Ambiguity determination method for satellite positioning, terminal and medium

Abstract

The invention discloses an ambiguity determination method for satellite positioning, a terminal and a medium in the field of satellite navigation and positioning, and the method comprises the steps: obtaining observation data of a base station and a mobile station, eliminating errors through employing a double-difference technology, and carrying out the cycle slip correction, and obtaining the corrected observation data; preliminarily estimating the speed and position of the mobile station; based on the corrected observation data, extracting an optimal ambiguity subset through satellite-level and ambiguity-level screening; constructing a factor graph model by using the optimal ambiguity subset, taking the preliminarily estimated speed and position of the mobile station as initial values, minimizing an error function in a factor graph, and optimizing to obtain a floating solution of ambiguity; obtaining an integer ambiguity solution based on the floating point solution; and verifying the stability of an ambiguity resolving result through consistency, and finally obtaining an ambiguity fixed solution. According to the method provided by the invention, high precision, high efficiency and high stability of ambiguity calculation are realized, and the method is suitable for a high-precision satellite positioning system in a complex environment.

Description

Technical Field

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

[0002] Satellite positioning technology is a core technology in modern navigation and geographic information systems, and is widely used in fields such as surveying and mapping, agriculture, autonomous driving, and UAV navigation. Traditional satellite positioning systems can provide positioning accuracy at the meter level, but for application scenarios such as autonomous driving and high-precision surveying and mapping, the meter-level accuracy is far from sufficient. To meet this demand, the need for high-precision positioning technology is becoming increasingly urgent. With the application requirements of high-speed mobile devices, comprehensive requirements are put forward for high-precision positioning solutions in terms of processing time limit, accuracy, and computing resources of the receiver. Exploring high-performance and high-precision positioning solutions is one of the efforts in the development of satellite positioning technology.

[0003] Currently, high-precision ranging and satellite positioning are generally achieved through carrier phase positioning. However, in carrier phase positioning, the integer ambiguity needs to be determined, and high-precision ranging and satellite positioning can be achieved only when the integer ambiguity is reliable. The existing technology cannot calculate and determine the integer ambiguity well, which affects the accuracy of satellite positioning. Summary of the Invention

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

[0005] To achieve the above object, the present invention is implemented by the following technical solutions:

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

[0007] Obtain the observation data of the reference station and the mobile station, use the double-difference technique to eliminate errors and perform cycle slip correction to obtain the corrected observation data;

[0008] Construct an error function between the observed value and the model predicted value, minimize the error function, and initially estimate the speed and position of the mobile station;

[0009] Based on the corrected observation data, extract the optimal ambiguity subset through satellite-level and ambiguity-level screening;

[0010] Use the optimal ambiguity subset to construct a factor graph model, use the initially estimated speed and position of the mobile station as the initial value, minimize the error function in the factor graph, and optimize to obtain a floating-point solution including the position, speed, and ambiguity of the mobile station;

[0011] Based on the floating-point solution, decorrelate the ambiguity and combine it with the integerization process to obtain the integer ambiguity solution;

[0012] Verify the reliability of the integer ambiguity solution through the residual ratio, resample the floating-point solution to generate multiple solutions, and verify the stability of the ambiguity resolution result through consistency, and finally obtain the fixed ambiguity solution.

[0013] Furthermore, obtain the observation data of the reference station and the mobile station, including:

[0014] Obtain satellite signal data from the reference station and the mobile station, including pseudorange, carrier phase, and Doppler effect data; estimate the distance from the satellite to the mobile station through pseudorange measurement, accurately calculate the distance using carrier phase measurement, and deduce the speed of the mobile station through Doppler measurement;

[0015] The formula for the pseudorange measurement is as follows:

[0016] ;

[0017] In the formula: is the pseudorange, representing the estimated distance from the satellite to the mobile station; represents the speed of light; represents the time when the mobile station receives the satellite signal; represents the time when the satellite transmits the signal; represents the error in the pseudorange measurement;

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

[0019] ;

[0020] In the formula: is the carrier phase, representing the more accurate distance from the satellite to the mobile station; represents the integer ambiguity, represents the wavelength of the carrier; represents the error in the carrier phase measurement;

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

[0022] ;

[0023] In the formula: represents the frequency of the received wave; represents the frequency of the transmitted wave; represents the speed of the mobile station relative to the wave source; represents the speed of the wave source relative to the propagation medium;

[0024] Error in pseudorange measurement Including atmospheric delay and clock errors caused by the inconsistency between the mobile station and satellite time, and using the double-difference technique to eliminate the errors, including:

[0025] First, eliminate the clock bias of the mobile station through single-difference. The single-difference represents the observed values of the same satellite, and is obtained by taking the difference between the reference station and the mobile station The single-difference formula is shown as follows:

[0026] ;

[0027] In the formula: and respectively represent the pseudorange measurement values of the reference station and the mobile station for the satellite;

[0028] Based on the single-difference, further take the difference between the observed values of the reference station and the mobile station through double-difference to further eliminate the atmospheric delay and satellite clock errors. The double-difference formula is shown as follows:

[0029] ;

[0030] In the formula: and respectively represent the pseudorange measurement values of the reference station and the mobile station for the satellite ; and respectively represent the pseudorange measurement values of the reference station and the mobile station for the satellite ; represents the single-difference of the reference station and the mobile station for the satellite ; represents the single-difference of the reference station and the mobile station for the satellite ;

[0031] Furthermore, perform cycle slip correction on the observed data to obtain the corrected observed data, including:

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

[0033] ;

[0034] In the formula: Represents the carrier phase observation value of the current epoch; Represents the carrier phase observation value of the previous epoch;

[0035] By comparing the phase changes of consecutive epochs, a threshold is set as the criterion for judging whether a phase mutation occurs; if the phase difference exceeds the threshold and conforms to the characteristics of cycle slips, it is determined that a cycle slip has occurred; the detected cycle slip data is corrected to obtain the corrected observation data.

[0036] Furthermore, an error function between the observation value and the model prediction value is constructed, and the error function is minimized to preliminarily estimate the speed and position of the mobile station, including:

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

[0038] ;

[0039] In the formula: Represents the position of the mobile station predicted by the model at epoch ; Represents the speed; Represents the position offset;

[0040] Combined with the model prediction values at n epochs and the actually observed position of the mobile station , construct an error function to minimize the error between the observation value and the model prediction value, as shown in the following formula:

[0041] ;

[0042] In the formula: Represents the deviation between the position of the mobile station predicted by the model at each epoch and the actually observed position of the mobile station ;

[0043] Use the LDLT decomposition method to solve the optimal solution of the error function.

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

[0045] At the satellite level, divide the satellite subset according to the satellite elevation angle and azimuth angle, remove one satellite from the subset, and select the satellite subset with the smallest geometric dilution of precision GDOP;

[0046] The ambiguity level determines the optimal ambiguity subset by performing disambiguation calculations on several ambiguities with the largest Ambiguity Dilution of Precision (ADOP) in the satellite subset, and successively eliminating the ambiguity combinations with the largest Geometric Dilution of Precision (GDOP).

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

[0048] Design the nodes of the factor graph, including variable nodes and factor nodes; the variable nodes include the position, speed, and ambiguity of the mobile station; the factor nodes include the pseudorange factor and the carrier phase factor; through bidirectional connection, the position and ambiguity are constrained using the pseudorange factor and the carrier phase factor, and the position and speed are constrained using the Doppler factor;

[0049] Take the preliminarily estimated speed and position of the mobile station as the initial values for factor graph optimization, input the optimal ambiguity subset into the factor graph, and obtain the floating-point solution through the following steps:

[0050] Define the state of the mobile station as shown in the following equation:

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

[0052] ;

[0053] In the formula: represents the set of states of the mobile station at n epochs; n represents the total number of measurement epochs considered in factor graph optimization; represents the state of the mobile station at epoch t, ; represents the position of the mobile station at epoch t; represents the speed of the mobile station at epoch t; represents the clock bias of the mobile station at epoch t;

[0054] Define the pseudorange measurement model between satellite s and the mobile station as shown in the following equation:

[0055] ;

[0056] In the formula: represents the pseudorange value between satellite s and the mobile station output by the pseudorange measurement model at epoch t; represents the position of satellite s at epoch t;

[0057] Define the pseudo-range actually observed between satellite s and the mobile station as shown in the following equation:

[0058] ;

[0059] In the formula: represents the pseudo-range value actually observed between satellite s and the mobile station at epoch t; represents the noise related to ;

[0060] Combining the actually observed pseudo-range value and the pseudo-range value output by the model define the error function of pseudo-range measurement as shown in the following equation:

[0061] ;

[0062] In the formula: represents the covariance matrix of the error function of pseudo-range measurement;

[0063] Define the velocity measurement model of the mobile station as shown in the following equation:

[0064] ;

[0065] In the formula: represents the velocity of the mobile station output by the velocity measurement model at epoch t; represents the state of the mobile station at epoch t + 1; , and respectively represent the position representations of the mobile station on the x-axis, y-axis, and z-axis at epoch t + 1; , and respectively represent the position representations of the mobile station on the x-axis, y-axis, and z-axis at epoch t: represents the time difference between epoch t and epoch t + 1;

[0066] Define the actually observed velocity of the mobile station as shown in the following equation:

[0067] ;

[0068] In the formula: represents the mobile station The velocity actually observed at epoch t; Denotes the noise associated with the velocity measurement;

[0069] Combined with the actually observed velocity and the velocity output by the model , define the error function of the velocity measurement , as shown in the following formula:

[0070] ;

[0071] In the formula: Denotes the covariance matrix of the error function of the velocity measurement;

[0072] Combined with the error function of the pseudorange measurement and the error function of the velocity measurement, construct the objective function of the factor graph, as shown in the following formula:

[0073] ;

[0074] Solve the optimal solution of the said objective function, and the factor graph optimization outputs the optimal floating-point solution of the rover at epoch t , as shown in the following formula:

[0075] ;

[0076] The said optimal floating-point solution includes the position, velocity and ambiguity of the rover .

[0077] Furthermore, based on the floating-point solution, perform decorrelation processing on the ambiguity, and combine the integerization process to obtain the integer ambiguity solution, including:

[0078] Perform decorrelation on the ambiguity , convert the originally correlated ambiguities into an uncorrelated pattern, first calculate the covariance matrix , as shown in the following formula:

[0079] ;

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

[0081] Perform eigenvalue decomposition on the covariance matrix , obtain the eigenvalues and the corresponding eigenvectors, and use the eigenvectors to transform the ambiguity from the original coordinate system to a new coordinate system, as shown in the following formula:

[0082] ;

[0083] Wherein: represents the ambiguity after decorrelation; v represents the selected eigenvector matrix; represents the transpose of matrix v;

[0084] For each ambiguity after decorrelation , construct a matrix H related to the integer ambiguity solution N as shown in the following formula:

[0085] ;

[0086] Wherein: represents the standard deviation of the error;

[0087] By minimizing the following objective function, the integer ambiguity solution N is obtained, and the objective function is as shown in the following formula:

[0088] .

[0089] Furthermore, the reliability of the integer ambiguity solution is verified by the residual ratio, and the floating-point solution is resampled to generate multiple solutions. The stability of the ambiguity resolution result 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] For the 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] In a second aspect, the present invention provides an electronic terminal, including a processor and a memory connected to the processor. A computer program is stored in the memory. When the computer program is executed by the processor, the steps of the above-mentioned method for determining the ambiguity of satellite positioning are performed.

[0093] In a third aspect, the present invention provides a computer-readable storage medium, on which a computer program is stored. The program is characterized in that when it is executed by a processor, the steps of the above-mentioned method for determining the ambiguity of satellite positioning are implemented.

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

[0095] The satellite positioning ambiguity determination method provided by the present invention can effectively correct the errors in the observed data and improve the positioning accuracy by eliminating errors and performing cycle slip correction through the double-difference technique. By using the optimal ambiguity subset screening strategy, the computational complexity in the ambiguity resolution process can be significantly reduced, and the resolution efficiency can be improved. By introducing the factor graph optimization technique, the ambiguity resolution problem is modeled as an optimization problem. With the factor graph model as the core, an error function between the observed data and the model prediction value is constructed, and the mutual constraints among the observed values such as pseudorange, carrier phase, and Doppler are fully utilized, so as to simultaneously optimize the position, speed, and ambiguity variables of the mobile station, greatly improving the accuracy and efficiency of the resolution. Through the residual ratio verification and the Bootstrapping resampling consistency test, the reliability of the ambiguity resolution result is fully verified, and finally a stable and reliable ambiguity fixed solution is obtained.

[0096] The method of the present invention can provide higher-precision and more stable positioning results in complex environments, and is applicable to real-time and high-precision satellite positioning systems, especially applicable to dynamic tracking and large-scale application scenarios. Brief Description of the Drawings

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

[0098] The technical solution of the present invention will be described in detail below through the drawings and specific embodiments. It should be understood that the specific features in the embodiments of the present application and the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations on the technical solution of the present application. Without conflict, the technical features in the embodiments of the present application and the embodiments can be combined with each other.

[0099] Embodiment 1:

[0100] Figure 1 It is a flowchart of the satellite positioning ambiguity determination method in Embodiment 1 of the present invention. This flowchart only shows the logical order of the method described in this embodiment. On the premise of non-conflict, in other possible embodiments of the present invention, the steps shown or described can be completed in a different order from Figure 1 that shown. Referring to Figure 1 , the method of this embodiment specifically includes the following steps:

[0101] Obtain the observed data of the reference station and the mobile station, eliminate errors and perform cycle slip correction using the double-difference technique to obtain the corrected observed data;

[0102] Construct an error function between the observed value and the model prediction value, minimize the error function, and initially estimate 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 screening;

[0104] Using the optimal ambiguity subset to construct a factor graph model, with the preliminarily estimated rover speed and position as initial values, minimize the error function in the factor graph, and optimize to obtain a floating-point solution including the rover position, speed, and ambiguity;

[0105] Based on the floating-point solution, perform decorrelation processing on the ambiguity, and combine the integerization process to obtain the integer ambiguity solution;

[0106] Verify the reliability of the integer ambiguity solution through the residual ratio, resample the floating-point solution to generate multiple solutions, and verify the stability of the ambiguity solution result through consistency, and finally obtain the ambiguity fixed solution.

[0107] In this embodiment, in order to verify the effectiveness of the method, a standard positioning data set in network RTK (Real-Time Kinematic) positioning is used as the experimental data source. The selection of the data set in this embodiment is not limited, and public or custom data sets can be selected according to actual needs. For example, the RTKLIB data set is used, which contains observation data in various environments, namely urban environments (urban38 and urban39), campus environment (campus), and building environment (building), with a total of 8000 samples. In each scenario, the time lengths of the positioning data are 2154 seconds, 856 seconds, 950 seconds, and 1820 seconds respectively, and the corresponding trajectory lengths are 11191 meters, 10678 meters, 1337 meters, and 2560 meters. The satellite systems support GPS and Beidou, and the measurement values used include pseudorange, carrier phase, and Doppler measurements, and the data is organized in batch windows.

[0108] In practical applications, the reference station and the rover of the selected data set respectively provide observation data, including pseudorange, Doppler frequency change, and carrier phase measurement values. 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 calculation.

[0109] First, calculate the propagation time of the satellite signal through pseudorange measurement to estimate the distance between the satellite and the rover. Since the pseudorange is usually an estimated value containing errors, its measurement accuracy is affected by factors such as atmospheric delay and clock bias. The formula for pseudorange measurement is as follows:

[0110] ;

[0111] In the formula: is the pseudorange, representing the estimated distance from the satellite to the rover; represents the speed of light; Indicates the time when the mobile station receives the satellite signal; Indicates the time when the satellite transmits the signal; Indicates the error in pseudorange measurement;

[0112] After obtaining the estimated distance between the satellite and the mobile station Further calculate the change in carrier phase, and by virtue of the high-frequency characteristics of the carrier signal, achieve high-precision measurement of the distance between the mobile station and the satellite. The formula for carrier phase measurement is as follows:

[0113] ;

[0114] In the formula: Is the carrier phase, indicating a more accurate distance from the satellite to the mobile station; Indicates the integer ambiguity, Indicates the wavelength of the carrier; Indicates the error in carrier phase measurement;

[0115] In addition, according to the principle of the Doppler effect, when the wave source approaches the mobile station, the frequency of the received signal will increase and the wavelength will become shorter; when the wave source moves away from the mobile station, the frequency of the received signal will decrease and the wavelength will become longer. Therefore, by observing the Doppler frequency shift, the speed of the mobile station relative to the satellite can be estimated. The formula for Doppler measurement is as follows:

[0116] ;

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

[0118] The error in pseudorange measurement Includes atmospheric delay and clock error caused by the time inconsistency between the mobile station and the satellite. The double-difference technique is used to eliminate the error, including:

[0119] First, eliminate the clock bias of the mobile station through single-difference. Single-difference represents the observed values of the same satellite, and perform differencing between the reference station and the mobile station The single-difference formula is as follows:

[0120] ;

[0121] In the formula: and respectively represent the pseudorange measurement values of the satellite by the reference station and the mobile station ;

[0122] Based on the single difference, the double difference is further used to perform differencing on the observation values of the reference station and the mobile station to further eliminate the atmospheric delay and the satellite clock error. The double difference formula is shown as follows:

[0123] ;

[0124] In the formula: and respectively represent the pseudorange measurement values of the reference station and the mobile station for the satellite ; and respectively represent the pseudorange measurement values of the reference station and the mobile station for the satellite ; represents the single difference of the reference station and the mobile station for the satellite ; represents the single difference of the reference station and the mobile station for the satellite .

[0125] Since the satellite signal will cause a sudden jump in data after being blocked or reflected, in this embodiment, after eliminating the atmospheric delay and the clock error through the double difference technology, the cycle slip correction is further performed to eliminate the 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: represents the carrier phase observation value of the current epoch; represents the carrier phase observation value of the previous epoch;

[0129] By comparing the phase changes of consecutive epochs, a threshold is set as the criterion for judging whether a phase mutation occurs; if the phase difference exceeds the threshold and conforms to the characteristics of cycle slips, it is determined that a cycle slip has 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 parameter is a class instance used to encapsulate the pseudorange, carrier phase, and Doppler measurement data processed by the double-difference technique; the second parameter is a preset threshold for phase mutation, used to detect the phase mutation between two adjacent epochs, that is, whether there is a cycle slip phenomenon. Inside the function, the weighted moving average algorithm is called for data smoothing, and the window size of the smoothing algorithm is set. If the change amount between two adjacent sets of data is detected to exceed the preset threshold, these data are smoothly corrected using the algorithm. Finally, the function returns the corrected observation data for subsequent processing.

[0131] Next, the moving speed of the mobile station is further estimated. The moving speed is a key variable in the positioning calculation, and the accuracy of the speed estimation directly affects the accuracy of the overall positioning result. For this purpose, this embodiment constructs an error function to measure the difference between the model prediction value (the value calculated based on mathematical formulas) and the actual observation value, as follows:

[0132] ;

[0133] where ; represents the position of the mobile station predicted by the model at epoch ; represents the speed; represents the position offset; represents the actually observed position of the mobile station; represents at each epoch the position of the mobile station predicted by the model and the actually observed position of the mobile station the deviation between them;

[0134] By adjusting the speed and the position offset , making the sum of squared errors as small as possible, thereby optimizing the model prediction value to make it more consistent with the actual observation data. In this embodiment, the LDLT decomposition method is used to quickly solve the optimal solution of the error function, and finally the optimal solution including the speed and the position offset is obtained.

[0135] In satellite positioning, ambiguity resolution is a crucial step in positioning, and the accuracy depends on whether the selected satellite data is of high quality. However, if all satellite signals are processed, the computational amount is too large and errors are easily introduced.

[0136] Therefore, in this embodiment, in order to improve the ambiguity positioning rate and reduce the computational complexity of ambiguity resolution, an optimal ambiguity subset screening method based on a partial ambiguity algorithm is proposed. This method is divided into two levels: satellite-level screening and ambiguity-level screening, gradually optimizing and screening out a high-quality ambiguity subset for subsequent resolution.

[0137] First, in the satellite-level screening stage, all satellite signals are preliminarily screened according to the satellite elevation angle and azimuth angle. For high-elevation satellites (exceeding 90°), their data is preferentially considered as candidate signals to make full use of satellites with higher signal quality. Within the azimuth angle range (0° to 360°), all satellites are divided into four subsets, denoted as Q1, Q2, Q3, and Q4 respectively, and each subset represents a group of satellites in one azimuth. Subsequently, one satellite is removed from each subset, and the geometric dilution of precision (GDOP) of the subset after removal is calculated. By comparing the magnitudes of the GDOPs, the combination with the smallest GDOP is selected to construct a preliminary subset H1 containing high-quality satellite signals.

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

[0139] 1. After eliminating the ambiguity of and , calculate the GDOP1 value of the remaining satellites;

[0140] 2. After eliminating the ambiguity of and , calculate the GDOP2 value of the remaining satellites;

[0141] 3. After eliminating the ambiguity of and , calculate the GDOP3 value of the remaining satellites.

[0142] Finally, by comparing the magnitudes 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, finally obtaining the optimal ambiguity subset for subsequent factor graph optimization.

[0143] This method significantly reduces the resolution variables through hierarchical screening, improves the efficiency and accuracy of ambiguity resolution, and provides a reliable data basis for subsequent positioning and navigation calculations.

[0144] Next, a mathematical model is constructed through factor graph optimization, and the position, velocity, and ambiguity solutions of the mobile station 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. Among them, 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 connection, 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, the state of the mobile station is defined as shown in the following formula:

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

[0148] ;

[0149] In the formula: represents the state set of the mobile station at n epochs; n represents the total number of measurement epochs considered in the factor graph optimization; represents the state of the mobile station at epoch t, ; represents the position of the mobile station at epoch t; represents the velocity of the mobile station at epoch t; represents the clock bias of the mobile station at epoch t;

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

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

[0152] Define the actually observed pseudorange between satellite s and the mobile station as shown in the following formula:

[0153] ;

[0154] In the formula: represents the actually observed pseudorange value between satellite s and the mobile station at epoch t; represents the noise related to ;

[0155] Combined with the actually observed pseudorange value and the pseudorange value output by the model , define the error function of pseudorange measurement , as shown in the following formula:

[0156] ;

[0157] In the formula: represents the covariance matrix of the error function of pseudorange measurement;

[0158] The error of velocity measurement is obtained through the following steps:

[0159] Define the velocity measurement model of the rover , as shown in the following formula:

[0160] ;

[0161] In the formula: represents the velocity of the rover output by the velocity measurement model at epoch t; represents the state of the rover at epoch t + 1; , and respectively represent the positions of the rover on the x-axis, y-axis and z-axis at epoch t + 1; , and respectively represent the positions of the rover on the x-axis, y-axis and z-axis at epoch t: represents the time difference between epoch t and epoch t + 1;

[0162] Define the actually observed velocity of the rover , as shown in the following formula:

[0163] ;

[0164] In the formula: represents the actually observed velocity of the rover at epoch t; represents the noise related to velocity measurement;

[0165] Combining the actually observed velocity and the velocity output by the model , define the error function of velocity measurement , as shown in the following formula:

[0166] ;

[0167] Wherein: represents the error function of speed measurement and the covariance matrix of;

[0168] By combining the error function of pseudorange measurement and the error function of speed measurement, the objective function of the factor graph is obtained as shown in the following equation:

[0169] ;

[0170] Continuously adjust the values of the variable nodes (position, speed, ambiguity) to minimize the error of the objective function, thereby obtaining the position, speed, and ambiguity of the mobile station and the optimal floating-point solution .

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

[0172] The covariance matrix of the floating-point solution of the ambiguity has strong correlation and is complex to solve. To simplify the calculation, a decorrelation operation is first performed, and the covariance matrix is as shown in the following equation:

[0173] ;

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

[0175] Perform eigenvalue decomposition on the covariance matrix to obtain the eigenvalues and corresponding eigenvectors, and use the eigenvectors to transform the ambiguity from the original coordinate system to a new coordinate system as shown in the following equation:

[0176] ;

[0177] Wherein: represents the ambiguity after decorrelation; v represents the selected eigenvector matrix; represents the transpose of matrix v;

[0178] For each ambiguity after decorrelation, construct a matrix H related to the integer ambiguity solution N as shown in the following equation:

[0179] ;

[0180] Wherein: represents the standard deviation of the error;

[0181] By minimizing the following objective function, the integer ambiguity solution N is obtained, and the objective function is as shown in the following equation:

[0182] 。

[0183] In ambiguity resolution, there are multiple candidate integer ambiguity solutions. To verify the reliability of the finally determined fixed ambiguity solution, a method combining residual ratio check and Bootstrapping verification is adopted. First, the residual ratio check is used to preliminarily evaluate the ambiguity resolution result. The residual ratio check determines the reliability of the optimal solution by comparing the differences between the optimal ambiguity solution and the sub-optimal ambiguity solution. When the error of the optimal solution is significantly smaller than that of the sub-optimal solution, the residual ratio value will exceed the preset threshold of 2.0. At this time, it is considered that the difference between the optimal solution and other candidate solutions is large enough, and the resolution result is credible.

[0184] Based on the residual ratio check, Bootstrapping verification is further used to evaluate the stability of the ambiguity resolution. Bootstrapping verification generates multiple new ambiguity candidate solutions by applying random perturbations to the floating-point ambiguity solution, and performs integerization processing on these candidate solutions, thereby obtaining a new set of resolution results. Subsequently, the stability of the resolution result 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, it is considered that the optimal ambiguity solution is stable and reliable and can be used as the fixed solution; if the consistency is low, it indicates that there may be errors in the ambiguity resolution and it is not suitable as the fixed solution.

[0185] Through the above two-step verification method, the residual ratio check quickly screens out the possible optimal ambiguity solution, and Bootstrapping verification further ensures the stability and reliability of the resolution result under different perturbation conditions, thereby finally confirming the fixed solution and providing a strong guarantee for the high-precision positioning result.

[0186] Embodiment 2:

[0187] The embodiment of the present invention also provides an electronic terminal, which is characterized in that it includes a processor and a memory connected to the processor. A computer program is stored in the memory. When the computer program is executed by the processor, the steps of the method for determining the ambiguity of satellite positioning described in Embodiment 1 above are executed.

[0188] Embodiment 3:

[0189] The embodiment of the present invention also provides a computer-readable storage medium, on which a computer program is stored. When the program is executed by a processor, the steps of the method for determining the ambiguity of satellite positioning described in Embodiment 1 above are first implemented.

[0190] The computer-readable storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard disks, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical discs.

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

[0192] The present application is described with reference to the flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, and the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate a device for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0193] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including an instruction device, and the instruction device implements the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0194] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0195] The above are only the preferred embodiments of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the technical principle of the present invention, several improvements and modifications can be made, and these improvements and modifications should also be regarded as the protection scope of the present invention.

Claims

1. A method for determining ambiguity of satellite positioning, characterized in that: include: Obtain observation data from the base station and mobile station, use double difference technology to eliminate errors and perform cycle slip correction to obtain corrected observation data; Constructing an error function between the observed value and the model predicted value, minimizing the error function, and preliminarily estimating 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 screening; The optimal ambiguity subset is used to construct a factor graph model, and the initially estimated mobile station speed and position are used as initial values ​​to minimize the error function in the factor graph, and the floating-point solution including the mobile station position, speed and ambiguity is obtained through optimization. Based on the floating point solution, the ambiguity is decorrelated and combined with the integerization process to obtain the integer ambiguity solution; The reliability of the integer ambiguity solution is verified by the residual ratio, and the floating-point solution is resampled to generate multiple solutions. The stability of the ambiguity resolution result is verified by consistency, and finally the ambiguity fixed solution is obtained.

2. The satellite positioning ambiguity determination method according to claim 1, characterized in that: Obtain observation data from base stations and rover stations, including: Obtain satellite signal data from the base station and the mobile station, including pseudorange, carrier phase and Doppler effect data; estimate the distance from the satellite to the mobile station through pseudorange measurements, accurately calculate the distance using carrier phase measurements, and infer the speed of the mobile station through Doppler measurements; The formula for the pseudorange measurement is as follows: ； Where: is the pseudorange, which represents the estimated distance from the satellite to the mobile station; represents the speed of light; Indicates the time when the mobile station receives the satellite signal; Indicates the time when the satellite transmits the signal; represents the error in pseudorange measurement; The carrier phase measurement formula is as follows: ； Where: is the carrier phase, indicating a more precise distance from the satellite to the mobile station; represents the integer ambiguity, Indicates the wavelength of the carrier; represents the error in the carrier phase measurement; The Doppler measurement formula is as follows: ； Where: Indicates the frequency of the received wave; Indicates the frequency of the transmitted wave; represents the speed of the mobile station relative to the wave source; It represents the speed of the wave source relative to the propagation medium; Errors in Pseudorange Measurements Including atmospheric delay and clock error caused by inconsistency between mobile station and satellite time, the double difference technique is used to eliminate the error, including: First, the clock bias of the mobile station is eliminated by single difference. The single difference represents the observation value of the same satellite. and mobile stations The difference is performed between them, and the single difference formula is as follows: ； Where: and Represents the base station and mobile stations Pseudorange measurements to satellites; Based on the single difference, the reference station is adjusted by double difference. and mobile stations The observation values ​​are differentiated to further eliminate the atmospheric delay and the satellite clock error. The double difference formula is as follows: ； Where: and Represents the base station and mobile stations Satellite Pseudorange measurement value of ; and Represents the base station and mobile stations Satellite Pseudorange measurement value of ; Indicates the base station and mobile stations Satellite The single difference of Indicates the base station and mobile stations Satellite The single difference.

3. The satellite positioning ambiguity determination method according to claim 1, characterized in that: Perform cycle slip correction on the observed data to obtain corrected observed data, including: Calculate the phase difference between adjacent epochs , as shown below: ； Where: Represents the carrier phase observation value of the current epoch; Represents the carrier phase observation value of the previous epoch; By comparing the phase changes of consecutive epochs, a threshold is set as a criterion for judging whether a phase mutation occurs; if the phase difference If the value exceeds the threshold and meets the cycle jump characteristics, it is determined that a cycle slip occurs; and the detected cycle slip data is corrected to obtain corrected observation data.

4. The satellite positioning ambiguity determination method according to claim 3, characterized in that: Constructing an error function between the observed value and the model predicted value, minimizing the error function, and preliminarily estimating the speed and position of the mobile station, including: Define the prediction model as shown below: ； Where: Indicates the epoch The position of the mobile station predicted by the above model; Indicates speed; Indicates position offset; Combine n epochs The model predicts the value of and the actual observed mobile station position , construct an error function to minimize the error between the observed value and the model predicted value, as shown in the following formula: ； Where: Indicates each epoch When the model predicts the location of the mobile station Compared with the actual observed mobile station position The deviation between The optimal solution of the error function is solved by LDLT decomposition method .

5. The satellite positioning ambiguity determination method according to claim 4, characterized in that: Based on the corrected observation data, the optimal ambiguity subset is extracted through satellite-level and ambiguity-level screening, including: At the satellite level, satellite subsets are divided according to the satellite elevation angle and azimuth angle, and one satellite in the subset is removed to select the satellite subset with the smallest collective precision reduction factor GDOP; The ambiguity level is determined by performing disambiguation calculation on several ambiguities with the largest ambiguity dilution of precision factor ADOP in the satellite subset, eliminating the ambiguity combination with the largest GDOP in turn, and finally determining the optimal ambiguity subset.

6. The method for determining ambiguity of satellite positioning according to claim 5, characterized in that: The factor graph model is constructed using the optimal fuzzy subset, including: Designing nodes of a factor graph, including variable nodes and factor nodes; the variable nodes include the position, speed and ambiguity of the mobile station; the factor nodes include pseudorange factors and carrier phase factors; through bidirectional connection, using pseudorange factors and carrier phase factors to constrain the position and ambiguity, and using Doppler factors to constrain the position and speed; The initial estimate of the mobile station's speed and location As the initial value of factor graph optimization, the optimal fuzzy subset is input into the factor graph, and the floating point solution is obtained by the following steps: Define Mobile Station The state is as shown below: ； ； Where: Indicates mobile station The state set of n epochs; n represents the total number of measurement epochs considered in factor graph optimization; Indicates mobile station The state at epoch t, ; represents the mobile station at epoch t location; represents the mobile station at epoch t speed; represents the mobile station at epoch t The clock deviation of Definition of satellites and mobile stations The pseudo-range measurement model is as follows: ； Where: The satellite s and the mobile station are represented by the pseudo-range measurement model output Pseudorange value at epoch t; represents the position of satellite s at epoch t; Definition of satellites and mobile stations The actual observed pseudorange is as follows: ； Where: Indicates satellite s and mobile station The actual observed pseudorange value at epoch t; Representation and Correlated noise; Combined with the actual observed pseudorange value And the pseudorange value output by the model , defines the error function of pseudorange measurement , as shown below: ； Where: The error function representing the pseudorange measurement The covariance matrix of Define Mobile Station The speed measurement model is as follows: ； Where: 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 They represent the mobile station at epoch t+1 respectively. Position on the x-, y-, and z-axes; , and They represent the mobile station at epoch t. Position on the x-, y-, and z-axes: Represents the time difference between epoch t and epoch t+1; Define Mobile Station The actual observed speed is shown as follows: ； Where: Indicates mobile station The actual observed velocity at epoch t; represents the noise associated with the velocity measurement; Combined with the actual observed speed and the speed of model output , defines the error function of velocity measurement , as shown below: ； Where: Represents the error function of velocity measurement The covariance matrix of Combining the error function of pseudorange measurement and the error function of velocity measurement, the objective function of the factor graph is constructed as shown in the following formula: ； Solve the optimal solution of the objective function, and optimize the factor graph to output the mobile station at epoch t The optimal floating point solution , as shown below: ； The optimal floating point solution Contains the position, velocity and ambiguity of the mobile station .

7. The satellite positioning ambiguity determination method according to claim 6, characterized in that: Based on the floating point solution, the ambiguity is decorrelated and combined with the integerization process to obtain the integer ambiguity solution, including: For fuzziness To decorrelate, the originally correlated ambiguities are converted into uncorrelated patterns. First, the covariance matrix is ​​calculated , as shown below: ； Where: , represents the mean vector of blur; Covariance matrix Perform eigenvalue decomposition to obtain eigenvalues ​​and corresponding eigenvectors, and use the eigenvectors to transform the ambiguity from the original coordinate system to the new coordinate system, as shown in the following formula: ； Where: represents the ambiguity after decorrelation; v represents the selected eigenvector matrix; represents the transpose of the matrix v; For each decorrelated ambiguity , construct the matrix H related to the integer ambiguity solution N, as shown in the following formula: ； Where: represents the standard deviation of the error; The integer ambiguity solution N is obtained by minimizing the following objective function, which is shown in the following formula: 。 8. The method for determining ambiguity of satellite positioning according to claim 7, characterized in that: The reliability of the integer ambiguity solution is verified by the residual ratio, and the floating point solution is resampled to generate multiple solutions. The stability of the ambiguity resolution result is verified by consistency, including: After the integer ambiguity solution N is obtained, 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. For fuzziness 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 ambiguity fixed solution.

9. An electronic terminal, characterized in that: The method comprises 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 ambiguity determination method for satellite positioning as described in any one of claims 1 to 8 are executed.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the ambiguity determination method for satellite positioning described in any one of claims 1 to 8 are implemented.

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