A high-precision positioning method and system based on a single-beidou radio signal delay weighted optimization model

Abstract

This invention discloses a high-precision positioning method and system based on a single BeiDou radio signal delay weighted optimization model. First, it collects single BeiDou radio signal observation data from various single BeiDou stations. Then, it processes the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. This invention achieves high-precision and high-reliability calculation of radio signal delay parameters applicable to single BeiDou radio navigation and positioning processes at different times and locations. Furthermore, by constructing a weighted loss function with adaptive weight update capabilities, it enhances the contribution of accurate sample data in the modeling process. This not only utilizes real-time high-precision tropospheric prior information to enhance the single BeiDou solution model and reduce the correlation between tropospheric delay and station elevation parameters, but also improves the stability and convergence speed of short-time and real-time positioning solutions, making it suitable for widespread application.

Description

Technical Field

[0001] This invention relates to the field of high-precision positioning technology, specifically to a high-precision positioning method and system based on a single BeiDou radio signal delay weighted optimization model. Background Technology

[0002] Tropospheric total delay (ZTD) is one of the major error sources in global navigation satellite system measurements. It not only directly limits the accuracy of precise positioning using a single BeiDou radio signal, but also contains atmospheric information that has significant application value in meteorological monitoring and atmospheric sounding. Tropospheric total delay (ZTD) mainly consists of two parts: tropospheric hydrostatic delay (ZHD) and tropospheric wet delay (ZWD). The tropospheric hydrostatic delay (ZHD) is primarily controlled by surface air pressure and exhibits relatively stable spatiotemporal variations; while the tropospheric wet delay (ZWD) is mainly determined by tropospheric water vapor distribution, exhibiting significant nonlinearity and strong time-varying characteristics, and is the main source of uncertainty in ZTD estimation. Due to the influence of complex meteorological conditions, the drastic temporal and spatial variations of tropospheric water vapor make the high spatiotemporal accuracy calculation and stable estimation of the tropospheric wet delay (ZWD) a consistently significant challenge.

[0003] Currently, existing single-BeiDou radio signal delay models are mainly divided into models that rely on measured meteorological parameters and models that do not require meteorological parameters. Models that rely on measured meteorological parameters require meteorological parameters such as atmospheric temperature, atmospheric pressure, and water vapor pressure. However, more than 70% of single-BeiDou radio signal stations worldwide are not equipped with co-located meteorological sensors, making it impossible to obtain real-time data such as surface air pressure and temperature, which seriously hinders the modeling of single-BeiDou radio signal propagation delay. On the other hand, models that do not require meteorological parameters are usually built on the assumption of an ideal atmosphere, making it difficult to accurately depict the real changes in meteorological elements at different spatiotemporal scales. Therefore, the accuracy of radio signal delay calculation under complex meteorological conditions is limited. At the same time, existing models... Neural network models typically employ a standard mean squared error loss function during training. This traditional loss function treats all sample data equally, easily ignoring the non-uniformity of precision in the training data. This results in significant differences in the precision of single-BeiDou radio signal ZTD data obtained through single-BeiDou radio signal data processing at different times and locations. Consequently, the neural network model is susceptible to the influence of low-precision samples, leading to insufficient generalization and severely impacting the calculation accuracy and stability of single-BeiDou radio signal delay, thus resulting in low positioning accuracy. Therefore, it is necessary to design a high-precision positioning method and system based on a single-BeiDou radio signal delay weighted optimization model. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings of existing technologies and to better and more effectively solve the problem of low accuracy in modeling the propagation delay of single BeiDou radio signals due to the accuracy differences of single BeiDou radio signal delay in different samples. This invention provides a high-precision positioning method and system based on a weighted optimization model of single BeiDou radio signal delay. It achieves high-precision and high-reliability calculation of radio signal delay parameters applicable to single BeiDou radio navigation and positioning processes at different times and locations. Furthermore, by constructing a weighted loss function with adaptive weight update capabilities, it can improve the contribution of accurate sample data in the modeling process. This not only enhances the single BeiDou solution model and weakens the correlation between tropospheric delay and station elevation parameters by utilizing real-time high-precision tropospheric prior information, but also improves the stability and convergence speed of short-time and real-time positioning solutions.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A high-precision positioning method based on a single BeiDou radio signal delay-weighted optimization model includes the following steps: Step A: Collect single BeiDou radio signal observation data from each single BeiDou station, then process the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. Step B: Collect atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculate the tropospheric static delay information at the location of each single BeiDou station. Step C: Extract non-static delay information at the location of each individual BeiDou station based on the tropospheric static delay information at each individual BeiDou station location. Step D: Construct a sample dataset based on the location and non-static delay information of each individual BeiDou station, and then use the sample dataset to calculate the adaptive weight information of the sample data. Step E: Using the adaptive weight information of the sample data, construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability. Then, model the delay of a single BeiDou radio signal based on the adaptive weighted residual minimum criterion loss function and obtain a weighted optimization model for the delay of a single BeiDou radio signal. Step F involves using a single BeiDou radio signal delay weighted optimization model to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process and completing the high-precision positioning operation.

[0006] The aforementioned high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model includes step A, which involves collecting single BeiDou radio signal observation data from each single BeiDou station, processing the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. The specific steps are as follows. Step A1: Collect single BeiDou radio signal observation data from each single BeiDou station, specifically, collect single BeiDou radio signal observation data monitored by single BeiDou stations that are evenly distributed within the target area. Step A2 involves processing the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. Specifically, the processing of the single BeiDou radio signal observation data includes quality control and correction modeling of various error sources. Then, observation equations are established to estimate parameters and output the location and radio signal delay information of each single BeiDou station. The location and radio signal delay information of each single BeiDou station includes the observation time information, latitude and longitude information, elevation information, zenith tropospheric delay information and zenith tropospheric delay standard deviation information of each single BeiDou station.

[0007] The aforementioned high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model, in step B, involves collecting atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculating the tropospheric static delay information at the location of each single BeiDou station. Specifically, based on the atmospheric reanalysis data, surface air pressure data at the location of each single BeiDou station is calculated using bilinear interpolation, and then the tropospheric static delay information is calculated based on the surface air pressure data, as shown in formula (1). (1) in, This represents the tropospheric static delay value at the location of a single BeiDou satellite station. This refers to the surface air pressure at a single Beidou satellite station. and This refers to the latitude and elevation of a single BeiDou satellite navigation station.

[0008] The aforementioned high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model, in step C, extracts non-static delay information at the location of each single BeiDou station based on the tropospheric static delay information at the location of each single BeiDou station. Specifically, it obtains the non-static delay information at the location of each single BeiDou station by subtracting the tropospheric static delay from the zenith tropospheric delay at the location of each single BeiDou station.

[0009] The aforementioned high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model, step D, involves constructing a sample dataset based on the location and non-static delay information of each single BeiDou station, and then using the sample dataset to calculate adaptive weight information for the sample data. The specific steps are as follows. Step D1: Construct a sample dataset based on the location and non-hydrostatic delay information of each Beidou station. Specifically, sort the location and non-hydrostatic delay information of each Beidou station by time and use it as a sample dataset. Then, use the top 70% of the sample data in the sample dataset as the training sample set and the remaining 30% as the test sample set. Step D2 involves calculating adaptive weight information for the sample data using the sample dataset. Specifically, this involves calculating adaptive weight information for the sample data using the training sample set within the sample dataset. The specific steps are as follows. Step D21: Calculate the relative standard deviation of the zenith tropospheric delay based on the zenith tropospheric delay information and the standard deviation of the zenith tropospheric delay at each individual BeiDou station in the training sample set, as shown in formula (2). (2) in, , and These represent the standard deviation of the zenith tropospheric delay, the relative standard deviation of the zenith tropospheric delay, and the zenith tropospheric delay value for the k-th sample at the i-th single BeiDou station, respectively. Let be the mean zenith tropospheric delay of the i-th single BeiDou station; Step D22: Calculate the in-station weight information of sample data at different times within the same single BeiDou station. Specifically, as shown in formula (3), (3) in, This represents the median of the relative standard deviations of all sample data within the same single BeiDou satellite station. These are sample data from different times within the same single BeiDou satellite navigation station. Step D23: Calculate the average relative standard deviation of a single BeiDou station using the relative standard deviations of all sample data within the same BeiDou station, as shown in formula (4). (4) in, Let be the average relative standard deviation of the i-th single BeiDou station. Let be the relative standard deviation of the k-th sample within the i-th single BeiDou station. This represents the total number of samples for the i-th single BeiDou station; Step D24: Calculate the inter-station weight information of sample data from different individual BeiDou stations. Specifically, as shown in formula (5), (5) in, This represents the median of the average relative standard deviation of all individual BeiDou stations. Step D25: Calculate the adaptive weight information of sample data from different single BeiDou stations at different times. Specifically, as shown in formula (6), (6).

[0010] The aforementioned high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model, in step E, involves constructing an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information from sample data. Then, based on this adaptive weighted residual minimum criterion loss function, the delay of the single BeiDou radio signal is modeled to obtain a single BeiDou radio signal delay weighted optimization model. The specific steps are as follows. Step E1 involves constructing an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information from the sample data. The specific steps are as follows: Step E11: Calculate the training process weights of the sample data based on the sample training residuals. Specifically, as shown in formula (7), ; (7) in, and These are the model's predicted values ​​and the actual label values, respectively. Let be the training residual of the t-th sample in the training sample set. The median of the training residuals for all samples in the training sample set; Step E12, based on the adaptive weight information of the training sample set and training process weights Construct an adaptive weighted residual minimum criterion loss function that integrates the weights of the training sample set. Specifically, as shown in formula (8), ; (8) in, For mixed weighted information, As a regulating factor, The total number of training samples, For the training set One sample, For the training set The mixed weighted information corresponding to each sample; Step E2 involves modeling the delay of a single BeiDou radio signal based on an adaptive weighted residual minimum criterion loss function and obtaining a weighted optimization model for the delay of the single BeiDou radio signal. Specifically, an artificial neural network structure is used to model the delay of the single BeiDou radio signal and obtain a weighted optimization model for the delay of the single BeiDou radio signal. The artificial neural network structure is specifically a BP neural network. The inputs to the weighted optimization model for the delay of the single BeiDou radio signal are time, longitude, latitude, and elevation, and the output of the weighted optimization model for the delay of the single BeiDou radio signal is non-static delay information.

[0011] The aforementioned high-precision positioning method based on a single BeiDou radio signal delay-weighted optimization model, step F, utilizes the single BeiDou radio signal delay-weighted optimization model to perform real-time correction of the tropospheric delay caused by the propagation of the single BeiDou radio signal during the single BeiDou wireless positioning process and completes the high-precision positioning operation. The specific steps are as follows. Step F1: Input the location and observation time of a single Beidou station into the single Beidou radio signal delay weighted optimization model and obtain the corresponding radio signal delay information in real time. Then, add the obtained radio signal delay information as a priori constraint to the single Beidou radio signal observation equation and obtain the constrained single Beidou radio signal observation equation. Step F2 involves using robust least squares to solve the constrained single BeiDou radio signal observation equations and obtain the precise location information of a single BeiDou station.

[0012] A high-precision positioning system based on a single BeiDou radio signal delay weighted optimization model includes a data acquisition module, a tropospheric static delay calculation module, a non-static delay extraction module, an adaptive weight calculation module, a model construction module, and a tropospheric delay correction module. The data acquisition module collects single BeiDou radio signal observation data from various single BeiDou stations, processes the data, and obtains the location and radio signal delay information of each station. The tropospheric static delay calculation module collects atmospheric reanalysis data synchronized with the single BeiDou radio signal observation data and calculates the tropospheric static delay information at each station's location. The non-static delay extraction module extracts the tropospheric delay information based on the tropospheric static delay information at each station's location. The non-static delay information at the location of each BeiDou station is collected. The adaptive weight calculation module is used to construct a sample dataset based on the location and non-static delay information of each BeiDou station, and then use the sample dataset to calculate the adaptive weight information of the sample data. The model construction module is used to construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using the adaptive weight information of the sample data, and then model the delay of the single BeiDou radio signal based on the adaptive weighted residual minimum criterion loss function to obtain a weighted optimization model of the single BeiDou radio signal delay. The tropospheric delay correction module is used to use the weighted optimization model of the single BeiDou radio signal delay to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process and complete the high-precision positioning operation.

[0013] The beneficial effects of this invention are as follows: This invention provides a high-precision positioning method and system based on a single BeiDou radio signal delay weighted optimization model. First, it collects single BeiDou radio signal observation data from various single BeiDou stations. Then, it processes the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. Next, it collects atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculates the tropospheric static delay information at the location of each single BeiDou station. Then, based on the tropospheric static delay information at the location of each single BeiDou station, it extracts the non-static delay information at the location of each single BeiDou station. Subsequently, it constructs a sample dataset based on the location and non-static delay information of each single BeiDou station. Then, it uses the sample dataset to calculate the adaptive weight information of the sample data. Finally, it uses the adaptive weight information of the sample data to construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability. Then, based on... An adaptive weighted residual minimum criterion loss function is used to model the delay of a single BeiDou radio signal and obtain a weighted optimization model for the delay. Finally, this model is used to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process, thus completing high-precision positioning. This effectively realizes that the high-precision positioning method and system can perform high-precision and high-reliability calculation of radio signal delay parameters in single BeiDou radio navigation and positioning processes at different times and locations. Furthermore, by constructing a weighted loss function with adaptive weight update capability, the contribution of accurate sample data in the modeling process can be improved. This not only enhances the single BeiDou solution model and weakens the correlation between tropospheric delay and station elevation parameters by utilizing real-time high-precision tropospheric prior information, but also improves the stability and convergence speed of short-time and real-time positioning solutions, exhibiting high real-time performance and reliability. Attached Figure Description

[0014] Figure 1 This is an overall flowchart of a high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model according to the present invention; Figure 2 This is a diagram showing the overall modeling accuracy of the single Beidou radio signal delay weighted optimization model in an embodiment of the present invention, where a is the weighted loss function model and b is the unweighted loss function model. Figure 3 This is a graph showing the variation in modeling accuracy of the single Beidou radio signal delay weighted optimization model in different months in an embodiment of the present invention; Figure 4 This is a comparison chart of positioning deviations between unconstrained single BeiDou positioning and single BeiDou positioning with additional tropospheric constraints in an embodiment of the present invention. Detailed Implementation

[0015] The present invention will now be further described with reference to the accompanying drawings.

[0016] like Figure 1 As shown, the present invention provides a high-precision positioning method based on a single BeiDou radio signal delay-weighted optimization model, comprising the following steps: Step A involves collecting single BeiDou radio signal observation data from each individual BeiDou station, then processing the data to obtain the location and radio signal delay information for each station. The specific steps are as follows. Step A1: Collect single BeiDou radio signal observation data from each single BeiDou station, specifically, collect single BeiDou radio signal observation data monitored by single BeiDou stations that are evenly distributed within the target area. Step A2 involves processing the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. Specifically, the processing of the single BeiDou radio signal observation data includes quality control and correction modeling of various error sources. Then, observation equations are established to estimate parameters and output the location and radio signal delay information of each single BeiDou station. The location and radio signal delay information of each single BeiDou station includes the observation time information, latitude and longitude information, elevation information, zenith tropospheric delay information and zenith tropospheric delay standard deviation information of each single BeiDou station.

[0017] Step B involves collecting atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculating the tropospheric static delay information at each single BeiDou station location. Specifically, based on the atmospheric reanalysis data, surface air pressure data at each single BeiDou station location is calculated using bilinear interpolation. Then, based on the surface air pressure data, the tropospheric static delay information is calculated, as shown in formula (1). (1) in, This represents the tropospheric static delay value at the location of a single BeiDou satellite station. This refers to the surface air pressure at a single Beidou satellite station. and This refers to the latitude and elevation of a single BeiDou satellite navigation station.

[0018] Step C: Extract non-static delay information at each BeiDou station location based on the tropospheric static delay information at each BeiDou station location. Specifically, subtract the tropospheric static delay from the zenith tropospheric delay at each BeiDou station location to obtain the non-static delay information at each BeiDou station location.

[0019] Step D involves constructing a sample dataset based on the location and non-static delay information of each individual BeiDou station, and then using this sample dataset to calculate adaptive weight information for the sample data. The specific steps are as follows. Step D1: Construct a sample dataset based on the location and non-hydrostatic delay information of each Beidou station. Specifically, sort the location and non-hydrostatic delay information of each Beidou station by time and use it as a sample dataset. Then, use the top 70% of the sample data in the sample dataset as the training sample set and the remaining 30% as the test sample set. Step D2 involves calculating adaptive weight information for the sample data using the sample dataset. Specifically, this involves calculating adaptive weight information for the sample data using the training sample set within the sample dataset. The specific steps are as follows. Step D21: Calculate the relative standard deviation of the zenith tropospheric delay based on the zenith tropospheric delay information and the standard deviation of the zenith tropospheric delay at each individual BeiDou station in the training sample set, as shown in formula (2). (2) in, , and These represent the standard deviation of the zenith tropospheric delay, the relative standard deviation of the zenith tropospheric delay, and the zenith tropospheric delay value for the k-th sample at the i-th single BeiDou station, respectively. Let be the mean zenith tropospheric delay of the i-th single BeiDou station; Step D22: Calculate the in-station weight information of sample data at different times within the same single BeiDou station. Specifically, as shown in formula (3), (3) in, This represents the median of the relative standard deviations of all sample data within the same single BeiDou satellite station. These are sample data from different times within the same single BeiDou satellite navigation station. Step D23: Calculate the average relative standard deviation of a single BeiDou station using the relative standard deviations of all sample data within the same BeiDou station, as shown in formula (4). (4) in, Let be the average relative standard deviation of the i-th single BeiDou station. Let be the relative standard deviation of the k-th sample within the i-th single BeiDou station. This represents the total number of samples for the i-th single BeiDou station; Step D24: Calculate the inter-station weight information of sample data from different individual BeiDou stations. Specifically, as shown in formula (5), (5) in, This represents the median of the average relative standard deviation of all individual BeiDou stations. Step D25: Calculate the adaptive weight information of sample data from different single BeiDou stations at different times. Specifically, as shown in formula (6), (6).

[0020] Step E involves constructing an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information from the sample data. Then, based on this adaptive weighted residual minimum criterion loss function, the delay of a single BeiDou radio signal is modeled, and a weighted optimization model for the delay of a single BeiDou radio signal is obtained. The specific steps are as follows. Step E1 involves constructing an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information from the sample data. The specific steps are as follows: Step E11: Calculate the training process weights of the sample data based on the sample training residuals. Specifically, as shown in formula (7), ; (7) in, and These are the model's predicted values ​​and the actual label values, respectively. Let be the training residual of the t-th sample in the training sample set. The median of the training residuals for all samples in the training sample set; Step E12, based on the adaptive weight information of the training sample set and training process weights Construct an adaptive weighted residual minimum criterion loss function that integrates the weights of the training sample set. Specifically, as shown in formula (8), ; (8) in, For mixed weighted information, As a regulating factor, The total number of training samples, For the training set One sample, For the training set The mixed weighted information corresponding to each sample; Step E2 involves modeling the delay of a single BeiDou radio signal based on an adaptive weighted residual minimum criterion loss function and obtaining a weighted optimization model for the delay of the single BeiDou radio signal. Specifically, an artificial neural network structure is used to model the delay of the single BeiDou radio signal and obtain a weighted optimization model for the delay of the single BeiDou radio signal. The artificial neural network structure is specifically a BP neural network. The inputs to the weighted optimization model for the delay of the single BeiDou radio signal are time, longitude, latitude, and elevation, and the output of the weighted optimization model for the delay of the single BeiDou radio signal is non-static delay information.

[0021] Step F involves using a single BeiDou radio signal delay weighted optimization model to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process, thereby completing the high-precision positioning operation. The specific steps are as follows. Step F1: Input the location and observation time of a single Beidou station into the single Beidou radio signal delay weighted optimization model and obtain the corresponding radio signal delay information in real time. Then, add the obtained radio signal delay information as a priori constraint to the single Beidou radio signal observation equation and obtain the constrained single Beidou radio signal observation equation. Step F2 involves using robust least squares to solve the constrained single BeiDou radio signal observation equations and obtain the precise location information of a single BeiDou station.

[0022] A high-precision positioning system based on a single BeiDou radio signal delay weighted optimization model includes a data acquisition module, a tropospheric static delay calculation module, a non-static delay extraction module, an adaptive weight calculation module, a model construction module, and a tropospheric delay correction module. The data acquisition module collects single BeiDou radio signal observation data from various single BeiDou stations, processes the data, and obtains the location and radio signal delay information of each station. The tropospheric static delay calculation module collects atmospheric reanalysis data synchronized with the single BeiDou radio signal observation data and calculates the tropospheric static delay information at each station's location. The non-static delay extraction module extracts the tropospheric delay information based on the tropospheric static delay information at each station's location. The non-static delay information at the location of each BeiDou station is collected. The adaptive weight calculation module is used to construct a sample dataset based on the location and non-static delay information of each BeiDou station, and then use the sample dataset to calculate the adaptive weight information of the sample data. The model construction module is used to construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using the adaptive weight information of the sample data, and then model the delay of the single BeiDou radio signal based on the adaptive weighted residual minimum criterion loss function to obtain a weighted optimization model of the single BeiDou radio signal delay. The tropospheric delay correction module is used to use the weighted optimization model of the single BeiDou radio signal delay to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process and complete the high-precision positioning operation.

[0023] To verify the reliability of the method proposed in this invention, the radio signal propagation delay of a single BeiDou radio station is taken as the research object. Based on the same network architecture, a weighted loss function model and an unweighted loss function model are used respectively. To test the generalization performance of the model, radio observation data from a single global BeiDou radio station are used as an example. The prediction results of the two loss function models at each station are compared with the actual values ​​of the radio signal delay, and the root mean square error of each station is calculated to evaluate its spatial performance.

[0024] Depend on Figure 2 It can be seen that both schemes achieved a correlation coefficient of 0.99, indicating that their overall forecast trends were highly consistent with the observed values. However, the weighted loss function model showed a significant advantage in controlling precision and systematic bias. Its root mean square error decreased from 12.28 mm in the unweighted model to 10.05 mm, improving forecast accuracy by approximately 18.2%, and the scatter distribution became more compact and converged towards the standard line. Meanwhile, the bias of the unweighted loss function model was 2.9 mm, while the weighted loss function model further reduced it to -1.8 mm, effectively weakening the systematic bias in the forecast process.

[0025] Figure 3The error timing comparison of the two methods is shown. From Figure 3 It can be seen that the unweighted loss function model exhibits poor stability throughout the year, with the error curve fluctuating dramatically with the seasons, especially in the summer when signal propagation delay is high, and its maximum daily average error once exceeded 30 mm. In contrast, the weighted loss function model showed more stable error performance throughout 2024, with error fluctuations mostly compressed within ±10 mm. The standard deviation of the error of the weighted loss function model was reduced by approximately 35.2% compared to the unweighted loss function model. This effectively solves the problem that the standard model is prone to large biases when dealing with nonlinear and highly fluctuating data.

[0026] like Figure 4 As shown, the positioning errors of unconstrained single BeiDou positioning and single BeiDou positioning with tropospheric constraints over time are illustrated in the EW, UD, and NS directions. Compared to unconstrained single BeiDou positioning, single BeiDou positioning with tropospheric constraints exhibits smaller error fluctuations and faster convergence in the initial positioning stage, especially in the EW and NS directions, where it significantly suppresses abrupt changes in initial error. In the UD direction, both methods eventually stabilize, but the overall curve of single BeiDou positioning with tropospheric constraints is smoother. These results demonstrate that single BeiDou positioning with tropospheric constraints effectively improves the convergence performance in the initial positioning stage and enhances the stability and reliability of the positioning solution.

[0027] In summary, the high-precision positioning method and system based on a single BeiDou radio signal delay weighted optimization model of the present invention first collects single BeiDou radio signal observation data from various single BeiDou stations, then processes the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station, then collects atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculates the tropospheric static delay information at the location of each single BeiDou station, then extracts the non-static delay information at the location of each single BeiDou station based on the tropospheric static delay information, then constructs a sample dataset based on the location and non-static delay information of each single BeiDou station, then uses the sample dataset to calculate the adaptive weight information of the sample data, then uses the adaptive weight information of the sample data to construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability, and finally... The weighted residual minimum criterion loss function is used to model the delay of a single BeiDou radio signal and obtain a weighted optimization model for the delay. Finally, the weighted optimization model is used to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process, and complete the high-precision positioning operation. This effectively realizes that the high-precision positioning method and system can perform high-precision and high-reliability calculation of radio signal delay parameters in the single BeiDou radio navigation and positioning process at different times and locations. Moreover, by constructing a weighted loss function with adaptive weight update capability, the contribution of accurate sample data in the modeling process can be improved. This not only enhances the single BeiDou solution model and weakens the correlation between tropospheric delay and station elevation parameters by utilizing real-time high-precision tropospheric prior information, but also improves the stability and convergence speed of short-time and real-time positioning solutions, exhibiting high real-time performance and reliability.

[0028] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A high-precision positioning method based on a single BeiDou radio signal delay-weighted optimization model, characterized in that: Includes the following steps, Step A: Collect single BeiDou radio signal observation data from each single BeiDou station, then process the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. Step B: Collect atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculate the tropospheric static delay information at the location of each single BeiDou station. Step C: Extract non-static delay information at the location of each individual BeiDou station based on the tropospheric static delay information at each individual BeiDou station location. Step D: Construct a sample dataset based on the location and non-static delay information of each individual BeiDou station, and then use the sample dataset to calculate the adaptive weight information of the sample data. Step E: Using the adaptive weight information of the sample data, construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability. Then, model the delay of a single BeiDou radio signal based on the adaptive weighted residual minimum criterion loss function and obtain a weighted optimization model for the delay of a single BeiDou radio signal. Step F involves using a single BeiDou radio signal delay weighted optimization model to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process and completing the high-precision positioning operation.

2. The high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model according to claim 1, characterized in that: Step A involves collecting single BeiDou radio signal observation data from each individual BeiDou station, then processing the data to obtain the location and radio signal delay information for each station. The specific steps are as follows. Step A1: Collect single BeiDou radio signal observation data from each single BeiDou station, specifically, collect single BeiDou radio signal observation data monitored by single BeiDou stations that are evenly distributed within the target area. Step A2 involves processing the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. Specifically, the processing of the single BeiDou radio signal observation data includes quality control and correction modeling of various error sources. Then, observation equations are established to estimate parameters and output the location and radio signal delay information of each single BeiDou station. The location and radio signal delay information of each single BeiDou station includes the observation time information, latitude and longitude information, elevation information, zenith tropospheric delay information and zenith tropospheric delay standard deviation information of each single BeiDou station.

3. The high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model according to claim 2, characterized in that: Step B involves collecting atmospheric reanalysis data synchronized with the observation time of the single BeiDou radio signal observation data and calculating the tropospheric static delay information at each single BeiDou station location. Specifically, based on the atmospheric reanalysis data, surface air pressure data at each single BeiDou station location is calculated using bilinear interpolation. Then, based on the surface air pressure data, the tropospheric static delay information is calculated, as shown in formula (1). （1） in, This represents the tropospheric static delay value at the location of a single BeiDou satellite station. This represents the surface air pressure at a single Beidou satellite monitoring station. and This refers to the latitude and elevation of a single BeiDou satellite navigation station.

4. The high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model according to claim 3, characterized in that: Step C: Extract non-static delay information at each BeiDou station location based on the tropospheric static delay information at each BeiDou station location. Specifically, subtract the tropospheric static delay from the zenith tropospheric delay at each BeiDou station location to obtain the non-static delay information at each BeiDou station location.

5. The high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model according to claim 4, characterized in that: Step D involves constructing a sample dataset based on the location and non-static delay information of each individual BeiDou station, and then using this sample dataset to calculate adaptive weight information for the sample data. The specific steps are as follows. Step D1: Construct a sample dataset based on the location and non-hydrostatic delay information of each Beidou station. Specifically, sort the location and non-hydrostatic delay information of each Beidou station by time and use it as a sample dataset. Then, use the top 70% of the sample data in the sample dataset as the training sample set and the remaining 30% as the test sample set. Step D2 involves calculating adaptive weight information for the sample data using the sample dataset. Specifically, this involves calculating adaptive weight information for the sample data using the training sample set within the sample dataset. The specific steps are as follows. Step D21: Calculate the relative standard deviation of the zenith tropospheric delay based on the zenith tropospheric delay information and the standard deviation of the zenith tropospheric delay at each individual BeiDou station in the training sample set, as shown in formula (2). （2） in, , and These represent the standard deviation of the zenith tropospheric delay, the relative standard deviation of the zenith tropospheric delay, and the zenith tropospheric delay value for the k-th sample at the i-th single BeiDou station, respectively. Let be the mean zenith tropospheric delay of the i-th single BeiDou station; Step D22: Calculate the in-station weight information of sample data at different times within the same single BeiDou station. Specifically, as shown in formula (3), （3） in, This represents the median of the relative standard deviations of all sample data within the same single BeiDou satellite station. These are sample data from different times within the same single BeiDou satellite navigation station. Step D23: Calculate the average relative standard deviation of a single BeiDou station using the relative standard deviations of all sample data within the same BeiDou station, as shown in formula (4). （4） in, Let be the average relative standard deviation of the i-th single BeiDou station. Let be the relative standard deviation of the k-th sample within the i-th single BeiDou station. This represents the total number of samples for the i-th single BeiDou station; Step D24: Calculate the inter-station weight information of sample data from different individual BeiDou stations. Specifically, as shown in formula (5), （5） in, This represents the median of the average relative standard deviation of all individual BeiDou stations. Step D25: Calculate the adaptive weight information of sample data from different single BeiDou stations at different times. Specifically, as shown in formula (6), （6）。 6. The high-precision positioning method based on a single BeiDou radio signal delay weighted optimization model according to claim 5, characterized in that: Step E involves constructing an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information from the sample data. Then, based on this adaptive weighted residual minimum criterion loss function, the delay of a single BeiDou radio signal is modeled, and a weighted optimization model for the delay of a single BeiDou radio signal is obtained. The specific steps are as follows. Step E1 involves constructing an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information from the sample data. The specific steps are as follows: Step E11: Calculate the training process weights of the sample data based on the sample training residuals. Specifically, as shown in formula (7), ； （7） in, and These are the model's predicted values ​​and the actual label values, respectively. Let be the training residual of the t-th sample in the training sample set. The median of the training residuals for all samples in the training sample set; Step E12, based on the adaptive weight information of the training sample set and training process weights Construct an adaptive weighted residual minimum criterion loss function that integrates the weights of the training sample set. Specifically, as shown in formula (8), ； （8） in, For mixed weighted information, As a regulating factor, The total number of training samples, For the training set One sample, For the training set The mixed weighted information corresponding to each sample; Step E2 involves modeling the delay of a single BeiDou radio signal based on an adaptive weighted residual minimum criterion loss function and obtaining a weighted optimization model for the delay of the single BeiDou radio signal. Specifically, an artificial neural network structure is used to model the delay of the single BeiDou radio signal and obtain a weighted optimization model for the delay of the single BeiDou radio signal. The artificial neural network structure is specifically a BP neural network. The inputs to the weighted optimization model for the delay of the single BeiDou radio signal are time, longitude, latitude, and elevation, and the output of the weighted optimization model for the delay of the single BeiDou radio signal is non-static delay information.

7. A high-precision positioning method based on a single BeiDou radio signal delay-weighted optimization model according to claim 6, characterized in that: Step F involves using a single BeiDou radio signal delay weighted optimization model to correct the tropospheric delay caused by the propagation of the single BeiDou radio signal in real time during the single BeiDou wireless positioning process, thereby completing the high-precision positioning operation. The specific steps are as follows. Step F1: Input the location and observation time of a single Beidou station into the single Beidou radio signal delay weighted optimization model and obtain the corresponding radio signal delay information in real time. Then, add the obtained radio signal delay information as a priori constraint to the single Beidou radio signal observation equation and obtain the constrained single Beidou radio signal observation equation. Step F2 involves using robust least squares to solve the constrained single BeiDou radio signal observation equations and obtain the precise location information of a single BeiDou station.

8. A high-precision positioning system based on a single BeiDou radio signal delay weighted optimization model, wherein the specific positioning process of the high-precision positioning system is based on the high-precision positioning method according to any one of claims 1-7, characterized in that: It includes a data acquisition module, a tropospheric static delay calculation module, a non-static delay extraction module, an adaptive weight calculation module, a model building module, and a tropospheric delay correction module. The data acquisition module is used to collect single BeiDou radio signal observation data from each single BeiDou station, and then process the single BeiDou radio signal observation data to obtain the location and radio signal delay information of each single BeiDou station. The tropospheric static delay calculation module is used to collect atmospheric reanalysis data that is synchronized with the observation time of the single BeiDou radio signal observation data and to calculate the tropospheric static delay information at the location of each single BeiDou station. The non-static delay extraction module is used to extract non-static delay information at the location of each individual BeiDou station based on the tropospheric static delay information at the location of each individual BeiDou station. The adaptive weight calculation module is used to construct a sample dataset based on the location and non-static delay information of each single Beidou station, and then use the sample dataset to calculate the adaptive weight information of the sample data. The model building module is used to construct an adaptive weighted residual minimum criterion loss function with adaptive weight update capability using adaptive weight information of sample data, and then to model the delay of a single Beidou radio signal based on the adaptive weighted residual minimum criterion loss function to obtain a weighted optimization model of the delay of a single Beidou radio signal. The tropospheric delay correction module is used to perform real-time correction of the tropospheric delay caused by the propagation of the single BeiDou radio signal during the single BeiDou wireless positioning process using a single BeiDou radio signal delay weighted optimization model, and to complete the high-precision positioning operation.

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