Satellite positioning ambiguity determination method, terminal and medium

Abstract

The application discloses a satellite positioning ambiguity determination method, a terminal and a medium in the field of satellite navigation and positioning, and the method comprises the following steps: acquiring observation data of a reference station and a mobile station, eliminating errors and correcting cycle slips by using double difference technology to obtain corrected observation data; preliminarily estimating the speed and position of the mobile station; based on the corrected observation data, an optimal ambiguity subset is extracted through satellite level and ambiguity level screening; a factor graph model is constructed by using the optimal ambiguity subset, the preliminarily estimated speed and position of the mobile station are taken as initial values, an error function in the factor graph is minimized, and a floating point solution of ambiguity is obtained by optimization; a whole ambiguity solution is obtained based on the floating point solution; and the stability of the ambiguity solution result is verified through consistency, and finally, a fixed ambiguity solution is obtained. The method provided by the application realizes high precision, high efficiency and high stability of ambiguity solution, and is suitable for a high-precision satellite positioning system in a complex environment.

Description

Technical Field

[0001] This invention belongs to the field of satellite navigation and positioning, and specifically relates to a method for determining ambiguity in satellite positioning, a terminal, and a medium. Background Technology

[0002] Satellite positioning technology is a core technology in modern navigation and geographic information systems, widely used in surveying, agriculture, autonomous driving, and drone navigation. Traditional satellite positioning systems can provide meter-level positioning accuracy, but for applications such as autonomous driving and high-precision surveying, meter-level accuracy is far from sufficient. To address this need, the demand for high-precision positioning technology is becoming increasingly urgent. With the application of high-speed mobile devices, comprehensive requirements have been placed on high-precision positioning solutions in terms of processing time, accuracy, and receiver computing resources. Exploring high-performance, high-precision positioning solutions is one of the key directions for the development of satellite positioning technology.

[0003] Currently, high-precision ranging and satellite positioning are generally achieved through carrier phase positioning. However, carrier phase positioning requires determining integer ambiguity, and high-precision ranging and satellite positioning can only be achieved when the integer ambiguity is reliable. Existing technologies cannot perform the calculation and determination of integer ambiguity well, which affects the accuracy of satellite positioning. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, terminal and medium for determining ambiguity in satellite positioning, which achieves high precision, high efficiency and high stability in ambiguity resolution and is suitable for high-precision satellite positioning systems in complex environments.

[0005] To achieve the above objectives, the present invention is implemented using the following technical solution:

[0006] In a first aspect, the present invention provides a method for determining ambiguity in satellite positioning, comprising:

[0007] The observation data from the base station and the rover station are acquired, and the double difference technique is used to eliminate errors and perform cycle slip correction to obtain the corrected observation data.

[0008] Construct an error function between the observed values ​​and the model predictions, minimize the error function, and make a preliminary estimate of the speed and position of the mobile station;

[0009] Based on the corrected observation data, the optimal ambiguity subset is extracted through satellite-level and ambiguity-level filtering;

[0010] A factor graph model is constructed using the optimal ambiguity subset. The initially estimated speed and position of the mobile station are used as initial values. The error function in the factor graph is minimized to obtain a floating-point solution that includes the position, speed and ambiguity of the mobile station.

[0011] Based on the floating-point solution, the ambiguity is subjected to decorrelation processing, and combined with the integerization process, the integer ambiguity solution is obtained;

[0012] The reliability of the integer ambiguity solution is verified by the residual ratio, and multiple solutions are generated by resampling the floating-point solution. The stability of the ambiguity solution is verified by the consistency, and finally the fixed ambiguity solution is obtained.

[0013] Furthermore, observational data from the base station and rover station are acquired, including:

[0014] Satellite signal data, including pseudorange, carrier phase, and Doppler effect data, are acquired from the base station and the rover station. The distance from the satellite to the rover station is estimated by pseudorange measurement, the distance is accurately calculated by carrier phase measurement, and the speed of the rover station is estimated by Doppler measurement.

[0015] The formula for pseudorange measurement is shown below:

[0016] ;

[0017] In the formula: It is a pseudorange, representing the estimated distance from the satellite to the rover station; Represents the speed of light; Indicates the time when the mobile station received the satellite signal; Indicates the time when the satellite transmitted the signal; This indicates the error in pseudorange measurement;

[0018] The formula for carrier phase measurement is as follows:

[0019] ;

[0020] In the formula: It is the carrier phase, which indicates a more precise distance from the satellite to the mobile station; Indicates the ambiguity of the integer period. Indicates the wavelength of the carrier wave; This indicates the error in carrier phase measurement;

[0021] The formula for the Doppler measurement is as follows:

[0022] ;

[0023] In the formula: Indicates the frequency of the received wave; Indicates the frequency of the transmitted wave; This indicates the velocity of the mobile station relative to the wave source; This indicates the velocity of the wave source relative to the propagation medium;

[0024] Errors in pseudorange measurement This includes atmospheric delay and clock errors caused by inconsistencies between the rover and satellite time. The double-difference technique is used to eliminate these errors, including:

[0025] First, clock skew at the rover station is eliminated using single-difference, where single-difference represents the difference between the observations of the same satellite at the base station. and mobile station The difference is calculated between the two values, and the simple difference formula is shown below:

[0026] ;

[0027] In the formula: and Representing the base station and mobile station Pseudorange measurements of the satellite;

[0028] Based on single-difference, double-difference is then used to recalibrate the base station. and mobile station The observed values ​​are differencing to further eliminate atmospheric delay and satellite clock errors. The double-difference formula is shown below:

[0029] ;

[0030] In the formula: and Representing the base station and mobile station For satellite The pseudorange measurement value; and Representing the base station and mobile station For satellite The pseudorange measurement value; Indicates the base station and mobile station For satellite The single difference; Indicates the base station and mobile station For satellite The single difference.

[0031] Furthermore, cycle slip correction is applied to the observation data to obtain corrected observation data, including:

[0032] Calculate the phase difference between adjacent epochs As shown in the following formula:

[0033] ;

[0034] In the formula: This represents the carrier phase observation value at the current epoch; This represents the carrier phase observation value from the previous epoch;

[0035] By comparing the phase changes across consecutive epochs, a threshold is set as the criterion for determining whether a phase abrupt change has occurred; if the phase difference... If the value exceeds the threshold and meets the integer cycle jump characteristics, a cycle slip is determined to have occurred; the detected cycle slip data is corrected to obtain the corrected observation data.

[0036] Furthermore, an error function is constructed between the observed values ​​and the model predictions. By minimizing this error function, the velocity and position of the mobile station are initially estimated, including:

[0037] Define the prediction model as shown in the following equation:

[0038] ;

[0039] In the formula: Indicates the epoch The location of the mobile station predicted by the model; Indicates speed; Indicates position offset;

[0040] Combining n epochs Model predictions and the actual observed location of the mobile station The error function is constructed to minimize the error between the observed values ​​and the model predictions, as shown in the following equation:

[0041] ;

[0042] In the formula: Represents each epoch At that time, the model predicted the location of the mobile station. Compared with the actual observed location of the mobile station Deviation between;

[0043] The optimal solution of the error function was obtained using the LDLT decomposition method. .

[0044] Furthermore, based on the corrected observation data, the optimal ambiguity subset is extracted through satellite-level and ambiguity-level filtering, including:

[0045] The satellites are divided into subsets based on their elevation and azimuth angles, and one satellite is removed from each subset. The subset with the smallest set precision attenuation factor (GDOP) is then selected.

[0046] The ambiguity level is determined by performing disambiguation calculations on several ambiguities with the largest ambiguity accuracy attenuation factor (ADOP) in the satellite subset, successively eliminating the ambiguity combination with the largest GDOP, and finally determining the optimal ambiguity subset.

[0047] Furthermore, a factor graph model is constructed using the optimal subset of fuzziness, including:

[0048] The nodes of the design factor graph include variable nodes and factor nodes; the variable nodes include the position, velocity, and ambiguity of the mobile station; the factor nodes include pseudorange factors and carrier phase factors; through bidirectional connections, the position and ambiguity are constrained by pseudorange factors and carrier phase factors, and the position and velocity are constrained by Doppler factors.

[0049] The initial estimated speed of the mobile station and location As the initial value for factor graph optimization, the optimal subset of fuzziness is input into the factor graph, and the floating-point solution is obtained through the following steps:

[0050] Define mobile site The state is as shown in the following formula:

[0051] x = [ x r , 1 , x r , 2 , … , x r , n ] ;

[0052] ;

[0053] In the formula: Indicates mobile station The set of states for n epochs; n represents the total number of measurement epochs considered in factor graph optimization; Indicates mobile station In the state of epoch t ; Indicates the moving station at epoch t. Location; Indicates the moving station at epoch t. speed; Indicates the moving station at epoch t. Clock deviation;

[0054] Define satellites and rover stations The pseudorange measurement model is shown in the following equation:

[0055] ;

[0056] In the formula: This represents the output of the pseudorange measurement model for satellite 's' and the rover station. The pseudo-distance value at epoch t; This indicates the position of satellite s at epoch t;

[0057] Define satellites and rover stations The actual observed pseudorange is shown in the following formula:

[0058] ;

[0059] In the formula: Indicates satellite s and rover station The pseudorange value actually observed at epoch t; Indicates and Related noise;

[0060] Combined with actual observations of pseudorange values and the pseudo-range value output by the model Define the error function for pseudorange measurement. As shown in the following formula:

[0061] ;

[0062] In the formula: Error function representing pseudorange measurement The covariance matrix;

[0063] Define mobile site The velocity measurement model is shown in the following equation:

[0064] ;

[0065] In the formula: The mobile station representing the output of the velocity measurement model The velocity at epoch t; Indicates mobile station The state at epoch t+1; , and These represent the moving station at epoch t+1. The position is indicated on the x-axis, y-axis, and z-axis; , and These represent the moving station at epoch t. Position on the x-axis, y-axis, and z-axis: This represents the time difference between epoch t and epoch t+1;

[0066] Define mobile site The actual observed velocity is shown in the following formula:

[0067] ;

[0068] In the formula: Indicates mobile station The velocity actually observed at epoch t; This indicates noise associated with velocity measurements;

[0069] Combined with actual observation speed and the speed of model output Define the error function for speed measurement. As shown in the following formula:

[0070] ;

[0071] In the formula: Error function representing speed measurement The covariance matrix;

[0072] Combining the error functions of pseudorange measurement and velocity measurement, the objective function of the factor map is constructed as follows:

[0073] ;

[0074] Solve for the optimal solution of the objective function, and output the mobile station at epoch t using factor graph optimization. Optimal floating-point solution As shown in the following formula:

[0075] ;

[0076] The optimal floating-point solution Includes the location, speed, and ambiguity of the mobile station. .

[0077] Furthermore, based on the floating-point solution, the ambiguity is subjected to decorrelation processing, and combined with the integerization process, the integer ambiguity solution is obtained, including:

[0078] Ambiguity To perform discorrelation, which converts the originally correlated ambiguities into uncorrelated patterns, the covariance matrix is ​​first calculated. As shown in the following formula:

[0079] ;

[0080] In the formula: , representing the mean vector of ambiguity;

[0081] For covariance matrix Eigenvalue decomposition is performed to obtain eigenvalues ​​and corresponding eigenvectors. The eigenvectors are then used to transform the ambiguity from the original coordinate system to a new coordinate system, as shown in the following equation:

[0082] ;

[0083] In the formula: The variable represents the ambiguity after discorrelation; v represents the selected eigenvector matrix. This represents the transpose of matrix v;

[0084] Ambiguity after correlation for each solution Construct the matrix H related to the integer ambiguity solution N, as shown in the following equation:

[0085] ;

[0086] In the formula: The standard deviation represents the error;

[0087] The integer ambiguity solution N is obtained by minimizing the following objective function, which is shown in the following equation:

[0088] .

[0089] Furthermore, the reliability of the integer ambiguity solution is verified by the residual ratio, and multiple solutions are generated by resampling the floating-point solution. The stability of the ambiguity solution results is verified by consistency, including:

[0090] After obtaining the integer ambiguity solution N, its reliability is verified by the residual ratio R-ratio function. When the R-ratio value is greater than the preset threshold, N is accepted as the optimal solution.

[0091] Ambiguity Random perturbation resampling is performed to generate multiple new integer ambiguity solutions. The stability of the optimal solution is verified by comparing whether these solutions are consistent with the optimal solution. When the consistency meets the preset conditions, the optimal solution is determined as the final fixed solution.

[0092] Secondly, the present invention provides an electronic terminal, including a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the above-described satellite positioning ambiguity determination method are performed.

[0093] Thirdly, the present invention provides a computer-readable storage medium having a computer program stored thereon, characterized in that, when the program is executed by a processor, it implements the steps of the above-described satellite positioning ambiguity determination method.

[0094] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:

[0095] The satellite positioning ambiguity determination method provided by this invention eliminates errors and performs cycle slip correction through double-difference technology, effectively correcting errors in observation data and improving positioning accuracy. Utilizing an optimal ambiguity subset selection strategy significantly reduces computational complexity and improves efficiency in ambiguity resolution. By introducing factor graph optimization technology, the ambiguity resolution problem is modeled as an optimization problem. Using the factor graph model as the core, an error function is constructed between the observation data and the model predictions. By fully utilizing the mutual constraints between pseudorange, carrier phase, and Doppler measurements, the method simultaneously optimizes the rover's position, velocity, and ambiguity variables, significantly improving the accuracy and efficiency of the resolution. Residual ratio verification and Bootstrapping resampling consistency checks fully verify the reliability of the ambiguity resolution results, ultimately obtaining a stable and reliable fixed ambiguity solution.

[0096] The method of this invention can provide more accurate and stable positioning results in complex environments, and is suitable for real-time, high-precision satellite positioning systems, especially for dynamic tracking and large-scale application scenarios. Attached Figure Description

[0097] Figure 1 This is a flowchart of the satellite positioning ambiguity determination method provided in Embodiment 1 of the present invention. Detailed Implementation

[0098] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0099] Example 1:

[0100] Figure 1 This is a flowchart of the satellite positioning ambiguity determination method in Embodiment 1 of the present invention. This flowchart only illustrates the logical sequence of the method described in this embodiment. Provided there are no conflicts, different methods may be used in other possible embodiments of the present invention. Figure 1 Perform the steps shown or described in the order indicated. See also Figure 1 The method implemented in this way specifically includes the following steps:

[0101] The observation data from the base station and the rover station are acquired, and the double difference technique is used to eliminate errors and perform cycle slip correction to obtain the corrected observation data.

[0102] Construct an error function between the observed values ​​and the model predictions, minimize the error function, and make a preliminary estimate of the speed and position of the mobile station;

[0103] Based on the corrected observation data, the optimal ambiguity subset is extracted through satellite-level and ambiguity-level filtering;

[0104] A factor graph model is constructed using the optimal ambiguity subset. The initially estimated speed and position of the mobile station are used as initial values. The error function in the factor graph is minimized to obtain a floating-point solution that includes the position, speed and ambiguity of the mobile station.

[0105] Based on the floating-point solution, the ambiguity is subjected to decorrelation processing, and combined with the integerization process, the integer ambiguity solution is obtained;

[0106] The reliability of the integer ambiguity solution is verified by the residual ratio, and multiple solutions are generated by resampling the floating-point solution. The stability of the ambiguity solution is verified by the consistency, and finally the fixed ambiguity solution is obtained.

[0107] In this embodiment, to verify the effectiveness of the method, a standard positioning dataset from network RTK (Real-Time Kinematic) positioning was used as the experimental data source. This embodiment does not restrict the choice of dataset; publicly available or custom datasets can be used according to actual needs. For example, the RTKLIB dataset was used, which contains observation data in various environments: urban environment (urban38 and urban39), campus environment, and building environment, totaling 8000 samples. In each scenario, the positioning data time lengths are 2154 seconds, 856 seconds, 950 seconds, and 1820 seconds, with corresponding trajectory lengths of 11191 meters, 10678 meters, 1337 meters, and 2560 meters. The satellite system supports GPS and BeiDou, and the measurements used include pseudorange, carrier phase, and Doppler measurements. The data is organized in batch windows.

[0108] In practical applications, the base station and rover station of the selected dataset provide observation data, including pseudorange, Doppler frequency variation, and carrier phase measurements. By performing double-difference processing and cycle slip correction on these data, corrected observation data is generated, which serves as the basis for subsequent ambiguity resolution and positioning calculations.

[0109] First, the propagation time of the satellite signal is calculated using pseudorange measurements to estimate the distance between the satellite and the rover. Since pseudorange is typically an estimate containing errors, its accuracy is affected by factors such as atmospheric delay and clock skew. The formula for pseudorange measurement is as follows:

[0110] ;

[0111] In the formula: It is a pseudorange, representing the estimated distance from the satellite to the rover station; Represents the speed of light; Indicates the time when the mobile station received the satellite signal; Indicates the time when the satellite transmitted the signal; This indicates the error in pseudorange measurement;

[0112] After obtaining the estimated distance between the satellite and the rover station Next, the change in carrier phase is calculated. By utilizing the high-frequency characteristics of the carrier signal, a high-precision measurement of the distance between the mobile station and the satellite is achieved. The formula for carrier phase measurement is shown below:

[0113] ;

[0114] In the formula: It is the carrier phase, which indicates a more precise distance from the satellite to the mobile station; Indicates the ambiguity of the integer period. Indicates the wavelength of the carrier wave; This indicates the error in carrier phase measurement;

[0115] Furthermore, according to the Doppler effect, when the wave source is closer to the mobile station, the frequency of the received signal increases and the wavelength becomes shorter; when the wave source is farther away from the mobile station, the frequency of the received signal decreases and the wavelength becomes longer. Therefore, by observing the Doppler frequency shift, the velocity of the mobile station relative to the satellite can be estimated. The formula for Doppler measurement is shown below:

[0116] ;

[0117] In the formula: Indicates the frequency of the received wave; Indicates the frequency of the transmitted wave; This indicates the velocity of the mobile station relative to the wave source; This indicates the velocity of the wave source relative to the propagation medium;

[0118] Errors in pseudorange measurement This includes atmospheric delay and clock errors caused by inconsistencies between the rover and satellite time. The double-difference technique is used to eliminate these errors, including:

[0119] First, clock skew at the rover station is eliminated using single-difference, where single-difference represents the difference between the observations of the same satellite at the base station. and mobile station The difference is calculated between the two values, and the simple difference formula is shown below:

[0120] ;

[0121] In the formula: and Representing the base station and mobile station Pseudorange measurements of the satellite;

[0122] Based on single-difference, double-difference is then used to recalibrate the base station. and mobile station The observed values ​​are differencing to further eliminate atmospheric delay and satellite clock errors. The double-difference formula is shown below:

[0123] ;

[0124] In the formula: and Representing the base station and mobile station For satellite The pseudorange measurement value; and Representing the base station and mobile station For satellite The pseudorange measurement value; Indicates the base station and mobile station For satellite The single difference; Indicates the base station and mobile station For satellite The single difference.

[0125] Since satellite signals can cause sudden data jumps after being blocked or reflected, this embodiment, after eliminating atmospheric delay and clock error through double-difference technology, further performs cycle slip correction to eliminate abnormal observation data with sudden jumps.

[0126] First, calculate the phase difference between adjacent epochs. As shown in the following formula:

[0127] ;

[0128] In the formula: This represents the carrier phase observation value at the current epoch; This represents the carrier phase observation value from the previous epoch;

[0129] By comparing the phase changes across consecutive epochs, a threshold is set as the criterion for determining whether a phase abrupt change has occurred; if the phase difference... If the value exceeds the threshold and meets the integer cycle jump characteristics, a cycle slip is determined to have occurred; the detected cycle slip data is corrected to obtain the corrected observation data.

[0130] Specifically, in the code implementation, this embodiment defines a cycle slip detection function. This function receives two parameters: the first is a class instance that encapsulates the pseudorange, carrier phase, and Doppler measurement data processed using double-difference technology; the second parameter is a preset threshold for phase abrupt changes, used to detect phase abrupt changes between two adjacent epochs, i.e., whether a cycle slip has occurred. Internally, the function calls a weighted moving average algorithm for data smoothing and sets the window size for the smoothing algorithm. If the change in two adjacent data sets exceeds the preset threshold, the algorithm smoothly corrects these data. Finally, the function returns the corrected observation data for subsequent processing.

[0131] Next, the moving speed of the rover is estimated. Moving speed is a key variable in positioning calculations, and the accuracy of speed estimation directly affects the overall accuracy of the positioning results. Therefore, this embodiment constructs an error function to measure the difference between the model's predicted values ​​(values ​​calculated based on mathematical formulas) and the actual observed values, as follows:

[0132] ;

[0133] in ; Indicates the epoch The location of the mobile station predicted by the model; Indicates speed; Indicates position offset; This indicates the actual observed location of the mobile station; Represents each epoch At that time, the model predicted the location of the mobile station. Compared with the actual observed location of the mobile station Deviation between;

[0134] By adjusting the speed and position offset Let the sum of squared errors To minimize the error function and optimize model predictions, making them more closely reflect actual observations, this embodiment employs the LDLT decomposition method to quickly solve for the optimal solution, ultimately obtaining the velocity-inclusive error function. and position offset optimal solution .

[0135] In satellite positioning, ambiguity resolution is a crucial step, and its accuracy depends heavily on the quality of the selected satellite data. However, processing all satellite signals would be computationally intensive and prone to introducing errors.

[0136] Therefore, in this embodiment, to improve the fuzzy positioning rate and reduce the computational complexity of fuzziness resolution, an optimal fuzziness subset selection method based on a partial fuzziness algorithm is proposed. This method consists of two levels: satellite-level selection and fuzziness-level selection, progressively optimizing and selecting high-quality fuzziness subsets for subsequent resolution.

[0137] First, in the satellite-level screening stage, all satellite signals are initially screened based on their elevation and azimuth angles. For high-elevation satellites (above 90°), their data are given priority as candidate signals to fully utilize satellites with higher signal quality. Within the azimuth range (0°~360°), all satellites are divided into four subsets, denoted as Q1, Q2, Q3, and Q4, each representing a satellite constellation in one azimuth. Subsequently, one satellite is removed from each subset, and the set precision attenuation factor (GDOP) of the removed subset is calculated. By comparing the magnitudes of GDOP, the combination with the smallest GDOP is selected to construct an initial subset H1 containing high-quality satellite signals.

[0138] Next, in the ambiguity level screening stage, the ambiguity variables in satellite subset H1 are further optimized. In this stage, the ambiguity accuracy attenuation factor (ADOP) is used as the optimization index, and the three ambiguity variables with larger ADOP values ​​are selected from the subset, denoted as... , , By eliminating ambiguity in the ambiguity variables, the GDOP values ​​of the remaining satellites under different combinations are calculated. The specific process includes:

[0139] 1. Eliminate and After resolving the ambiguity, calculate the GDOP1 value for the remaining satellites;

[0140] 2. Eliminate and After resolving the ambiguity, calculate the GDOP2 value for the remaining satellites;

[0141] 3. Eliminate and After resolving the ambiguity, calculate the GDOP3 value for the remaining satellites.

[0142] Finally, by comparing the sizes of GDOP1, GDOP2, and GDOP3, the combination with the smallest GDOP is selected as the optimal ambiguity subset, and the two ambiguity variables with larger GDOPs are excluded, thus obtaining the optimal ambiguity subset for subsequent factor graph optimization.

[0143] This method significantly reduces the variables in the solution process through hierarchical screening, improving the efficiency and accuracy of ambiguity resolution and providing a reliable data foundation for subsequent positioning and navigation calculations.

[0144] Next, a mathematical model is constructed through factor graph optimization, and the position, velocity and ambiguity of the rover are optimized using the observation data (pseudorange, carrier phase, Doppler) corresponding to the optimal ambiguity subset.

[0145] First, the nodes of the factor graph are designed, including variable nodes and factor nodes. The variable nodes include the position, velocity, and ambiguity of the mobile station; the factor nodes include the pseudorange factor and the carrier phase factor. Through bidirectional connections, the position and ambiguity are constrained using the pseudorange factor and the carrier phase factor, and the position and velocity are constrained using the Doppler factor.

[0146] Secondly, define the mobile site. The state is as shown in the following formula:

[0147] x = [ x r , 1 , x r , 2 , … , x r , n ] ;

[0148] ;

[0149] In the formula: Indicates mobile station The set of states for n epochs; n represents the total number of measurement epochs considered in factor graph optimization; Indicates mobile station In the state of epoch t ; Indicates the moving station at epoch t. Location; Indicates the moving station at epoch t. speed; Indicates the moving station at epoch t. Clock deviation;

[0150] Next, an objective function is constructed to represent the sum of the "errors" of the factor nodes, including the errors of pseudorange measurement and velocity measurement.

[0151] The error of pseudorange measurement is obtained through the following steps:

[0152] Define satellites and rover stations The actual observed pseudorange is shown in the following formula:

[0153] ;

[0154] In the formula: Indicates satellite s and rover station The pseudorange value actually observed at epoch t; Indicates and Related noise;

[0155] Combined with actual observations of pseudorange values and the pseudo-range value output by the model Define the error function for pseudorange measurement. As shown in the following formula:

[0156] ;

[0157] In the formula: Error function representing pseudorange measurement The covariance matrix;

[0158] The error in speed measurement is obtained through the following steps:

[0159] Define mobile site The velocity measurement model is shown in the following equation:

[0160] ;

[0161] In the formula: The mobile station representing the output of the velocity measurement model The velocity at epoch t; Indicates mobile station The state at epoch t+1; , and These represent the moving station at epoch t+1. The position is indicated on the x-axis, y-axis, and z-axis; , and These represent the moving station at epoch t. Position on the x-axis, y-axis, and z-axis: This represents the time difference between epoch t and epoch t+1;

[0162] Define mobile site The actual observed velocity is shown in the following formula:

[0163] ;

[0164] In the formula: Indicates mobile station The velocity actually observed at epoch t; This indicates noise associated with velocity measurements;

[0165] Combined with actual observation speed and the speed of model output Define the error function for speed measurement. As shown in the following formula:

[0166] ;

[0167] In the formula: Error function representing speed measurement The covariance matrix;

[0168] Combining the error functions of pseudorange measurement and velocity measurement, the objective function of the factor map is obtained, as shown in the following equation:

[0169] ;

[0170] By continuously adjusting the values ​​of the variable nodes (position, velocity, ambiguity) to minimize the error of the objective function, a result is obtained that includes the position, velocity, and ambiguity of the mobile station. Optimal floating-point solution .

[0171] After obtaining the floating-point solution, the ambiguity needs to be further processed by converting it to integers to obtain the integer ambiguity solution.

[0172] Covariance matrix of fuzzy floating-point solution The correlation is strong and the solution is complex. To simplify the calculation, we first perform a solution operation to resolve the correlation matrix. As shown in the following formula:

[0173] ;

[0174] In the formula: , representing the mean vector of ambiguity;

[0175] For covariance matrix Eigenvalue decomposition is performed to obtain eigenvalues ​​and corresponding eigenvectors. The eigenvectors are then used to transform the ambiguity from the original coordinate system to a new coordinate system, as shown in the following equation:

[0176] ;

[0177] In the formula: The variable represents the ambiguity after discorrelation; v represents the selected eigenvector matrix. This represents the transpose of matrix v;

[0178] Ambiguity after correlation for each solution Construct the matrix H related to the integer ambiguity solution N, as shown in the following equation:

[0179] ;

[0180] In the formula: The standard deviation represents the error;

[0181] The integer ambiguity solution N is obtained by minimizing the following objective function, which is shown in the following equation:

[0182] .

[0183] In ambiguity resolution, multiple candidate integer ambiguity solutions exist. To verify the reliability of the final determined fixed ambiguity solution, a combination of residual ratio verification and bootstrapping verification is used. First, the ambiguity resolution results are preliminarily evaluated through residual ratio verification. Residual ratio verification judges the reliability of the optimal solution by comparing the difference between the optimal ambiguity solution and the second-best ambiguity solution. When the error of the optimal solution is significantly smaller than the error of the second-best solution, the residual ratio will exceed a preset threshold of 2.0. At this point, the difference between the optimal solution and other candidate solutions is considered sufficiently large, and the resolution result is reliable.

[0184] Based on the residual ratio verification, bootstrapping verification is further employed to evaluate the stability of ambiguity resolution. Bootstrapping verification generates multiple new candidate ambiguity solutions by applying random perturbations to the floating-point ambiguity solutions, and then integerizes these candidate solutions to obtain a new set of resolution results. Subsequently, the stability of the resolution results is judged by comparing the similarity between these newly generated solutions and the optimal ambiguity solution. If most of the newly generated solutions are consistent with the optimal ambiguity solution, the optimal ambiguity solution is considered stable and reliable and can be used as a fixed solution; if the consistency is low, it indicates that there may be errors in the ambiguity resolution and it is not suitable as a fixed solution.

[0185] Through the above two-step verification method, the residual ratio verification quickly screens out the possible optimal ambiguity solution, while the bootstrapping verification further ensures the stability and reliability of the solution under different disturbance conditions, thus finally confirming the fixed solution and providing a strong guarantee for high-precision positioning results.

[0186] Example 2:

[0187] This invention also provides an electronic terminal, characterized in that it includes a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the satellite positioning ambiguity determination method described in Embodiment 1 are executed.

[0188] Example 3:

[0189] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, first implements the steps of the satellite positioning ambiguity determination method described in Embodiment 1 above.

[0190] The computer-readable storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0191] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0192] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0193] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0194] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0195] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for determining ambiguity in satellite positioning, characterized in that, include: The observation data from the base station and the rover station are acquired, and the double difference technique is used to eliminate errors and perform cycle slip correction to obtain the corrected observation data. Construct an error function between the observed values ​​and the model predictions, minimize the error function, and make a preliminary estimate of the speed and position of the mobile station; Based on the corrected observation data, the optimal ambiguity subset is extracted through satellite-level and ambiguity-level filtering; A factor graph model is constructed using the optimal ambiguity subset. The initially estimated speed and position of the mobile station are used as initial values. The error function in the factor graph is minimized to obtain a floating-point solution that includes the position, speed and ambiguity of the mobile station. Based on the floating-point solution, the ambiguity is subjected to decorrelation processing, and combined with the integerization process, the integer ambiguity solution is obtained; The reliability of the integer ambiguity solution is verified by the residual ratio, and multiple solutions are generated by resampling the floating-point solution. The stability of the ambiguity solution result is verified by the consistency, and finally the fixed ambiguity solution is obtained. The extraction of the optimal ambiguity subset based on the corrected observation data, through satellite-level and ambiguity-level filtering, includes: The satellites are divided into subsets based on their elevation and azimuth angles, and one satellite is removed from each subset. The subset with the smallest set precision attenuation factor (GDOP) is then selected. The ambiguity level is determined by performing disambiguation calculations on several ambiguities with the largest ambiguity accuracy attenuation factor (ADOP) in the satellite subset, successively eliminating the ambiguity combination with the largest GDOP, and finally determining the optimal ambiguity subset. The step of constructing a factor graph model using an optimal subset of fuzziness includes: The nodes of the design factor graph include variable nodes and factor nodes; the variable nodes include the position, velocity, and ambiguity of the mobile station; the factor nodes include pseudorange factors and carrier phase factors; through bidirectional connections, the position and ambiguity are constrained by pseudorange factors and carrier phase factors, and the position and velocity are constrained by Doppler factors. The initial estimated speed of the mobile station and location As the initial value for factor graph optimization, the optimal subset of fuzziness is input into the factor graph, and the floating-point solution is obtained through the following steps: Define mobile site The state is as shown in the following formula: ； ； In the formula: Indicates mobile station The set of states for n epochs; n represents the total number of measurement epochs considered in factor graph optimization; Indicates mobile station In the state of epoch t ; Indicates the moving station at epoch t. Location; Indicates the moving station at epoch t. speed; Indicates the moving station at epoch t. Clock deviation; Define satellites and rover stations The pseudorange measurement model is shown in the following equation: ； In the formula: This represents the output of the pseudorange measurement model for satellite 's' and the rover station. The pseudo-distance value at epoch t; This indicates the position of satellite s at epoch t; Define satellites and rover stations The actual observed pseudorange is shown in the following formula: ； In the formula: Indicates satellite s and rover station The pseudorange value actually observed at epoch t; Indicates and Related noise; Combined with actual observations of pseudorange values and the pseudo-range value output by the model Define the error function for pseudorange measurement. As shown in the following formula: ； In the formula: Error function representing pseudorange measurement The covariance matrix; Define mobile site The velocity measurement model is shown in the following equation: ； In the formula: The mobile station representing the output of the velocity measurement model The velocity at epoch t; Indicates mobile station The state at epoch t+1; , and These represent the moving station at epoch t+1. Position on the x-axis, y-axis, and z-axis; , and These represent the moving station at epoch t. Position on the x-axis, y-axis, and z-axis: This represents the time difference between epoch t and epoch t+1; Define mobile site The actual observed velocity is shown in the following formula: ； In the formula: Indicates mobile station The velocity actually observed at epoch t; This indicates noise associated with velocity measurements; Combined with actual observed speed and the speed of model output Define the error function for speed measurement. As shown in the following formula: ； In the formula: Error function representing speed measurement The covariance matrix; Combining the error functions of pseudorange measurement and velocity measurement, the objective function of the factor map is constructed as follows: ； Solve for the optimal solution of the objective function, and output the mobile station at epoch t using factor graph optimization. Optimal floating-point solution As shown in the following formula: ； The optimal floating-point solution Includes the location, speed, and ambiguity of the mobile station. .

2. The ambiguity determination method for satellite positioning according to claim 1, characterized in that, Acquire observation data from the base station and the rover, including: Satellite signal data, including pseudorange, carrier phase, and Doppler effect data, are acquired from the base station and the rover station. The distance from the satellite to the rover station is estimated by pseudorange measurement, the distance is accurately calculated by carrier phase measurement, and the speed of the rover station is estimated by Doppler measurement. The formula for pseudorange measurement is shown below: ； In the formula: It is a pseudorange, representing the estimated distance from the satellite to the rover station; Represents the speed of light; Indicates the time when the mobile station received the satellite signal; Indicates the time when the satellite transmitted the signal; This indicates the error in pseudorange measurement; The formula for carrier phase measurement is as follows: ； In the formula: It is the carrier phase, which indicates a more precise distance from the satellite to the mobile station; Indicates the ambiguity of the integer period. Indicates the wavelength of the carrier wave; This indicates the error in carrier phase measurement; The formula for the Doppler measurement is shown below: ； In the formula: Indicates the frequency of the received wave; Indicates the frequency of the transmitted wave; This indicates the velocity of the mobile station relative to the wave source; This indicates the velocity of the wave source relative to the propagation medium; Errors in pseudorange measurement This includes atmospheric delay and clock errors caused by inconsistencies between the rover and satellite time. The double-difference technique is used to eliminate these errors, including: First, clock skew at the rover station is eliminated using single-difference, where single-difference represents the difference between the observations of the same satellite at the base station. and mobile station The difference is calculated between the two values, and the simple difference formula is shown below: ； In the formula: and Representing the base station and mobile station Pseudorange measurements of the satellite; Based on single-difference, double-difference is then used to recalibrate the base station. and mobile station The observed values ​​are differencing to further eliminate atmospheric delay and satellite clock errors. The double-difference formula is shown below: ； In the formula: and Representing the base station and mobile station For satellite The pseudorange measurement value; and Representing the base station and mobile station For satellite The pseudorange measurement value; Indicates the base station and mobile station For satellite The single difference; Indicates the base station and mobile station For satellite The single difference.

3. The ambiguity determination method for satellite positioning according to claim 1, characterized in that, Cycle slip correction is applied to the observation data to obtain the corrected observation data, including: Calculate the phase difference between adjacent epochs As shown in the following formula: ； In the formula: This represents the carrier phase observation value at the current epoch; This represents the carrier phase observation value from the previous epoch; By comparing the phase changes across consecutive epochs, a threshold is set as the criterion for determining whether a phase abrupt change has occurred; if the phase difference... If the value exceeds the threshold and meets the integer cycle jump characteristics, a cycle slip is determined to have occurred; the detected cycle slip data is corrected to obtain the corrected observation data.

4. The ambiguity determination method for satellite positioning according to claim 3, characterized in that, Constructing an error function between observed values ​​and model predictions, minimizing this error function, and initially estimating the velocity and location of the mobile station include: Define the prediction model as shown in the following equation: ； In the formula: Indicates the epoch The location of the mobile station predicted by the model; Indicates speed; Indicates position offset; Combining n epochs Model predictions and the actual observed location of the mobile station The error function is constructed to minimize the error between the observed values ​​and the model predictions, as shown in the following equation: ； In the formula: Represents each epoch At that time, the model predicted the location of the mobile station. Compared with the actual observed location of the mobile station Deviation between; The optimal solution of the error function was obtained using the LDLT decomposition method. .

5. The ambiguity determination method for satellite positioning according to claim 1, characterized in that, Based on the floating-point solution, the ambiguity is subjected to decorrelation processing, and combined with the integerization process, the integer ambiguity solution is obtained, including: Ambiguity To perform discorrelation, which converts the originally correlated ambiguities into uncorrelated patterns, the covariance matrix is ​​first calculated. As shown in the following formula: ； In the formula: , representing the mean vector of ambiguity; For covariance matrix Eigenvalue decomposition is performed to obtain eigenvalues ​​and corresponding eigenvectors. The eigenvectors are then used to transform the ambiguity from the original coordinate system to a new coordinate system, as shown in the following equation: ； In the formula: The variable represents the ambiguity after discorrelation; v represents the selected eigenvector matrix. This represents the transpose of matrix v; Ambiguity after correlation for each solution Construct the matrix H related to the integer ambiguity solution N, as shown in the following equation: ； In the formula: The standard deviation represents the error; The integer ambiguity solution N is obtained by minimizing the following objective function, which is shown in the following equation: 。 6. The ambiguity determination method for satellite positioning according to claim 5, characterized in that, The reliability of the integer ambiguity solution is verified by residual ratio, and multiple solutions are generated by resampling the floating-point solution. The stability of the ambiguity solution results is verified by consistency, including: After obtaining the integer ambiguity solution N, its reliability is verified by the residual ratio R-ratio function. When the R-ratio value is greater than the preset threshold, N is accepted as the optimal solution. Ambiguity Random perturbation resampling is performed to generate multiple new integer ambiguity solutions. The stability of the optimal solution is verified by comparing whether these solutions are consistent with the optimal solution. When the consistency meets the preset conditions, the optimal solution is determined as the final fixed ambiguity solution.

7. An electronic terminal, characterized in that, The system includes a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the satellite positioning ambiguity determination method as described in any one of claims 1 to 6 are performed.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the satellite positioning ambiguity determination method according to any one of claims 1 to 6.

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