Beidou multi-frequency positioning method and device, electronic equipment and storage medium

Abstract

The invention provides a Beidou multi-frequency positioning method and device, electronic equipment and a storage medium. The method comprises the following steps: S1, collecting observation data and satellite ephemeris data of two target frequency points of a Beidou satellite; s2, based on the satellite ephemeris data, modeling the Beidou satellite clock correction by adopting a quadratic polynomial to obtain a clock correction modeling error, and taking the clock correction modeling error as a constraint term of an original design matrix to generate a design matrix with clock correction constraint; s3, constructing an observation vector based on the observation data, and substituting the design matrix with the clock error constraint and the observation vector into a TLS resolving model for resolving to obtain a positioning parameter initial value and a corresponding resolving residual error; s4, fitting a mapping relation between the residual error and the noise intensity based on the resolving residual error, generating a weight matrix, and performing weighted updating on the TLS resolving model by using the weight matrix to obtain an updated TLS resolving model; according to the embodiment of the invention, effective constraint on the design matrix error can be realized, and the clock error modeling precision is improved.

Description

Technical Field

[0001] This disclosure relates to the field of satellite navigation and positioning technology, and in particular to a BeiDou multi-frequency positioning method, device, electronic equipment and storage medium. Background Technology

[0002] The BeiDou Navigation Satellite System (BDS) has been widely applied in high-precision positioning scenarios such as autonomous driving, precision surveying, and drone inspection. These scenarios have extremely high requirements for positioning accuracy (centimeter-level), robustness (anti-electromagnetic interference), and dynamic adaptability (complex noise environments). Currently, the mainstream technologies for BeiDou high-precision positioning are based on least squares (LS) and total least squares (TLS) solutions. However, due to design flaws, these technologies still suffer from accuracy bottlenecks and insufficient robustness in complex scenarios. In autonomous driving scenarios, vehicles moving at high speeds are susceptible to electromagnetic interference from onboard electronic devices and roadside base stations, leading to fluctuations in observation noise. Existing technologies use fixed-weighted solution models, which cannot adapt to noise variations, thus affecting positioning accuracy. In precision surveying scenarios, the ephemeris clock difference between the satellite clock and the system time introduces errors into the design matrix used for solution calculation. Traditional LS solutions ignore this error, easily causing positioning deviations exceeding 0.1m, failing to meet centimeter-level positioning requirements.

[0003] Specifically, the shortcomings of existing BeiDou multi-frequency positioning methods are mainly reflected in the following four aspects:

[0004] (1) The design matrix error is not effectively constrained: the traditional LS scheme completely ignores the ephemeris clock error, and the ordinary TLS scheme considers the error but does not model the characteristics of Beidou clock error, resulting in low design matrix accuracy and positioning deviation exceeding 0.08m;

[0005] (2) Poor adaptability of random models: Both schemes use fixed weights. In the case of strong electromagnetic interference, the carrier phase residual is smaller than the pseudorange residual, but the system cannot increase the carrier phase weight, and the solution accuracy is significantly reduced by noise.

[0006] (3) Insufficient accuracy of clock error modeling: The ordinary TLS scheme uses a first-order polynomial modeling, which does not match the characteristic of "high short-term stability" of Beidou clock error. The modeling error exceeds 0.02ns within 10 minutes, which indirectly leads to an increase in positioning deviation;

[0007] (4) No iterative mechanism for multi-frequency verification: When the deviation of the multi-frequency result exceeds the threshold, the existing solution outputs directly without backtracking to optimize the preceding steps (such as clock error modeling and weight adjustment), resulting in insufficient robustness and an abnormal scene localization success rate of <85%. Summary of the Invention

[0008] This disclosure provides a BeiDou multi-frequency positioning method, device, electronic device, and storage medium to solve the problems of existing BeiDou multi-frequency positioning methods, such as unconstrained design matrix errors, poor adaptability of random models, insufficient accuracy of clock error modeling, and lack of iterative mechanism for multi-frequency verification.

[0009] Firstly, this disclosure provides a BeiDou multi-frequency positioning method, the method comprising:

[0010] S1 collects observation data and satellite ephemeris data from two target frequency points of the BeiDou satellite;

[0011] S2, Based on the satellite ephemeris data, a quadratic polynomial is used to model the clock bias of the BeiDou satellite to obtain the clock bias modeling error. The clock bias modeling error is used as a constraint term of the original design matrix to generate a design matrix with clock bias constraints.

[0012] S3. Based on the observation data, construct the observation vector, and substitute the design matrix with clock bias constraints and the observation vector into the overall least squares TLS solution model to obtain the initial values ​​of the positioning parameters and the corresponding solution residuals.

[0013] S4. Based on the mapping relationship between the solution residual fitting residual and the noise intensity, a weight matrix is ​​generated, and the weight matrix is ​​used to perform a weighted update on the TLS solution model to obtain the updated TLS solution model.

[0014] S5. The optimized positioning parameter value is obtained by solving the updated TLS solution model. Based on the optimized positioning parameter value and the observation data of the two target frequency points, the positioning results of the two target frequency points are determined, and the coordinate deviation of the two positioning results is calculated. If the coordinate deviation is less than a preset threshold, the optimized positioning parameter value is output as the final positioning result; otherwise, the process returns to step S2.

[0015] Furthermore, the observation data includes pseudorange observations and carrier phase observations. The acquisition of observation data and satellite ephemeris data at two target frequency points of the BeiDou satellite specifically includes:

[0016] At a preset sampling rate, pseudorange observations, carrier phase observations, and satellite ephemeris data for the two target frequency points are collected using a BeiDou dual-mode receiver.

[0017] Furthermore, the formula for calculating the design matrix with clock bias constraints is as follows:

[0018] ;

[0019] In the formula, For the design matrix with clock bias constraints, The original design matrix is ​​constructed based on satellite ephemeris data. To model errors for clock bias, This represents a diagonal matrix.

[0020] Furthermore, the step of generating a weight matrix based on the mapping relationship between the calculated residuals and the noise intensity specifically includes:

[0021] Based on the calculated residuals, the probability distribution of the residuals is fitted using a Gaussian mixture model (GMM) to establish a mapping relationship between the residuals and the noise intensity.

[0022] Based on the mapping relationship between residuals and noise intensity, calculate the global unified weight of pseudorange observations. Global unified weights of carrier phase observations The globally unified weight and Satisfy normalization constraints ;

[0023] Based on the global unified weight and Generate the weight matrix.

[0024] Furthermore, the calculation formula for the updated TLS resolution model is as follows:

[0025] ;

[0026] In the formula, A Let E be the design matrix with clock bias constraints, and E be the design matrix error. The positioning parameters to be determined are: Let F be the observation vector, and F be the observation vector error. For the Frobenius norm, This is the weight matrix.

[0027] Furthermore, the formula for calculating the coordinate deviation is:

[0028]

[0029] In the formula, The coordinate deviation of the positioning results for the two target frequency points. This is the localization result for one of the two target frequency points. This is the location result of the other target frequency among two target frequency points.

[0030] Furthermore, the two target frequency points are any two of the BeiDou satellite frequency points B1C, B1I, B2a, and B3I.

[0031] Secondly, this disclosure provides a BeiDou multi-frequency positioning device, the device comprising:

[0032] The frequency point data acquisition module is used to collect observation data and satellite ephemeris data of two target frequency points of Beidou satellites;

[0033] The clock bias modeling and constraint module is connected to the frequency point data acquisition module. It is used to model the clock bias of Beidou satellites based on the satellite ephemeris data using a quadratic polynomial, obtain the clock bias modeling error, and use the clock bias modeling error as a constraint term of the original design matrix to generate a design matrix with clock bias constraints.

[0034] The overall least squares solution module is connected to the clock error modeling and constraint module. It is used to construct an observation vector based on the observation data, and substitute the design matrix with clock error constraints and the observation vector into the overall least squares TLS solution model to obtain the initial values ​​of the positioning parameters and the corresponding solution residuals.

[0035] The solution model update module is connected to the overall least squares solution module. It is used to generate a weight matrix based on the mapping relationship between the solution residuals and the noise intensity, and to use the weight matrix to perform a weighted update on the TLS solution model to obtain the updated TLS solution model.

[0036] The positioning result determination module, connected to the solution model update module, is used to obtain the optimized value of the positioning parameters according to the updated TLS solution model, determine the positioning result of each of the two target frequency points based on the optimized value of the positioning parameters and the observation data of the two target frequency points, and calculate the coordinate deviation of the two positioning results. If the coordinate deviation is less than a preset threshold, the optimized value of the positioning parameters is output as the final positioning result; otherwise, the module returns to the clock error modeling and constraint module.

[0037] Thirdly, this disclosure provides an electronic device comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores one or more computer programs executable by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to perform the BeiDou multi-frequency positioning method described in the first aspect above.

[0038] Fourthly, this disclosure provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the BeiDou multi-frequency positioning method described in the first aspect.

[0039] The BeiDou multi-frequency positioning method, device, electronic equipment, and storage medium disclosed herein employ a quadratic polynomial for BeiDou satellite clock bias modeling and integrate the clock bias modeling error into the original design matrix to form a design matrix with clock bias constraints. This effectively constrains the design matrix error and improves the accuracy of clock bias modeling. By substituting the clock bias-constrained design matrix and observation vectors into the TLS solution model, the initial values ​​of positioning parameters and the solution residuals are obtained. Then, based on the solution residuals, a weight matrix is ​​generated by fitting the mapping relationship between the residuals and noise intensity and the TLS solution model for weighted updates, enabling the positioning solution to adapt to complex noise environments. Simultaneously, through an iterative mechanism that triggers the re-optimization of preceding steps by multi-frequency verification results, the reliability and robustness of the positioning system are significantly enhanced. This solves the problems of existing BeiDou multi-frequency positioning methods, such as ineffective constraint of design matrix errors, poor adaptability of random models, insufficient accuracy of clock bias modeling, and lack of an iterative mechanism for multi-frequency verification. Attached Figure Description

[0040] The accompanying drawings are provided to further illustrate the present disclosure and form part of the specification. They are used together with the embodiments of the present disclosure to explain the disclosure and do not constitute a limitation thereof. In the drawings:

[0041] Figure 1 A flowchart of a BeiDou multi-frequency positioning method provided in this embodiment of the disclosure;

[0042] Figure 2 This is a schematic diagram of the structure of the BeiDou multi-frequency positioning system provided in the embodiments of this disclosure;

[0043] Figure 3 A flowchart illustrating yet another BeiDou multi-frequency positioning method provided in this embodiment of the disclosure;

[0044] Figure 4 A block diagram of a BeiDou multi-frequency positioning device provided in an embodiment of this disclosure;

[0045] Figure 5 This is a block diagram of an electronic device provided in an embodiment of the present disclosure. Detailed Implementation

[0046] To enable those skilled in the art to better understand the technical solutions of this disclosure, exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments of this disclosure to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art should recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0047] Where there is no conflict, the various embodiments of this disclosure and the features thereof in the embodiments may be combined with each other.

[0048] As used herein, the term “and / or” includes any and all combinations of one or more related enumerated entries.

[0049] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit this disclosure. As used herein, the singular forms “a” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will also be understood that when the terms “comprising” and / or “made of” are used in this specification, the presence of the stated feature, integral, step, operation, element, and / or component is specified, but the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or groups thereof is not excluded. Words such as “connected” or “linked” are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect.

[0050] Unless otherwise specified, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art. It will also be understood that terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant art and this disclosure, and will not be interpreted as having an idealized or overly formal meaning, unless expressly so defined herein.

[0051] Figure 1 A flowchart illustrating a BeiDou multi-frequency positioning method provided in this embodiment of the disclosure. (Refer to...) Figure 1 The method includes:

[0052] S1 collects observation data and satellite ephemeris data from two target frequency points of the BeiDou satellite.

[0053] Specifically, the BeiDou system includes multiple operating frequency points such as B1I, B1C, B2I, B2a, and B3I. Two frequency points with complementary signal characteristics and different anti-interference capabilities can be selected as target frequency points. The two target frequency points are preferably any two frequency points among the BeiDou satellite frequency points B1C, B1I, B2a, and B3I, such as a combination of B1C and B2a, a combination of B1I and B2a, or a combination of B1C and B3I.

[0054] In some embodiments, the observation data includes pseudorange observations and carrier phase observations. The acquisition of observation data and satellite ephemeris data at two target frequencies of the BeiDou satellite specifically includes:

[0055] At a preset sampling rate, pseudorange observations, carrier phase observations, and satellite ephemeris data for the two target frequency points are collected using a BeiDou dual-mode receiver.

[0056] Specifically, the preset sampling rate is preferably 1Hz to 5Hz, and pseudorange observations, carrier phase observations, and satellite ephemeris data of two target frequency points (e.g., B1C and B2a) of Beidou satellites are collected by a Beidou dual-mode receiver.

[0057] S2. Based on the satellite ephemeris data, a quadratic polynomial is used to model the clock bias of the BeiDou satellite to obtain the clock bias modeling error. The clock bias modeling error is used as a constraint term of the original design matrix to generate a design matrix with clock bias constraints.

[0058] Specifically, based on the short-term stability of BeiDou satellite clock errors, a quadratic polynomial is adopted. The satellite clock bias is modeled, and the clock bias modeling error is calculated. ,Will The constraints are incorporated into the original design matrix A constructed based on satellite ephemeris data to generate a constrained design matrix. .

[0059] The method for calculating clock error modeling error is as follows:

[0060] Clock difference modeling uses a quadratic polynomial The residual calculation consists of three steps:

[0061] 1) Obtain raw clock bias data: Extract data from BeiDou satellite navigation messages or measured data at different times. Corresponding satellite clock bias observations .

[0062] 2) Fitting polynomial coefficients: The historical clock error observations are fitted using the least squares method to obtain the quadratic polynomial coefficients. ;

[0063] 3) Calculate the residuals: for each time step Calculate the fitted clock error value The residual is the difference between the actual observed value and the fitted value: that is... The residual is the clock error modeling error, which will be incorporated into the design matrix as a constraint term.

[0064] The formula for calculating the design matrix with clock bias constraints is as follows:

[0065] ;

[0066] In the formula, For the design matrix with clock bias constraints, The original design matrix is ​​constructed based on satellite ephemeris data. To model errors for clock bias, Represents a diagonal matrix. This means that the error vector is modeled using clock bias. The elements in the matrix are diagonal elements, and the remaining positions are zeros.

[0067] S3. Based on the observation data, construct the observation vector, and substitute the design matrix with clock bias constraints and the observation vector into the overall least squares TLS solution model to obtain the initial values ​​of the positioning parameters and the corresponding solution residuals.

[0068] Specifically, the design matrix A' with clock bias constraints and the observation vector L constructed based on the observation data are substituted into the TLS solution model, and the initial values ​​of the positioning parameters are solved by singular value decomposition. and calculate residuals The formula for the TLS resolution model is:

[0069] ,in For the design matrix with clock bias constraints, An observation vector constructed based on observation data. Let E be the positioning parameters to be determined, E be the error matrix of the design matrix, and F be the error matrix of the observation vector. It is the Frobenius norm.

[0070] S4. Based on the mapping relationship between the solution residual fitting residual and the noise intensity, a weight matrix is ​​generated, and the weight matrix is ​​used to perform a weighted update on the TLS solution model to obtain the updated TLS solution model.

[0071] Specifically, based on the calculated residuals, the mapping relationship between the residuals and noise intensity is fitted using a Gaussian Mixture Model (GMM) to achieve adaptive dynamic adjustment of the observation weights with noise intensity. A weight matrix adapted to the actual noise characteristics of multi-frequency positioning is generated based on the adjusted weights. The observation vectors of the TLS solution model are then weighted and corrected using this weight matrix to complete the weighted update of the TLS solution model, resulting in a more adaptable updated TLS solution model. This effectively improves the model's adaptability to multi-frequency positioning noise and its solution accuracy.

[0072] In some embodiments, generating a weight matrix based on the mapping relationship between the solved residual fitting residual and the noise intensity specifically includes:

[0073] Based on the calculated residuals, the probability distribution of the residuals is fitted using a Gaussian mixture model (GMM) to establish a mapping relationship between the residuals and the noise intensity.

[0074] Based on the mapping relationship between residuals and noise intensity, calculate the global unified weight of pseudorange observations. Global unified weights of carrier phase observations The globally unified weight and Satisfy normalization constraints ;

[0075] Based on the global unified weight and Generate the weight matrix.

[0076] The formula for calculating the weight matrix is ​​as follows:

[0077] ;

[0078] The calculation formula for the updated TLS resolution model is as follows:

[0079] ;

[0080] In the formula, A Let E be the design matrix with clock bias constraints, and E be the design matrix error. The positioning parameters to be determined are: Let F be the observation vector, and F be the observation vector error. For the Frobenius norm, This is the weight matrix.

[0081] S5. The optimized positioning parameter value is obtained by solving the updated TLS solution model. Based on the optimized positioning parameter value and the observation data of the two target frequency points, the positioning results of the two target frequency points are determined, and the coordinate deviation of the two positioning results is calculated. If the coordinate deviation is less than a preset threshold, the optimized positioning parameter value is output as the final positioning result; otherwise, the process returns to step S2.

[0082] Specifically, the localization results of the two target frequency points can be determined in two ways: one is to solve the frequency points independently, by substituting the observation data of the two target frequency points into the TLS model and solving them independently, thus obtaining their respective localization results. and The second method involves directly separating the results from the joint solution. The sub-matrices corresponding to the two target frequency points are extracted from the design matrix of the multi-frequency joint solution. By combining the obtained optimized positioning parameter values, the positioning results corresponding to the two frequency points can be obtained.

[0083] Specifically, the formula for calculating the coordinate deviation is:

[0084]

[0085] In the formula, The coordinate deviation of the positioning results for the two target frequency points. This is the localization result for one of the two target frequency points. This is the location result of the other target frequency among two target frequency points.

[0086] Specifically, if the coordinate deviation is less than a preset threshold (e.g., 0.05m), the optimized positioning parameter value is output as the final positioning result. If the coordinate deviation is greater than or equal to the preset threshold, i.e., the multi-frequency consistency check fails, the process returns to step S2 to adjust the clock bias modeling coefficient. The specific operations include:

[0087] 1) Data update: Obtain the residual data after multi-frequency consistency verification (containing new positioning deviation information) as a new input for clock error modeling;

[0088] 2) Refitting the polynomial: Refitting a quadratic polynomial using the least squares method for the new clock error observations (including residual feedback). The updated coefficients are obtained. ;

[0089] 3) Update the design matrix: Model the new clock error residuals As a constraint, update the design matrix with clock bias constraints. ;

[0090] 4) Iterative verification: Substitute the updated design matrix into the subsequent S3 to S5 steps, repeat the calculation and verification until the multi-frequency deviation meets the requirements.

[0091] It should be noted that the BeiDou multi-frequency positioning method provided in this disclosure has the following beneficial effects:

[0092] (a) Construct a constraint model based on the short-term stability of BeiDou clock bias to reduce the design matrix error and improve the positioning accuracy to within ±0.05m;

[0093] (b) Design a dynamic stochastic model for residual feedback to achieve adaptive adjustment of observation weights according to noise intensity, and maintain a solution accuracy of ≥95% in complex noise scenarios;

[0094] (c) Optimize the clock error modeling method, and use a quadratic polynomial to match the BeiDou clock error characteristics to control the modeling error within 10 minutes to below 0.01ns;

[0095] (d) Establish a multi-frequency verification-preceding step iterative feedback mechanism to improve the success rate of abnormal scene positioning to over 98% and meet the robustness requirements of high-precision scenes.

[0096] In one specific embodiment, the BeiDou multi-frequency positioning method is applied to a BeiDou multi-frequency positioning system, the structural diagram of which is shown below. Figure 2As shown, it includes an observation data acquisition module, a clock bias modeling and constraint module, a TLS solution module, a stochastic model dynamic optimization module, and a multi-frequency signal consistency verification module. These modules are interconnected sequentially, as detailed below:

[0097] 1) Observation data acquisition module: used to receive observation signals from two target frequency points (such as B1C and B2a) in the Beidou satellite multi-frequency system, collect pseudorange observation values, carrier phase observation values ​​and satellite ephemeris data, and transmit the data to the clock error modeling and constraint module;

[0098] 2) Clock bias modeling and constraint module: Based on the characteristic of "high short-term stability of clock bias" of Beidou satellite, a quadratic polynomial model is used to model the clock bias of Beidou satellite, calculate the clock bias modeling error, and use the error as a constraint term of the design matrix to generate a design matrix with clock bias constraints, which is then transmitted to the TLS solution module.

[0099] 3) TLS solution module: Receives the design matrix and observation data with clock bias constraints, constructs the TLS solution model (Formula 1), solves the joint error of the design matrix and observation vector through singular value decomposition (SVD), outputs the initial solution results and solution residuals, and transmits them to the stochastic model optimization module and the consistency verification module respectively.

[0100] (Formula 1)

[0101] Where A is the original design matrix, E is the design matrix error (including ephemeris error and clock error modeling error), L is the observation vector, F is the observation vector error, and X is the positioning parameter to be determined. It is the Frobenius norm;

[0102] It should be noted that the parameters are obtained as follows:

[0103] Observation vector L: comes from the observation data acquisition module and includes raw observation values ​​such as pseudorange and carrier phase.

[0104] Original design matrix A: A geometric matrix calculated based on BeiDou satellite ephemeris data, initial receiver position values, etc.

[0105] Design matrix error E includes ephemeris error, clock error modeling error, etc. Ephemeris error comes from navigation messages, and clock error modeling error is obtained by fitting the residuals of clock error modeling and constraint modules through quadratic polynomial fitting.

[0106] The observation vector error F includes observation noise, multipath error, etc., and is obtained by fitting the residuals through the Gaussian mixture model of the stochastic model dynamic optimization module.

[0107] The location parameter X to be determined is obtained by solving Formula 1 using the Singular Value Decomposition (SVD) of the TLS solution module.

[0108] Residual: The difference between the TLS solution and the original observations.

[0109] Weight matrix: The stochastic model dynamic optimization module obtains the weight matrix by fitting the residual-noise intensity mapping relationship of the residuals through a Gaussian mixture model. For example, under strong electromagnetic interference, the optimized weight matrix is ​​generated by reducing the weight of pseudorange observations (0.7~0.8).

[0110] 4) Stochastic Model Dynamic Optimization Module: Based on the residuals of TLS solution, a mapping relationship between "residuals and noise intensity" is established (the residual distribution is fitted by a Gaussian mixture model). The weights of the observations are adjusted in real time (e.g., when there is strong electromagnetic interference, the residual of the carrier phase observation is less than the pseudorange residual, so the weight of the carrier phase observation is increased to 0.7-0.8). The optimized weight matrix is ​​generated and fed back to the TLS solution module to update the solution model.

[0111] It should be noted that the residual-noise intensity mapping fitting uses a Gaussian mixture model (GMM) to fit the TLS solution residuals, dividing the residuals into components with different noise intensities. Based on the probability density of each component, the weights of different observations (such as pseudorange and carrier phase) are dynamically adjusted to generate an optimized weight matrix.

[0112] 5) Multi-frequency signal consistency verification module: Receives the initial solution result output by the TLS solution module, extracts the positioning solution corresponding to the B1C and B2a frequency points, calculates the deviation between the solution results of the two frequency points. If the deviation is less than 0.05m, the solution result is determined to be valid and the final positioning result is output; if the deviation is greater than or equal to 0.05m, the TLS solution module is triggered to re-iterate the solution.

[0113] Based on the above system, such as Figure 3 As shown, the BeiDou multi-frequency positioning method may include the following steps:

[0114] Step 1: Observation Data Acquisition

[0115] The pseudorange observations, carrier phase observations, and satellite ephemeris data at the B1C and B2a frequencies of the BeiDou satellites were collected using a BeiDou dual-mode receiver, with the sampling rate set to 1Hz ~ 5Hz.

[0116] It should be noted that the BeiDou system includes multiple frequency points such as B1I, B1C, B2I, B2a, and B3I. In this step, B1C and B2a are selected based on the engineering practice principle of "complementary signal characteristics and adaptable anti-interference capabilities" (both are the mainstream civilian frequency points of BeiDou-3, with stable signals and compatible with the algorithm of this scheme). The core of multi-frequency consistency verification is to cross-verify the positioning reliability using the observation results of different frequency points. Theoretically, any combination of two frequency points with stable signals (such as B1I+B2a, B1C+B3I) can be adapted to this step, but it is necessary to ensure that the observation data of the selected frequency points can be compatible with the subsequent clock bias modeling and TLS calculation modules.

[0117] Step 2: Clock Fault Modeling and Design Matrix Constraint Construction

[0118] Based on the short-term stability of BeiDou satellite clock errors, a quadratic polynomial is used. , ( Let t be the clock difference. Model clock errors using modeling coefficients and calculate clock error modeling error. ,Will This constraint term is incorporated into the original design matrix A to generate a design matrix with clock bias constraints. ;

[0119] The method for calculating clock error modeling error is as follows:

[0120] Clock difference modeling uses a quadratic polynomial The residual calculation consists of three steps:

[0121] Obtain raw clock bias data: Extract data from BeiDou satellite navigation messages or measured data at different times. Corresponding satellite clock bias observations .

[0122] Fitting polynomial coefficients: The historical clock error observations are fitted using the least squares method to obtain polynomial coefficients. ;

[0123] Calculate the residuals: for each time step Calculate the fitted clock error value The residual is the difference between the actual observed value and the fitted value: This residual is the clock error modeling error, which will be incorporated into the design matrix as a constraint term.

[0124] Step 3: Initial TLS Calculation

[0125] Substituting the design matrix A' with clock bias constraints and the observation vector L into the TLS solution model, the initial values ​​of the positioning parameters are solved by singular value decomposition. and calculate residuals :

[0126] ,in For the design matrix with clock bias constraints, For the observation vector, Let E be the positioning parameter to be determined, E be the design matrix error, and F be the observation vector error. It is the Frobenius norm.

[0127] It should be noted that Singular Value Decomposition (SVD), as the core solution step of the TLS algorithm, can simultaneously output the initial values ​​of the location parameters. The estimation involves determining the design matrix error E and the observation vector error F; and then calculating the residuals. It is directly derived from the observation vector error F. This residual will serve as the core input data for the subsequent stochastic model dynamic optimization module, used to fit the noise characteristics and adjust the observation weights.

[0128] Step 4: Dynamic Optimization of the Stochastic Model

[0129] Based on residuals Fit the residual-noise intensity mapping relationship and calculate the pseudorange observation weights. Weighted with carrier phase observations (satisfy Generate weight matrix And update the TLS solution model to ,in This is the weight matrix. , The weights of pseudorange and carrier phase observations are respectively (satisfying) );

[0130] It should be noted that the weights in this step... , Solving residuals with TLS The noise intensity corresponding to different residuals is calculated using the input (including pseudorange and carrier phase residuals). First, the probability distribution of the residuals is fitted using a Gaussian mixture model (GMM) to obtain the noise intensity. Then, the weights are dynamically allocated based on the noise intensity: if the residual noise intensity is high (e.g., strong electromagnetic interference), the weight of the corresponding observation (e.g., pseudorange weight) is reduced. Carrier phase weight If the residual noise intensity is low, the weight of the corresponding observation is increased. After the allocation is completed, the weights are normalized to ensure... And generate the weight matrix ,and , To assign a globally uniform value for each observation type, where It is a unified weight for pseudorange observations at all frequencies. It is the uniform weight of all frequency point carrier phase observations.

[0131] It should be noted that Steps 2 to 4 of this scheme do not require separate operations for each frequency point: Step 2's clock bias modeling is based on unified modeling of satellite clock bias (an overall satellite attribute, not a frequency point attribute), and the generated constraint terms are integrated into the design matrix without distinguishing between frequency points; Step 3's TLS initial solution is based on the design matrix jointly constructed by multiple frequencies and the observation vector for unified solution, to obtain the global positioning initial value and solution residuals, rather than independent solution for each frequency point; In Step 4, the stochastic model optimization relies on the joint solution residuals of multiple frequencies to uniformly complete the optimization of the weight matrix, also without distinguishing between frequency points. Only in the multi-frequency consistency verification stage will the positioning result deviation of different frequency points (such as B1C and B2a) be compared separately to verify the validity of the solution results.

[0132] Step 5: Multi-frequency signal consistency verification

[0133] Solve for the localization parameters of the updated model (i.e., optimized positioning parameter values), extract the B1C frequency point positioning results. Location results with B2a frequency point Calculate the deviation :

[0134] like <0.05m, output As the final positioning result;

[0135] like Return to Step 2 to readjust the clock error modeling coefficients, and repeat Steps 2-5 until the deviation meets the requirements.

[0136] Specifically, when the multi-frequency consistency check fails, return to Step 2 to readjust the clock error modeling coefficients. This involves updating and optimizing the quadratic polynomial coefficients for clock error modeling: First, obtain the residual data containing new positioning error information after the multi-frequency consistency check, and use it as the new input for clock error modeling. Then, refit the quadratic polynomial with the new clock error observations incorporating this residual feedback using the least squares method to obtain the updated polynomial coefficients. Then, the new clock error modeling residuals are calculated. The residual is then used as a constraint term to update the design matrix with clock bias constraints. Finally, the updated design matrix is ​​substituted into the subsequent solution steps, and the TLS solution, random model optimization and multi-frequency consistency verification are repeated until the multi-frequency positioning deviation meets the preset requirements.

[0137] It should be noted that the positioning parameters The global result obtained from multi-frequency joint calculation is used to obtain the B1C frequency point location result. Location results with B2a frequency point This can be achieved in two ways: one is to solve the frequency points independently, by substituting the observation data of frequency points B1C and B2a into the TLS model and solving them independently, thus obtaining the corresponding results. and Secondly, the results are directly separated from the joint solution. The sub-matrices corresponding to the B1C and B2a frequency points are extracted from the design matrix of the multi-frequency joint solution and combined with the obtained positioning parameters. By working backwards, we can obtain the location results for the two frequency points.

[0138] It should be noted that the BeiDou multi-frequency positioning method provided in this disclosure has the following characteristics:

[0139] a) Quadratic polynomial constraint modeling adapted to BeiDou clock error characteristics: For the first time, the characteristic of "high short-term stability" of BeiDou clock error is utilized to model and construct a constraint matrix using quadratic polynomials, which reduces the design matrix error by more than 60%.

[0140] b) Dynamic stochastic model for residual feedback: Based on the mapping relationship between residuals and noise intensity fitted by GMM, the weights of observations are adaptively adjusted, and the accuracy retention rate is improved by 15%~20% in complex noise scenarios;

[0141] c) Multi-frequency verification - iterative feedback mechanism of preceding steps: When the multi-frequency deviation exceeds the threshold, it backtracks to the clock error modeling step instead of outputting directly, which improves the positioning success rate by more than 13%;

[0142] d) TLS solution model with weight update: Integrating dynamic weights into the TLS model to form a collaborative design of "constraint modeling + dynamic weights + TLS solution", the positioning accuracy is reduced to within ±0.05m.

[0143] The BeiDou multi-frequency positioning method provided in this disclosure employs a quadratic polynomial to model BeiDou satellite clock errors and integrates the clock error modeling error into the original design matrix to form a design matrix with clock error constraints. This effectively constrains the design matrix error and improves the accuracy of clock error modeling. By substituting the design matrix with clock error constraints and the observation vector into the TLS solution model, the initial values ​​of positioning parameters and the solution residuals are obtained. Then, based on the solution residuals, a weight matrix is ​​generated by fitting the mapping relationship between the residuals and noise intensity and the TLS solution model is updated with weights, enabling the positioning solution to adapt to complex noise environments. At the same time, the iterative mechanism that triggers the re-optimization of previous steps through multi-frequency verification results significantly enhances the reliability and robustness of the positioning system, solving the problems of ineffective constraint of design matrix errors, poor adaptability of random models, insufficient accuracy of clock error modeling, and lack of iterative mechanism for multi-frequency verification in existing BeiDou multi-frequency positioning methods.

[0144] It is understood that the various method embodiments mentioned above in this disclosure can be combined with each other to form combined embodiments without violating the principle and logic. Due to space limitations, this disclosure will not elaborate further. Those skilled in the art will understand that in the above methods of specific implementation, the specific execution order of each step should be determined by its function and possible internal logic.

[0145] Figure 4 This is a block diagram of a BeiDou multi-frequency positioning device provided in an embodiment of this disclosure.

[0146] Reference Figure 4 This disclosure provides a BeiDou multi-frequency positioning device for performing the above-described BeiDou multi-frequency positioning method. The device includes:

[0147] Frequency point data acquisition module 11 is used to acquire observation data and satellite ephemeris data of two target frequency points of Beidou satellite;

[0148] The clock bias modeling and constraint module 12 is connected to the frequency point data acquisition module 11. It is used to model the clock bias of Beidou satellites based on the satellite ephemeris data using a quadratic polynomial, obtain the clock bias modeling error, and use the clock bias modeling error as a constraint term of the original design matrix to generate a design matrix with clock bias constraints.

[0149] The overall least squares solution module 13 is connected to the clock error modeling and constraint module 12. It is used to construct an observation vector based on the observation data, and substitute the design matrix with clock error constraints and the observation vector into the overall least squares TLS solution model to obtain the initial values ​​of the positioning parameters and the corresponding solution residuals.

[0150] The solution model update module 14 is connected to the overall least squares solution module 13. It is used to generate a weight matrix based on the mapping relationship between the solution residual and the noise intensity, and to use the weight matrix to perform a weighted update on the TLS solution model to obtain the updated TLS solution model.

[0151] The positioning result determination module 15 is connected to the solution model update module 14. It is used to solve the optimized value of the positioning parameters according to the updated TLS solution model, determine the positioning result of each of the two target frequency points based on the optimized value of the positioning parameters and the observation data of the two target frequency points, and calculate the coordinate deviation of the two positioning results. If the coordinate deviation is less than a preset threshold, the optimized value of the positioning parameters is output as the final positioning result; otherwise, the process returns to the clock error modeling and constraint module.

[0152] Optionally, the observation data includes pseudorange observations and carrier phase observations, and the frequency point data acquisition module 11 is specifically used for:

[0153] At a preset sampling rate, pseudorange observations, carrier phase observations, and satellite ephemeris data for the two target frequency points are collected using a BeiDou dual-mode receiver.

[0154] Optionally, the formula for calculating the design matrix with clock bias constraints is:

[0155] ;

[0156] In the formula, For the design matrix with clock bias constraints, The original design matrix is ​​constructed based on satellite ephemeris data. To model errors for clock bias, This represents a diagonal matrix.

[0157] Optionally, the solution model update module 14 includes:

[0158] The fitting and mapping unit is used to fit the probability distribution of the residuals based on the solved residuals using a Gaussian mixture model (GMM) to establish a mapping relationship between the residuals and the noise intensity.

[0159] The weight calculation unit is used to calculate the global unified weight of the pseudorange observations based on the mapping relationship between the residuals and noise intensity. Global unified weights of carrier phase observations The globally unified weight and Satisfy normalization constraints ;

[0160] The weight matrix generation unit is used to generate the weight matrix based on the globally unified weights. and Generate the weight matrix.

[0161] Optionally, the calculation formula for the updated TLS resolution model is:

[0162] ;

[0163] In the formula, A Let E be the design matrix with clock bias constraints, and E be the design matrix error. The positioning parameters to be determined are: Let F be the observation vector, and F be the observation vector error. For the Frobenius norm, This is the weight matrix.

[0164] Optionally, the formula for calculating the coordinate deviation is:

[0165]

[0166] In the formula, The coordinate deviation of the positioning results for the two target frequency points. This is the localization result for one of the two target frequency points. This is the location result of the other target frequency among two target frequency points.

[0167] Optionally, the two target frequency points are any two of the BeiDou satellite frequency points B1C, B1I, B2a, and B3I.

[0168] Figure 5 This is a block diagram of an electronic device provided in an embodiment of the present disclosure.

[0169] Reference Figure 5 This disclosure provides an electronic device, which includes: at least one processor 701; at least one memory 702; and one or more I / O interfaces 703 connected between the processor 701 and the memory 702; wherein the memory 702 stores one or more computer programs that can be executed by the at least one processor 701, and the one or more computer programs are executed by the at least one processor 701 to enable the at least one processor 701 to execute the above-described BeiDou multi-frequency positioning method.

[0170] This disclosure also provides a computer-readable storage medium storing a computer program thereon, wherein the computer program, when executed by a processor, implements the aforementioned BeiDou multi-frequency positioning method. The computer-readable storage medium may be volatile or non-volatile.

[0171] In summary, the BeiDou multi-frequency positioning method, device, electronic device, and storage medium provided in this disclosure employ a quadratic polynomial to model BeiDou satellite clock bias and integrate the clock bias modeling error into the original design matrix to form a design matrix with clock bias constraints. This effectively constrains the design matrix error and improves the accuracy of clock bias modeling. By substituting the design matrix with clock bias constraints and the observation vector into the TLS solution model, the initial values ​​of positioning parameters and the solution residuals are obtained. Then, a weight matrix is ​​generated based on the mapping relationship between the solution residuals and noise intensity, and the TLS solution model is updated with weights, enabling the positioning solution to adapt to complex noise environments. Simultaneously, the iterative mechanism that triggers the re-optimization of preceding steps through multi-frequency verification results significantly enhances the reliability and robustness of the positioning system, solving the problems of ineffective constraint of design matrix error, poor adaptability of random models, insufficient accuracy of clock bias modeling, and lack of iterative mechanism for multi-frequency verification in existing BeiDou multi-frequency positioning methods.

[0172] Those skilled in the art will understand that all or some of the steps, systems, and apparatuses disclosed above, and their functional modules / units, can be implemented as software, firmware, hardware, or suitable combinations thereof. In hardware implementations, the division between functional modules / units mentioned above does not necessarily correspond to the division of physical components; for example, a physical component may have multiple functions, or a function or step may be performed collaboratively by several physical components. Some or all physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit (ASIC). Such software can be distributed on a computer-readable storage medium, which may include computer storage media (or non-transitory media) and communication media (or transient media).

[0173] As is known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information, such as computer-readable program instructions, data structures, program modules, or other data. Computer storage media includes, but is not limited to, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM), static random access memory (SRAM), flash memory or other memory technologies, portable compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, it is known to those skilled in the art that communication media typically contain computer-readable program instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0174] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0175] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0176] This disclosure has disclosed exemplary embodiments, and although specific terminology has been used, it is for general illustrative purposes only and should not be construed as limiting. In some instances, it will be apparent to those skilled in the art that features, characteristics, and / or elements described in conjunction with particular embodiments may be used alone, or in combination with features, characteristics, and / or elements described in conjunction with other embodiments, unless otherwise expressly indicated. Therefore, those skilled in the art will understand that various changes in form and detail may be made without departing from the scope of this disclosure as set forth by the appended claims.

Claims

1. A BeiDou multi-frequency positioning method, characterized in that, The method includes: S1 collects observation data and satellite ephemeris data from two target frequency points of the BeiDou satellite; S2, Based on the satellite ephemeris data, a quadratic polynomial is used to model the clock bias of the BeiDou satellite to obtain the clock bias modeling error. The clock bias modeling error is used as a constraint term of the original design matrix to generate a design matrix with clock bias constraints. S3. Based on the observation data, construct the observation vector, and substitute the design matrix with clock bias constraints and the observation vector into the overall least squares TLS solution model to obtain the initial values ​​of the positioning parameters and the corresponding solution residuals. S4. Based on the mapping relationship between the solution residual fitting residual and the noise intensity, a weight matrix is ​​generated, and the weight matrix is ​​used to perform a weighted update on the TLS solution model to obtain the updated TLS solution model. S5. The optimized positioning parameter value is obtained by solving the updated TLS solution model. Based on the optimized positioning parameter value and the observation data of the two target frequency points, the positioning results of the two target frequency points are determined, and the coordinate deviation of the two positioning results is calculated. If the coordinate deviation is less than a preset threshold, the optimized positioning parameter value is output as the final positioning result; otherwise, the process returns to step S2.

2. The method according to claim 1, characterized in that, The observation data includes pseudorange observations and carrier phase observations. Specifically, the acquisition of observation data and satellite ephemeris data from two target frequency points of the BeiDou satellite includes: At a preset sampling rate, pseudorange observations, carrier phase observations, and satellite ephemeris data for the two target frequency points are collected using a BeiDou dual-mode receiver.

3. The method according to claim 1, characterized in that, The formula for calculating the design matrix with clock bias constraints is as follows: ； In the formula, For the design matrix with clock bias constraints, The original design matrix is ​​constructed based on satellite ephemeris data. To model errors for clock bias, This represents a diagonal matrix.

4. The method according to claim 1, characterized in that, The step of generating a weight matrix based on the mapping relationship between the calculated residuals and the noise intensity specifically includes: Based on the calculated residuals, the probability distribution of the residuals is fitted using a Gaussian mixture model (GMM) to establish a mapping relationship between the residuals and the noise intensity. Based on the mapping relationship between residuals and noise intensity, calculate the global unified weight of pseudorange observations. Global unified weights of carrier phase observations The globally unified weight and Satisfy normalization constraints ; Based on the global unified weight and Generate the weight matrix.

5. The method according to claim 4, characterized in that, The calculation formula for the updated TLS resolution model is as follows: ； In the formula, A Let E be the design matrix with clock bias constraints, and E be the design matrix error. The positioning parameters to be determined are: Let F be the observation vector, and F be the observation vector error. For the Frobenius norm, This is the weight matrix.

6. The method according to claim 1, characterized in that, The formula for calculating the coordinate deviation is: In the formula, The coordinate deviation of the positioning results for the two target frequency points. This is the localization result for one of the two target frequency points. This is the location result of the other target frequency among two target frequency points.

7. The method according to claim 1, characterized in that, The two target frequency points are any two of the BeiDou satellite frequency points B1C, B1I, B2a, and B3I.

8. A BeiDou multi-frequency positioning device, characterized in that, The device includes: The frequency point data acquisition module is used to collect observation data and satellite ephemeris data of two target frequency points of Beidou satellites; The clock bias modeling and constraint module is connected to the frequency point data acquisition module. It is used to model the clock bias of Beidou satellites based on the satellite ephemeris data using a quadratic polynomial, obtain the clock bias modeling error, and use the clock bias modeling error as a constraint term of the original design matrix to generate a design matrix with clock bias constraints. The overall least squares solution module is connected to the clock error modeling and constraint module. It is used to construct an observation vector based on the observation data, and substitute the design matrix with clock error constraints and the observation vector into the overall least squares TLS solution model to obtain the initial values ​​of the positioning parameters and the corresponding solution residuals. The solution model update module is connected to the overall least squares solution module. It is used to generate a weight matrix based on the mapping relationship between the solution residuals and the noise intensity, and to use the weight matrix to perform a weighted update on the TLS solution model to obtain the updated TLS solution model. The positioning result determination module, connected to the solution model update module, is used to obtain the optimized value of the positioning parameters according to the updated TLS solution model, determine the positioning result of each of the two target frequency points based on the optimized value of the positioning parameters and the observation data of the two target frequency points, and calculate the coordinate deviation of the two positioning results. If the coordinate deviation is less than a preset threshold, the optimized value of the positioning parameters is output as the final positioning result; otherwise, the module returns to the clock error modeling and constraint module.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and A memory communicatively connected to the at least one processor; wherein, The memory stores one or more computer programs that can be executed by the at least one processor, and the one or more computer programs are executed by the at least one processor to enable the at least one processor to perform the BeiDou multi-frequency positioning method as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the BeiDou multi-frequency positioning method as described in any one of claims 1-7.

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