A GNSS raw pseudorange observation prediction method based on a GRU network

Abstract

The application discloses a GNSS original pseudorange observation value prediction method based on a GRU network, and comprises the following steps: acquiring a GNSS original pseudorange observation value sequence, and calculating a difference sequence; screening abnormal value elements, dividing the GNSS original pseudorange observation value sequence into subsequence segments, performing cubic polynomial fitting, and obtaining solving coefficients; calculating GNSS original pseudorange fitting values of the subsequence segments, splicing the GNSS original pseudorange fitting values of all the subsequence segments, and obtaining a trend item sequence; calculating a residual sequence by subtracting the trend item sequence from the GNSS original pseudorange observation value sequence; and taking the GNSS original pseudorange observation value sequence, the trend item sequence and the residual sequence as feature samples, inputting the feature samples into the GRU network, and outputting corresponding prediction results. The method can accurately predict original pseudorange observation values to compensate for GNSS interruption situations, and further expand the application of GNSS high-precision positioning technology in a shielding environment.

Description

Technical Field

[0001] This invention relates to the field of satellite positioning technology, and specifically to a method for predicting raw pseudorange observations of GNSS based on GRU networks. Background Technology

[0002] Global Navigation Satellite Systems (GNSS), with their all-weather, high-precision positioning capabilities, have become a core supporting technology in numerous fields such as surveying, transportation, low-altitude economy, and autonomous driving. Among these, pseudorange observations, as the fundamental data for GNSS positioning, directly determine the reliability of the positioning service based on their continuity and accuracy. However, in complex environments such as urban canyons, mountainous areas, and indoor spaces, GNSS signals are easily obstructed by buildings and terrain, leading to interruptions or distortions in pseudorange observations. This, in turn, causes positioning drift and navigation failure, severely restricting the application expansion of GNSS in complex scenarios.

[0003] Traditional solutions to GNSS signal loss often rely on multi-sensor fusion and differential positioning technologies. However, these methods suffer from limitations such as high hardware costs, high system complexity, and insufficient real-time performance. With breakthroughs in deep learning technology in time series forecasting, using data-driven models to intelligently predict pseudorange observations has become a new approach to solving the signal blockage problem.

[0004] Gated Recurrent Neural Networks (GRUs), as efficient time series forecasting models, can capture long-term dependencies in time series data through gating mechanisms. They also offer advantages such as fewer parameters and faster training speeds, making them suitable for processing data with strong time-series characteristics, such as GNSS pseudorange observations. Currently, GRUs have demonstrated excellent performance in fields such as weather forecasting and financial forecasting, but they have not yet been widely applied to the prediction compensation of GNSS pseudorange observations. Furthermore, GNSS pseudorange observations are prone to jumps, and directly inputting them into a GRU model for prediction would hinder the acquisition of high-precision model predictions.

[0005] Therefore, developing a prediction model for GNSS raw pseudorange observations based on GRU is of great significance for improving the continuity and reliability of GNSS positioning in complex environments and promoting the development of navigation technology towards intelligence and autonomy. Summary of the Invention

[0006] The purpose of this invention is to provide a method for predicting GNSS raw pseudorange observations based on GRU networks, which can achieve high-precision and high-reliability positioning using satellite positioning technology.

[0007] To achieve the above functions, this invention designs a method for predicting raw GNSS pseudorange observations based on a GRU network. The method is characterized by executing the following steps S1-S9 to complete the prediction of raw GNSS pseudorange observations:

[0008] Step S1: Obtain the raw GNSS pseudorange observation sequence, and perform an inter-epoch difference calculation on the raw GNSS pseudorange observation sequence to obtain a first difference sequence;

[0009] Step S2: Perform epoch-level quadratic difference calculations on the obtained first-order difference sequence to obtain the second-order difference sequence;

[0010] Step S3: For the obtained quadratic difference sequence, calculate the arithmetic mean and standard deviation of each element of the quadratic difference sequence;

[0011] Step S4: Based on the three-standard-deviation criterion, mark the elements in the quadratic difference sequence whose distance from the arithmetic mean exceeds three standard deviations as outlier elements, obtain the retrieval index corresponding to the outlier elements, and divide the GNSS raw pseudorange observation sequence into multiple continuous subsequence segments according to the retrieval index;

[0012] Step S5: Perform cubic polynomial fitting on each subsequence segment to construct a set of error equations in matrix vector form, and solve them using the least squares method to obtain the solution coefficients of the cubic polynomial corresponding to each subsequence segment.

[0013] Step S6: Using the solution coefficients of the cubic polynomials corresponding to each subsequence segment, calculate the GNSS original pseudorange fitting value of the corresponding subsequence segment respectively, and splice the GNSS original pseudorange fitting values ​​of all subsequence segments to obtain a trend term sequence of the same length as the GNSS original pseudorange observation value sequence.

[0014] Step S7: Subtract the original GNSS pseudorange observation sequence from the trend term sequence to calculate the residual sequence;

[0015] Step S8: Use the original GNSS pseudorange observation sequence, trend term sequence, and residual sequence as feature samples to divide the training set and test set;

[0016] Step S9: Input the feature samples from the training set and the test set into the gated recurrent neural network model, train and test the gated recurrent neural network model, and use the trained gated recurrent neural network model to output the corresponding prediction results for the raw pseudorange observations of GNSS to be predicted.

[0017] As a preferred technical solution of the present invention: In step S1, the GNSS raw pseudorange observation sequence Perform a first-order difference calculation between epochs to obtain a first-order difference sequence. Each element in the formula is as follows:

[0018] ;

[0019] In the formula, This represents the raw pseudorange observation of GNSS at the nth epoch. Let t be the raw pseudorange observation of GNSS at epoch n+1, and t be the sequence of raw pseudorange observations of GNSS. Total number of epochs, This is the element of the first-order difference sequence corresponding to the nth epoch;

[0020] Elements of the first-order difference sequence corresponding to each epoch Construct a first difference sequence .

[0021] As a preferred technical solution of the present invention: in step S2, the quadratic difference sequence is calculated. Each element in the formula is as follows:

[0022] ;

[0023] In the formula, For the element of the quadratic difference sequence corresponding to the m-th epoch;

[0024] Using the quadratic difference sequence elements corresponding to each epoch Constructing a quadratic difference sequence .

[0025] As a preferred embodiment of the present invention: in step S3, the formulas for calculating the arithmetic mean and standard deviation of each element of the quadratic difference sequence are as follows:

[0026] ;

[0027] ;

[0028] In the formula, For a quadratic difference sequence The arithmetic mean, For a quadratic difference sequence The standard deviation of t is the sequence of raw pseudorange observations from GNSS. Total epochs; is the element of the quadratic difference sequence corresponding to the m-th epoch.

[0029] As a preferred embodiment of the present invention, the specific steps of step S4 are as follows:

[0030] Step S4.1: Traverse the quadratic difference sequence Determine each element to the arithmetic mean Is the distance greater than three standard deviations? If so, mark it as an outlier; otherwise, check the next element, and so on, until all quadratic difference sequences have been processed. All elements in the set are evaluated;

[0031] Step S4.2: Extract all outlier elements from the quadratic difference sequence Search subscript ; Calculate the outlier elements in the GNSS raw pseudorange observation sequence The corresponding search index :

[0032] ;

[0033] In the formula, p represents the total number of search subscripts. This indicates that the k-th outlier element is in the quadratic difference sequence. The search subscript in the middle, This represents the k-th outlier element in the GNSS raw pseudorange observation sequence. The corresponding search index;

[0034] Step S4.3: Use the search index Using this as a dividing point, the sequence of raw GNSS pseudorange observations is... Divided into A continuous subsequence segment:

[0035] ;

[0036] In the formula, express There are 10 subsequence segments, among which... For subsequence segments GNSS raw pseudorange observations in For subsequence segments The raw pseudorange observations of GNSS in the data, and so on. For subsequence segments GNSS raw pseudorange observations in For subsequence segments The raw pseudorange observations of GNSS in the data.

[0037] As a preferred embodiment of the present invention, the specific steps of step S5 are as follows:

[0038] Step S5.1: For any divided subsequence segment, construct a cubic polynomial fitting model:

[0039] ;

[0040] in, For the raw pseudorange observation of GNSS at the l-th epoch, if for a subsequence segment ,but If targeting a sub-sequence segment ,but Similarly, if we are targeting a subsequence segment... ,but If targeting sub-sequence segments ,but ; , , , The coefficients of the cubic polynomial are to be solved.

[0041] Step S5.2: Based on the cubic polynomial fitting model, construct the corresponding linear equation system and convert it into an error equation system in matrix-vector form. For the first subsequence segment:

[0042] ;

[0043] In the formula, This is the vector of raw GNSS pseudorange observations for the subsequence segment. ; The fitting coefficient matrix, ; Let be the coefficient vector of the polynomial to be solved. ;

[0044] Step S5.3: Solve the system of error equations in matrix-vector form using the least squares method to obtain the estimated vector of the coefficients to be solved. The solution formula is:

[0045] ;

[0046] In the formula, The fitting coefficient matrix The transpose of the matrix, For square array The inverse matrix; , , , These are the solution coefficients of a cubic polynomial;

[0047] Step S5.4: Repeat steps S5.1 to S5.3 for all the divided subsequence segments to calculate the solution coefficients of the cubic polynomial corresponding to each subsequence segment, and form the solution coefficient vector of the cubic polynomial.

[0048] As a preferred embodiment of the present invention, the specific steps of step S6 are as follows:

[0049] Step S6.1: For each subsequence segment, based on the solution coefficients of its cubic polynomial, calculate the GNSS raw pseudorange fitting value corresponding to each epoch within that subsequence segment. The calculation formula is as follows:

[0050] ;

[0051] In the formula, The original pseudorange fitted value of GNSS in the l-th epoch;

[0052] Step S6.2: Arrange the GNSS raw pseudorange fitted values ​​of all subsequence segments according to the GNSS raw pseudorange observation value sequence. By splicing the epochs in chronological order, a sequence of original GNSS pseudorange observations is obtained. Equal-length trend term sequence t is the sequence of raw pseudorange observations from GNSS. Total number of epochs.

[0053] As a preferred technical solution of the present invention, the specific method of step S7 is as follows:

[0054] GNSS raw pseudorange observation sequence Compared with the trend term sequence obtained in step S6 The difference is calculated to obtain the residual sequence. The specific formula for each element in the residual sequence is:

[0055] ;

[0056] In the formula, This represents the residual value corresponding to the i-th epoch in the original pseudorange observation sequence. The final residual sequence is obtained. For the i-th epoch, the raw pseudorange observation value of GNSS is... This represents the trend value corresponding to the i-th epoch in the trend term sequence.

[0057] The present invention also designs a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the GNSS raw pseudorange observation prediction method based on GRU network.

[0058] The present invention also designs a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in the GNSS raw pseudorange observation prediction method based on GRU network.

[0059] Beneficial effects: Compared with the prior art, the advantages of the present invention include:

[0060] This invention designs a method for predicting raw GNSS pseudorange observations based on GRU networks. It focuses on the situation of GNSS signal interruption caused by obstruction environment. By using multiple feature inputs, it avoids the problem of poor prediction accuracy caused by the jump of GNSS pseudorange observations and realizes accurate prediction of raw pseudorange observations.

[0061] The main advantage of this method is that it enables the prediction of pseudorange observations in scenarios where GNSS signals are interrupted, further expanding the application scenarios of GNSS positioning. Attached Figure Description

[0062] Figure 1 This is a flowchart of a method for predicting raw pseudorange observations of GNSS based on a GRU network, according to an embodiment of the present invention. Detailed Implementation

[0063] The present invention will be further described below with reference to the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and should not be used to limit the scope of protection of the present invention.

[0064] This invention provides a method for predicting raw GNSS pseudorange observations based on a GRU network, referring to... Figure 1 Perform the following steps S1-S9 to complete the prediction of the raw GNSS pseudorange observations:

[0065] Step S1: Obtain the raw GNSS pseudorange observation sequence, and perform an inter-epoch difference calculation on the raw GNSS pseudorange observation sequence to obtain a first difference sequence;

[0066] The data in this embodiment comes from a set of vehicle-mounted GNSS data, and the receiver model is NovAtel GPSCard. The observation time interval is set to 1 second, for a total of 600 epochs. Data from epochs 1 to 510 of the GPS G31 satellite are used for model training to predict the pseudorange observation value of the satellite at epoch 511.

[0067] In step S1, the GNSS raw pseudorange observation sequence is processed. Perform a first-order difference calculation between epochs to obtain a first-order difference sequence. Each element in the formula is as follows:

[0068] ;

[0069] In the formula, This represents the raw pseudorange observation of GNSS at the nth epoch. Let t be the raw pseudorange observation of GNSS at epoch n+1, and t be the sequence of raw pseudorange observations of GNSS. Total number of epochs, For the element of the first-order difference sequence corresponding to the nth epoch;

[0070] Elements of the first-order difference sequence corresponding to each epoch Construct a first difference sequence .

[0071] In this embodiment, the sequence of raw GNSS pseudorange observations is as follows:

[0072] ;

[0073] The calculated first-order difference sequence for:

[0074] ;

[0075] Step S2: Perform epoch-level quadratic difference calculations on the obtained first-order difference sequence to obtain the second-order difference sequence;

[0076] In step S2, the quadratic difference sequence is calculated. Each element in the formula is as follows:

[0077] ;

[0078] In the formula, For the element of the quadratic difference sequence corresponding to the m-th epoch;

[0079] Using the quadratic difference sequence elements corresponding to each epoch Constructing a quadratic difference sequence .

[0080] In the embodiment, the quadratic difference sequence for:

[0081] ;

[0082] Step S3: For the obtained quadratic difference sequence, calculate the arithmetic mean and standard deviation of each element of the quadratic difference sequence;

[0083] In step S3, the formulas for calculating the arithmetic mean and standard deviation of each element in the quadratic difference sequence are as follows:

[0084] ;

[0085] ;

[0086] In the formula, For a quadratic difference sequence The arithmetic mean, For a quadratic difference sequence The standard deviation of t is the sequence of raw pseudorange observations from GNSS. Total number of epochs; is the element of the quadratic difference sequence corresponding to the m-th epoch.

[0087] In the embodiment, the arithmetic mean and standard deviation of the elements of the quadratic difference sequence are as follows:

[0088] ;

[0089] ;

[0090] Step S4: Based on the three-standard-deviation criterion, mark the elements in the quadratic difference sequence whose distance from the arithmetic mean exceeds three standard deviations as outlier elements, obtain the retrieval index corresponding to the outlier elements, and divide the GNSS raw pseudorange observation sequence into multiple continuous subsequence segments according to the retrieval index;

[0091] The specific steps of step S4 are as follows:

[0092] Step S4.1: Traverse the quadratic difference sequence Determine each element to the arithmetic mean Is the distance greater than three standard deviations? If so, mark it as an outlier; otherwise, check the next element, and so on, until all quadratic difference sequences have been processed. All elements in the set are evaluated;

[0093] Step S4.2: Extract all outlier elements from the quadratic difference sequence Search subscript ; Calculate the outlier elements in the GNSS raw pseudorange observation sequence The corresponding search index :

[0094] ;

[0095] In the formula, p represents the total number of search subscripts. This indicates that the k-th outlier element is in the quadratic difference sequence. The search subscript in the middle, This represents the k-th outlier element in the GNSS raw pseudorange observation sequence. The corresponding search index;

[0096] In the embodiment, all outlier elements are extracted from the quadratic difference sequence. Search subscript in:

[0097] ;

[0098] Based on this, the retrieval indices of these outlier elements in the GNSS raw pseudorange observation sequence are calculated:

[0099] ;

[0100] Step S4.3: Use the search index Using this as a dividing point, the sequence of raw GNSS pseudorange observations is... Divided into A continuous subsequence segment:

[0101] ;

[0102] In the formula, express There are 10 subsequence segments, among which... For subsequence segments GNSS raw pseudorange observations in For subsequence segments The raw pseudorange observations of GNSS in the data, and so on. For subsequence segments GNSS raw pseudorange observations in For subsequence segments The raw pseudorange observations of GNSS in the data.

[0103] In this embodiment, the divided continuous sub-sequence segments are as follows:

[0104] ;

[0105] Step S5: Perform cubic polynomial fitting on each subsequence segment to construct a set of error equations in matrix vector form, and solve them using the least squares method to obtain the solution coefficients of the cubic polynomial corresponding to each subsequence segment.

[0106] The specific steps of step S5 are as follows:

[0107] Step S5.1: For any divided subsequence segment, construct a cubic polynomial fitting model:

[0108] ;

[0109] in, For the raw pseudorange observation of GNSS at the l-th epoch, if for a subsequence segment ,but If targeting a sub-sequence segment ,but Similarly, if we are targeting a subsequence segment... ,but If targeting sub-sequence segments ,but ; , , , The coefficients of the cubic polynomial are to be solved.

[0110] With the first subsequence segment For example:

[0111] ;

[0112] Step S5.2: Based on the cubic polynomial fitting model, construct the corresponding linear equation system and convert it into an error equation system in matrix-vector form. For the first subsequence segment:

[0113] ;

[0114] In the formula, This is the vector of raw GNSS pseudorange observations for the subsequence segment. ; The fitting coefficient matrix, ; Let be the coefficient vector of the polynomial to be solved. ;

[0115] In the example:

[0116]

[0117] ;

[0118] Step S5.3: Solve the system of error equations in matrix-vector form using the least squares method to obtain the estimated vector of the coefficients to be solved. The solution formula is:

[0119] ;

[0120] In the formula, The fitting coefficient matrix The transpose of the matrix, For square array The inverse matrix; , , , These are the solution coefficients of a cubic polynomial;

[0121] In the example:

[0122] ;

[0123] Step S5.4: Repeat steps S5.1 to S5.3 for all the divided subsequence segments to calculate the solution coefficients of the cubic polynomial corresponding to each subsequence segment and form the solution coefficient vector of the cubic polynomial.

[0124] Step S6: Using the solution coefficients of the cubic polynomials corresponding to each subsequence segment, calculate the GNSS original pseudorange fitting value of the corresponding subsequence segment respectively, and splice the GNSS original pseudorange fitting values ​​of all subsequence segments to obtain a trend term sequence of the same length as the GNSS original pseudorange observation value sequence.

[0125] The specific steps of step S6 are as follows:

[0126] Step S6.1: For each subsequence segment, based on the solution coefficients of its cubic polynomial, calculate the GNSS raw pseudorange fitting value corresponding to each epoch within that subsequence segment. The calculation formula is as follows:

[0127] ;

[0128] In the formula, The original pseudorange fitted value of GNSS in the l-th epoch;

[0129] Taking the first sub-sequence segment as an example:

[0130] ;

[0131] The first subsequence segment obtained is:

[0132] ;

[0133] Step S6.2: Arrange the GNSS raw pseudorange fitted values ​​of all subsequence segments according to the GNSS raw pseudorange observation value sequence. By splicing the epochs in chronological order, a sequence of original GNSS pseudorange observations is obtained. Equal-length trend term sequence t is the sequence of raw pseudorange observations from GNSS. Total number of epochs.

[0134] In the embodiment, the trend term sequence as follows:

[0135] ;

[0136] Step S7: Subtract the original GNSS pseudorange observation sequence from the trend term sequence to calculate the residual sequence;

[0137] The specific method for step S7 is as follows:

[0138] GNSS raw pseudorange observation sequence Compared with the trend term sequence obtained in step S6 The difference is calculated to obtain the residual sequence. The specific formula for each element in the residual sequence is:

[0139] ;

[0140] In the formula, This represents the residual value corresponding to the i-th epoch in the original pseudorange observation sequence. The final residual sequence is obtained. For the i-th epoch, the raw pseudorange observation value of GNSS is... This represents the trend value corresponding to the i-th epoch in the trend term sequence.

[0141] In this example, the residual sequence is as follows:

[0142] ;

[0143] Step S8: Use the original GNSS pseudorange observation sequence, trend term sequence, and residual sequence as feature samples to divide the training set and test set;

[0144] Step S9: Input the feature samples from the training set and the test set into the gated recurrent neural network model (GRU) to train and test the GRU model. Using the trained GRU model, output the corresponding prediction results for the raw pseudorange observations of GNSS to be predicted.

[0145] In this embodiment, the training parameters of the gated recurrent neural network model are set as shown in Table 1 below:

[0146] Table 1. Training parameters of the gated recurrent neural network model

[0147] Learning rate 0.0001 Hidden layer dimension (hidden dim) 128 Batch size 32 Dropout 0.2 Optimizer AdamW Number of training rounds 100

[0148] In this embodiment, after the gated recurrent neural network model is trained, the predicted pseudorange observation value for the 511th epoch is:

[0149] (rice);

[0150] The actual pseudorange observation value of the G31 satellite at epoch 511 is:

[0151] (rice);

[0152] Therefore, it can be seen that the pseudorange observation accuracy predicted by the gated recurrent neural network model is within 3 meters.

[0153] This invention also provides a computer device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps of the GNSS raw pseudorange observation prediction method based on GRU network.

[0154] This invention also provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps in the method for predicting raw pseudorange observations of GNSS based on a GRU network.

[0155] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for predicting raw pseudorange observations of GNSS based on GRU networks, characterized in that, Perform the following steps S1-S9 to complete the prediction of the raw GNSS pseudorange observations: Step S1: Obtain the raw GNSS pseudorange observation sequence, and perform an inter-epoch difference calculation on the raw GNSS pseudorange observation sequence to obtain a first difference sequence; Step S2: Perform epoch-level quadratic difference calculations on the obtained first-order difference sequence to obtain the second-order difference sequence; Step S3: For the obtained quadratic difference sequence, calculate the arithmetic mean and standard deviation of each element of the quadratic difference sequence; Step S4: Based on the three-standard-deviation criterion, mark the elements in the quadratic difference sequence whose distance from the arithmetic mean exceeds three standard deviations as outlier elements, obtain the retrieval index corresponding to the outlier elements, and divide the GNSS raw pseudorange observation sequence into multiple continuous subsequence segments according to the retrieval index; Step S5: Perform cubic polynomial fitting on each subsequence segment to construct a set of error equations in matrix vector form, and solve them using the least squares method to obtain the solution coefficients of the cubic polynomial corresponding to each subsequence segment. Step S6: Using the solution coefficients of the cubic polynomials corresponding to each subsequence segment, calculate the GNSS original pseudorange fitting value of the corresponding subsequence segment respectively, and splice the GNSS original pseudorange fitting values ​​of all subsequence segments to obtain a trend term sequence of the same length as the GNSS original pseudorange observation value sequence. Step S7: Subtract the original GNSS pseudorange observation sequence from the trend term sequence to calculate the residual sequence; Step S8: Use the original GNSS pseudorange observation sequence, trend term sequence, and residual sequence as feature samples to divide the training set and test set; Step S9: Input the feature samples from the training set and the test set into the gated recurrent neural network model, train and test the gated recurrent neural network model, and use the trained gated recurrent neural network model to output the corresponding prediction results for the raw pseudorange observations of GNSS to be predicted.

2. The method for predicting raw pseudorange observations of GNSS based on GRU networks according to claim 1, characterized in that, In step S1, the GNSS raw pseudorange observation sequence is processed. Perform a first-order difference calculation between epochs to obtain a first-order difference sequence. Each element in the formula is as follows: ； In the formula, This represents the raw pseudorange observation of GNSS at the nth epoch. Let t be the raw pseudorange observation of GNSS at epoch n+1, and t be the sequence of raw pseudorange observations of GNSS. Total number of epochs, This is the element of the first-order difference sequence corresponding to the nth epoch; Elements of the first-order difference sequence corresponding to each epoch Construct a first difference sequence .

3. The method for predicting raw GNSS pseudorange observations based on a GRU network according to claim 1, characterized in that, In step S2, the quadratic difference sequence is calculated. Each element in the formula is as follows: ； In the formula, For the element of the quadratic difference sequence corresponding to the m-th epoch; Using the quadratic difference sequence elements corresponding to each epoch Constructing a quadratic difference sequence .

4. The method for predicting raw pseudorange observations of GNSS based on GRU networks according to claim 1, characterized in that, In step S3, the formulas for calculating the arithmetic mean and standard deviation of each element in the quadratic difference sequence are as follows: ； ； In the formula, For a quadratic difference sequence The arithmetic mean, For a quadratic difference sequence The standard deviation of t is the sequence of raw pseudorange observations from GNSS. Total epochs; is the element of the quadratic difference sequence corresponding to the m-th epoch.

5. The method for predicting raw pseudorange observations of GNSS based on GRU networks according to claim 1, characterized in that, The specific steps of step S4 are as follows: Step S4.1: Traverse the quadratic difference sequence Determine each element to the arithmetic mean Is the distance greater than three standard deviations? If so, mark it as an outlier; otherwise, check the next element, and so on, until all quadratic difference sequences have been processed. All elements in the set are evaluated; Step S4.2: Extract all outlier elements from the quadratic difference sequence Search subscript ; Calculate the outlier elements in the GNSS raw pseudorange observation sequence The corresponding search index : ； In the formula, p represents the total number of search subscripts. This indicates that the k-th outlier element is in the quadratic difference sequence. The search subscript in the middle, This represents the k-th outlier element in the GNSS raw pseudorange observation sequence. The corresponding search index; Step S4.3: Use the search index Using this as a dividing point, the sequence of raw GNSS pseudorange observations is... Divided into A continuous subsequence segment: ； In the formula, express There are 10 subsequence segments, among which... For subsequence segments GNSS raw pseudorange observations in For subsequence segments The raw pseudorange observations of GNSS in the data, and so on. For subsequence segments GNSS raw pseudorange observations in For subsequence segments The raw pseudorange observations of GNSS in the data.

6. The method for predicting raw pseudorange observations of GNSS based on GRU networks according to claim 1, characterized in that, The specific steps of step S5 are as follows: Step S5.1: For any divided subsequence segment, construct a cubic polynomial fitting model: ； in, For the raw pseudorange observation of GNSS at the l-th epoch, if for a subsequence segment ,but If targeting a sub-sequence segment ,but Similarly, if we are targeting a subsequence segment... ,but If targeting sub-sequence segments ,but ; , , , The coefficients of the cubic polynomial are to be solved. Step S5.2: Based on the cubic polynomial fitting model, construct the corresponding linear equation system and convert it into an error equation system in matrix-vector form, for the first subsequence segment: ； In the formula, This is the vector of raw GNSS pseudorange observations for the subsequence segment. ; The fitting coefficient matrix, ; Let be the coefficient vector of the polynomial to be solved. ; Step S5.3: Solve the system of error equations in matrix-vector form using the least squares method to obtain the estimated vector of the coefficients to be solved. The solution formula is: ； In the formula, The fitting coefficient matrix The transpose of the matrix, For square array The inverse matrix; , , , These are the solution coefficients of a cubic polynomial; Step S5.4: Repeat steps S5.1 to S5.3 for all the divided subsequence segments to calculate the solution coefficients of the cubic polynomial corresponding to each subsequence segment, and form the solution coefficient vector of the cubic polynomial.

7. The method for predicting raw pseudorange observations of GNSS based on GRU networks according to claim 1, characterized in that, The specific steps of step S6 are as follows: Step S6.1: For each subsequence segment, based on the solution coefficients of its cubic polynomial, calculate the GNSS raw pseudorange fitting value corresponding to each epoch within that subsequence segment. The calculation formula is as follows: ； In the formula, The original pseudorange fitted value of GNSS in the l-th epoch; Step S6.2: Arrange the GNSS raw pseudorange fitted values ​​of all subsequence segments according to the GNSS raw pseudorange observation value sequence. By splicing the epochs in chronological order, a sequence of original GNSS pseudorange observations is obtained. Equal-length trend term sequence t is the sequence of raw pseudorange observations from GNSS. Total number of epochs.

8. The method for predicting raw pseudorange observations of GNSS based on GRU networks according to claim 1, characterized in that, The specific method for step S7 is as follows: GNSS raw pseudorange observation sequence Compared with the trend term sequence obtained in step S6 The difference is calculated to obtain the residual sequence. The specific formula for each element in the residual sequence is: ； In the formula, This represents the residual value corresponding to the i-th epoch in the original pseudorange observation sequence. The final residual sequence is obtained. For the i-th epoch, the raw pseudorange observation value of GNSS is... This represents the trend value corresponding to the i-th epoch in the trend term sequence.

9. A computer device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements each step of the GNSS raw pseudorange observation prediction method based on GRU network according to any one of claims 1 to 8.

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 each step of the GNSS raw pseudorange observation prediction method based on GRU network as described in any one of claims 1 to 8.

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