation data, increase the weight of the high-quality data, and obtain new double-difference ambiguity parameters to achieve data-driven partial ambiguity selection. Step 4: After processing the preliminary solution results obtained from the raw observation data acquired in Step 2, Kalman filtering is performed to obtain the floating-point solutions of position and ambiguity parameters and their corresponding variance-covariance matrices. An improved model-driven approach is then adopted, and combined with the proportional test of the reliability of the fixed ambiguity solution in the data-driven approach, partial ambiguity fixation is achieved.

2. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 1, characterized in that: Step 1 includes: Establish GNSS non-differential observation equations, inter-station single-difference observation equations between the rover and the reference station, and inter-station double-difference observation equations between the rover and the reference station. The receiver clock error is further eliminated during the double-difference process, while two baseline vectors are used. and The baseline deviation for each positioning is obtained by subtraction. : ； in, For satellite To the mobile station receiver terminal and reference station receiver terminal Distance vector value and The baseline vector is obtained by subtraction; For satellite To the mobile station receiver terminal and reference station receiver terminal Distance vector value and The baseline vector obtained by subtraction; For receiver terminal For satellites In frequency Carrier phase observations on; For the satellite Wavelength of frequency; Reference station receiver terminal For satellites In frequency Carrier phase observations on; The RTK relative positioning function model is optimized into a dual dynamic carrier relative positioning function model with mutual differentiation between two terminals, and the mobile station receiver terminal is also derived. and reference station receiver terminal The baseline deviation after cross-differentiation is as follows: ； in, Therefore, the reference station receiver terminal For reference, the calculation of the mobile station receiver terminal After double difference processing at frequency Baseline deviation; and Therefore, the reference station receiver terminal For reference, at frequency Above by satellite and The calculated baseline vector; Therefore, the mobile station receiver terminal For reference, the reference station receiver terminal is calculated. After double difference processing at frequency Baseline deviation; and Therefore, the mobile station receiver terminal For reference, at frequency Above by satellite and The calculated baseline vector; For mobile station receiver terminals and reference station receiver terminal The baseline deviations obtained after mutual subtraction are averaged and used as the baseline deviation for the current epoch. This further reduces the impact of positioning errors. The baseline deviation value for this epoch is then calculated. for: 。 3. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 2, characterized in that: Step 3 includes: 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 reconstruct the double-difference partial ambiguity to reduce the maximum deviation of the baseline solution; Step 3.2: Assign weights to data at different frequencies based on the quality of the observations to obtain the re-optimized double-difference partial ambiguity.

4. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 3, characterized in that: Step 3.2 includes: 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, establish a Hopular-based weighting scheme using the Hopular method. This weighting scheme includes the observation variance of NLOS error in pseudorange and carrier phase measurements, and also uses the carrier-to-noise ratio and the loss-of-lock indicator LLI to provide additional constraints to calculate the GNSS observation variance.

5. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 4, characterized in that: Step 4 includes: Step 4.1: Fix the partial ambiguity through re-optimization using the LAMBDA algorithm; wherein, the SRC index method is added to the model-driven part to verify whether the success rate of fixing the candidate partial ambiguity meets the threshold requirement, thereby deciding whether to accept the fixed solution of the partial ambiguity. Step 4.2: In the data-driven part, the reliability of the ambiguity fixation solution is judged by the ratio test, which combines the actual measurement data of the rover and reference station receivers, to further verify the ambiguity fixation rate and positioning accuracy. During the fixation process, the satellites for ambiguity fixation in the next epoch are appropriately adjusted based on the magnitude of the ratio detection value between epochs and the ambiguity fixation status, and positioning gross errors are eliminated. After the solution is completed, the double-difference ambiguity will be brought back to the single-difference ambiguity, thus obtaining the integer solution of the integer ambiguity.

6. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 5, characterized in that: Step 4.2 includes: Step 4.2.1: After obtaining the integer bootstrap success rate, perform a ratio test on the partial ambiguity resolution results calculated by the model-driven part, combined with actual measurement data; Step 4.2.2: If the result of partial ambiguity resolution in the current epoch does not pass the ratio test, then filter out the ambiguities with small variance and remove the gross errors in positioning. Step 4.2.3: If the ratio value of the partial ambiguity resolution 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... And the current epoch's ratio value, ratio1, is less than... However, the ambiguity of the current epoch cannot be fixed; or pre_ratio is greater than twice ratio1. In these two states, satellites newly added in the current epoch compared to the previous epoch are removed, and a new set of preferred ambiguity parameters are constructed. Step 4.2.4: Check the Ratio value and success rate of the ambiguity group with the largest Ratio value. If the test conditions are not met, repeat step 4.1 until the test can be passed. If the conditions are met, fix the ambiguity at this time. Step 4.2.5: Apply variance constraints to the fixed solution with fixed partial or all ambiguities, re-estimate other ambiguities and obtain their variance-covariance matrix, and repeat steps 4.2.1-4.2.4 until there are ambiguities in the remaining ambiguities that cannot be fixed or the number of ambiguities fixed as integers is less than the set value, then the process ends.

7. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 6, characterized in that: Step 4.2.1 includes: During the ambiguity search process, the quadratic residual form of the suboptimal solution in some fixed ambiguity solutions is obtained. The quadratic form of the residual of the optimal solution And the success rate of fixing ambiguity; when Threshold for the greater than or equal to ratio test If the condition is met, it indicates that the current ambiguity meets the accuracy requirements; otherwise, the ambiguity parameters will be eliminated according to the conditional variance, and the success rate and the quadratic residual form of the suboptimal solution in the fixed solution will be recalculated. The quadratic form of the residual of the optimal solution until satisfied Greater than or equal to .

8. The method for fixing partial ambiguity in dual dynamic positioning based on baseline constraints and quality weighting according to claim 7, characterized in that: Step 4.2.3 includes: Suppose that after initial screening, the visible satellites at a certain epoch are... Each is respectively Set the reference star as Then it can constitute Each single-difference ambiguity is respectively If the number of fuzzy variables whose variance is less than the threshold is less than the set value, the algorithm will exit and fuzzy variable fixing will not be performed; otherwise, all fuzzy variables after preprocessing will be fixed. For all but the reference star Each satellite was screened one by one, and newly added satellites were removed to form [the following structure]. The partial ambiguity groups are as follows: ; Regarding Each partial ambiguity group is partially fixed, and the partial ambiguity group is calculated. The corresponding ratio value And integer bootstrap success rate The ratio values ​​of each ambiguity group are sorted. If a newly added satellite has stable observations for 20 consecutive epochs, it participates in the next ambiguity fixation process. Subsequently, model-driven partial ambiguity fixation is performed again to obtain a new ratio value, ratio2. When ratio2 is greater than or equal to... If the solution is obtained, a partial fixed solution is obtained; otherwise, the fuzzy floating-point solution will continue to be used for positioning calculation.

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