Tropospheric delay prediction method, device, equipment and medium based on deep learning

Abstract

The embodiment of the present application discloses a tropospheric delay prediction method, apparatus, device and medium based on deep learning, which relates to the field of navigation and positioning technology. The method includes: obtaining the tropospheric delay time series of the historical period and inputting a trained tropospheric delay prediction model; decomposing the tropospheric delay time series of the historical period into a periodic sequence and a residual sequence containing a trend term through Fourier analysis; performing prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, outputting the residual sequence containing the trend term within the prediction period, adding it to the fitted periodic sequence, and outputting the zenith tropospheric delay sequence within the prediction period. While reducing the computational complexity, the embodiment of the present application can also output high-precision tropospheric delay prediction results, and can provide real-time and accurate zenith tropospheric delay for positioning in complex and changing environments, thereby improving the efficiency of positioning solution.

Description

Technical Field

[0001] The present application relates to the field of navigation and positioning technology, and in particular to a method, device, equipment and medium for predicting tropospheric delay based on deep learning. Background Art

[0002] Zenith tropospheric delay (ZTD) is one of the key factors affecting the high-precision positioning of GNSS (Global Navigation Satellite System, GNSS). By accurately calculating the ZTD and eliminating the error caused by the ZTD, the positioning accuracy can be improved.

[0003] Currently, tropospheric models can be used to calculate the zenith tropospheric delay (ZWD), which can then be used to correct errors during positioning. However, the accuracy of most tropospheric models is limited, and most require predictions based on historical data to capture long-term trends in ZWD. However, these models fail to account for rapidly changing atmospheric conditions, making it difficult to reflect short-term variations in tropospheric delay. Furthermore, prediction accuracy fluctuates significantly across different regions. For example, in areas where the ZWD (zenith wet delay) is significantly affected by water vapor, the accuracy of these empirical models decreases, limiting the rapid resolution of real-time precise point positioning and the accuracy of ZTD water vapor inversion.

[0004] In addition, some tropospheric models can also introduce a large number of external parameters to improve the model's prediction accuracy. However, the complex calculation process of such models will lead to an increase in time cost. In a rapidly changing atmospheric environment, the prediction results cannot be output in a timely manner, resulting in low efficiency in practical applications.

[0005] Therefore, there is currently a lack of a method that can efficiently, quickly and accurately predict the zenith tropospheric delay, making it difficult to provide real-time and accurate zenith tropospheric delay for positioning in complex and changing environments, affecting the timeliness of high-precision positioning. Summary of the Invention

[0006] The embodiments of the present application provide a deep learning-based tropospheric delay prediction method, apparatus, device, and medium to address the deficiencies of the above-mentioned related technologies. The technical solutions are as follows:

[0007] In a first aspect, an embodiment of the present application provides a tropospheric delay prediction method based on deep learning, comprising:

[0008] Obtaining a tropospheric delay time series for a historical period, and inputting the tropospheric delay time series into a trained tropospheric delay prediction model;

[0009] Decomposing the tropospheric delay time series of the historical period into a periodic series and a residual series including a trend term by Fourier analysis, and fitting the periodic series;

[0010] Performing prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and outputting the residual sequence containing the trend term within the prediction period;

[0011] The residual sequence containing the trend term within the prediction period is combined with the fitted periodic sequence to output a tropospheric delay time series within the prediction period.

[0012] In an optional solution of the first aspect, after outputting the zenith tropospheric delay data within the prediction period, the method further includes:

[0013] performing positioning based on the tropospheric delay time series within the prediction period;

[0014] The zenith tropospheric delay at each moment is input into the pseudorange point positioning observation equation or the precise point positioning observation equation, and the positioning result at the corresponding moment is output.

[0015] In an optional solution of the first aspect, after decomposing the zenith tropospheric delay data into a periodic sequence and a residual sequence including a trend term by Fourier analysis, the method further includes:

[0016] Normalizing each residual value in the residual sequence containing the trend term to obtain normalized data;

[0017] performing the step of predicting by using the tropospheric delay prediction model in combination with the residual sequence including the trend term based on the standardized normalized data, and outputting a prediction result;

[0018] Performing an inverse normalization process corresponding to the normalization process on the prediction result, and outputting a residual sequence containing a trend term within the prediction period.

[0019] In an optional solution of the first aspect, the performing prediction by combining the tropospheric delay prediction model with the residual sequence including the trend term, and outputting the residual sequence including the trend term within the prediction period, includes:

[0020] Inputting the residual sequence including the trend term into the convolution layer of the trained tropospheric delay prediction model, extracting data features through the convolution layer, performing a dimension swap operation to swap the time feature dimension and the variable feature dimension of the data features, and outputting a feature vector after the dimension swap;

[0021] Inputting the dimension-swapped feature vector into the attention mechanism layer of the trained tropospheric delay prediction model to obtain an attention matrix output by the attention mechanism layer;

[0022] Inputting the attention matrix into the linear layer of the trained tropospheric delay prediction model, performing prediction based on the attention matrix, and outputting trend features and residual features at each moment in the prediction period;

[0023] The time dimensions and variable dimensions of the trend features and residual features at each moment in the prediction period are exchanged, and a residual sequence containing trend items in the prediction period is output.

[0024] In an optional solution of the first aspect, obtaining the tropospheric delay time series for the historical period includes:

[0025] Dividing the historical period into a time series consisting of multiple moments according to a preset time interval, and obtaining historical tropospheric delay data at each moment;

[0026] Determining a time to be interpolated for which historical tropospheric delay data is missing, and performing interpolation calculation based on historical tropospheric delay data at times adjacent to the time to be interpolated to obtain the historical tropospheric delay data at the time to be interpolated;

[0027] Output the tropospheric delay time series for the historical period.

[0028] In an optional solution of the first aspect, the training process of the tropospheric delay prediction model includes:

[0029] Generate a training set and a validation set based on a tropospheric delay time series collected by at least one observation device within a preset time period;

[0030] Inputting the training set into the tropospheric delay prediction model for training in each training cycle, so that the tropospheric delay prediction model learns the mapping relationship between the residual term including the trend term and the time;

[0031] Inputting the validation set into the trained tropospheric delay prediction model, and calculating the root mean square error of the corresponding training cycle based on the output result of the tropospheric delay prediction model and the corresponding parameters of the validation set;

[0032] If the change in the value of the root mean square error of a preset number of consecutive training cycles is less than a preset threshold, the training process is terminated and the trained tropospheric delay prediction model is output.

[0033] In a second aspect, an embodiment of the present application further provides a tropospheric delay prediction device based on deep learning, comprising:

[0034] A data input module is used to obtain a tropospheric delay time series of a historical period and input the tropospheric delay time series into a trained tropospheric delay prediction model;

[0035] a data processing module, configured to decompose the tropospheric delay time series of the historical period into a periodic sequence and a residual sequence including a trend term through Fourier analysis, and to fit the periodic sequence;

[0036] A prediction module, configured to perform prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and output a residual sequence containing the trend term within a prediction period;

[0037] The prediction module is further configured to combine the residual sequence containing the trend term within the prediction period with the fitted periodic sequence, and output a tropospheric delay time series within the prediction period.

[0038] In a third aspect, an embodiment of the present application further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method provided in the first aspect of the embodiment of the present application or any one of the implementations of the first aspect is implemented.

[0039] In a fourth aspect, the present application also provides a non-transitory computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, it implements the method provided by the first aspect of the embodiment of the present application or any one of the implementation methods of the first aspect.

[0040] The beneficial effects of the technical solutions provided by some embodiments of the present application include at least:

[0041] The embodiments of the present application provide a deep learning-based tropospheric delay prediction method, apparatus, device, and medium. By using Fourier analysis to separate the periodic sequence from the tropospheric delay time series, only the residual sequence containing the trend term is input into a trained tropospheric delay prediction model. By learning the correspondence between the residuals and time moments learned by the model, the residuals and trends corresponding to future moments can be captured even in the case of sudden environmental changes. Only the residuals and trends need to be predicted and combined with the overfitted periodic term to obtain the predicted tropospheric delay. While reducing computational complexity, the embodiments of the present application can also output high-precision tropospheric delay prediction results, providing real-time, accurate zenith tropospheric delay for positioning in complex and changing environments, thereby improving the efficiency of positioning solutions. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in this application or related technologies, the following briefly introduces the drawings required for use in the embodiments or related technical descriptions. Obviously, the drawings described below are some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0043] Figure 1 This is a flowchart of a deep learning-based tropospheric delay prediction method provided in an embodiment of the present application;

[0044] Figure 2 This is a flowchart of a deep learning-based tropospheric delay prediction method provided in an embodiment of the present application;

[0045] Figure 3 1 is a schematic structural diagram of a tropospheric delay prediction device based on deep learning provided in an embodiment of the present application;

[0046] Figure 4 It is a structural diagram of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0047] To make the objectives, technical solutions, and advantages of this application more clear, the technical solutions of this application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only part of the embodiments of this application, not all of them. Based on the embodiments of this application, all other embodiments obtained by ordinary technicians in this field without making any creative efforts are within the scope of protection of this application.

[0048] The terms "including" and "having," and any variations thereof, in the specification and claims of this application and the accompanying drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product, or apparatus comprising a series of steps or modules is not limited to the listed steps or modules, but may optionally include steps or modules not listed, or may optionally include other steps or modules inherent to the process, method, product, or apparatus.

[0049] It should be noted that the terms "first" and "second" used in this application are merely used to distinguish similar objects and do not represent a specific ordering of the objects. It is understood that the terms "first" and "second" may interchangeably represent a specific order or precedence, where permitted. It should be understood that the objects distinguished by "first" and "second" may interchangeably represent a specific order or precedence, where appropriate, such that the embodiments of the present application described herein can be implemented in an order other than that described or illustrated herein.

[0050] The present application is described in detail below with reference to specific embodiments.

[0051] Next, combine Figure 1 , introduces a tropospheric delay prediction method based on deep learning provided by the embodiment of this application. For details, please refer to Figure 1 , Figure 1 FIG1 shows a flow chart of a tropospheric delay prediction method based on deep learning provided by an embodiment of the present application. Figure 1 As shown, the method includes the following steps:

[0052] S101, obtaining a tropospheric delay time series for a historical period, and inputting the tropospheric delay time series into a trained tropospheric delay prediction model;

[0053] S102, decomposing the tropospheric delay time series of the historical period into a periodic sequence and a residual sequence including a trend term by Fourier analysis, and fitting the periodic sequence;

[0054] S103, performing prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and outputting the residual sequence containing the trend term within the prediction period;

[0055] S104 , combining the residual sequence containing the trend term within the prediction period with the fitted periodic sequence, and outputting the tropospheric delay time series within the prediction period.

[0056] In some embodiments, after obtaining the predicted tropospheric delay sequence based on the above S101-S104, the predicted tropospheric delay sequence can be further used in positioning calculations, and the zenith tropospheric delay at each moment is input into the pseudorange single-point positioning observation equation or the precise single-point positioning observation equation, and the positioning result at the corresponding moment is output.

[0057] For example, it can be used in pseudorange single point positioning (SPP), and the observation equation of pseudorange single point positioning is expressed as:

[0058]

[0059] In the above formula, P represents the pseudorange observation value, c is the speed of light, ρ represents the distance from the satellite to the ground station, and dt r Indicates the receiver clock error, dt s represents the satellite clock error, T represents the zenith tropospheric delay, NMF is the projection function, I is the ionospheric delay, ε is the noise term in the pseudorange equation, and e is the satellite elevation angle.

[0060] The tropospheric delay at the corresponding moment can be selected from the predicted tropospheric delay sequence and substituted into the observation equation of the above pseudorange single point positioning to obtain the positioning result.

[0061] For example, it can be used in Precise Point Positioning (PPP) by using the zenith tropospheric delay sequence within the prediction period obtained by the above tropospheric delay prediction model as an external virtual observation value to constrain the calculation of the tropospheric delay parameters for PPP. The precise point positioning formula under the tropospheric delay constraint is as follows:

[0062]

[0063] Where P and L represent the pseudorange and carrier phase observation values ​​of the ionosphere-free combination, respectively, and a i is the ionospheric frequency coefficient, N is the carrier ambiguity, λ is the carrier wavelength, ε P and ε L are the noise of pseudorange and carrier respectively, T R is the tropospheric delay data of the tropospheric delay prediction model; R is the variance matrix, ε T is the tropospheric delay noise of the tropospheric delay prediction model, where σ P , σ L and σ T are the variances of pseudorange, carrier and tropospheric delay, respectively.

[0064] Among them, relativistic effects, PCO (phase center offset, PCO) / PCV (phase center variation, PCV) corrections, phase wrapping and solid Earth tides have been corrected using existing models.

[0065] Specifically, the real-time tropospheric delay data collected by multiple tropospheric delay stations and the real-time positioning parameters collected by multiple positioning stations can be used to compare the values ​​predicted by the tropospheric delay prediction model with the values ​​collected by the multiple tropospheric delay stations. The accuracy of the tropospheric delay prediction model can be determined, and the values ​​predicted by the tropospheric delay prediction model can be used for positioning. The positioning results are compared with the values ​​collected by the positioning stations, thereby determining the role of the predicted tropospheric delay data in the actual positioning process.

[0066] In some embodiments, S101 may obtain tropospheric delay data of historical periods observed by multiple tropospheric delay stations, and generate a tropospheric delay time series according to the time sequence and the moment corresponding to each tropospheric delay value.

[0067] Specifically, the historical period can be divided into a time series consisting of multiple moments according to a preset time interval, and the historical tropospheric delay data at each moment can be obtained.

[0068] It should be noted that the tropospheric delay measurement station may not obtain or save the tropospheric delay data for every moment, or the preset time interval is less than the sampling interval of the tropospheric delay measurement station. The time to be interpolated for which the historical tropospheric delay data is missing can be determined, and interpolation calculation is performed based on the historical tropospheric delay data at adjacent moments to the time to be interpolated, so as to obtain the historical tropospheric delay data at the time to be interpolated, and output the tropospheric delay time series of the historical period.

[0069] Optionally, when generating samples for training the tropospheric delay prediction model, the training samples may be expanded based on the difference method applied in the above embodiment.

[0070] Specifically, in S102, the tropospheric delay time series of the historical period can be decomposed into a periodic series and a residual series containing a trend term through Fourier analysis. The periodic series also needs to be fitted. After fitting, the tropospheric delay periodic function (including annual period and semi-annual period) in which the value of the tropospheric delay changes with time can be obtained.

[0071] Specifically, in S104, the tropospheric delay prediction model performs a prediction based on the input residual sequence, obtaining a residual sequence for the prediction period. This residual sequence is then combined with the fitted tropospheric delay period function. This can be understood as follows: the residual term at each moment is obtained based on the predicted residual sequence, and the periodic term at the corresponding moment is obtained using the tropospheric delay period function. The residual term and the periodic term are directly added together to obtain the tropospheric delay at the corresponding moment. Combining the predicted tropospheric delays at each moment, the tropospheric delay time series for the prediction period is output.

[0072] In some embodiments, after S101 inputs the tropospheric delay time series into the trained tropospheric delay prediction model, steps S102-S103 are executed to obtain a residual sequence containing a trend term within the prediction period through the trained tropospheric delay prediction model. Figure 2 , Figure 2 This is a flow chart of the tropospheric delay prediction model provided in the embodiment of the present application processing input data, such as Figure 2 As shown, the tropospheric delay prediction model provided in the embodiment of the present application is a PRMFAT model, which consists of a data processing layer, a normalization layer, a convolution layer, a dimension exchange layer, a self-attention layer, a linear layer, and an anti-normalization layer;

[0073] The processing process specifically includes:

[0074] After obtaining the input data, Fourier analysis is first performed to decompose the original data into periodic terms and residual terms containing trend terms. The decomposed periodic terms are then fitted to obtain the tropospheric delay period function, in which the value of the tropospheric delay changes with time.

[0075] The residual sequence containing the trend term is normalized through the normalization layer.

[0076] Furthermore, the normalized data is input into the convolutional layer, the data features are extracted by the convolutional layer, and the dimension exchange operation is performed through the dimension exchange layer to exchange the time feature dimension and the variable feature dimension of the data features.

[0077] Furthermore, the multi-head self-attention mechanism of the self-attention layer is used to further enhance the feature extraction capability. The feature vector after dimension swapping is output to the self-attention layer.

[0078] Specifically, the self-attention mechanism calculates the dot product between the query, key, and value to obtain an attention score, and then takes a weighted average of these attention scores to generate a new feature representation. This mechanism enables the model to simultaneously focus on different time points in the sequence, improving its ability to model complex temporal dependencies. The formula is as follows:

[0079]

[0080] Among them, Q, K and V are input matrices, representing query matrix, key matrix and value matrix respectively, d k is the vector dimension. By using the above attention formula, the similarity of Q and K is weighted to obtain the weighted sum of V corresponding to the input. Since the dimensions of Q and K may be large, they can be divided by To scale, avoid the problem of gradient disappearance or gradient explosion in Softmax calculation. i is the i-th element of the input vector. The Softmax function converts each element in the input vector into a probability value. The Softmax operation is further performed on the similarity matrix to obtain the weight distribution of each query vector and all key vectors. These weights are then multiplied by the value matrix V to obtain the attention matrix of the self-attention mechanism.

[0081] Furthermore, the attention matrix is ​​input into the linear layer, prediction is performed based on the attention matrix, and the trend features and residual features of each moment in the prediction period are output.

[0082] The time and variable dimensions are exchanged again, and the data is restored from the normalized space to the original data space through the denormalization layer to obtain the trend term and residual term at each moment in the prediction period output by the tropospheric delay prediction model, and then the residual sequence including the trend term is obtained.

[0083] Finally, the residual sequence and the fitted periodic sequence are combined to output the tropospheric delay at each moment in the prediction period.

[0084] Therefore, the residual term of the tropospheric delay at a given moment and / or time period can be predicted by the trained tropospheric delay prediction model, and the tropospheric delay at a given moment and / or time period can be obtained by combining the residual term with the fitted periodic term.

[0085] During the training of the tropospheric delay prediction model:

[0086] Generate a training set and a validation set based on a tropospheric delay time series collected by at least one observation device within a preset time period;

[0087] Inputting the training set into the tropospheric delay prediction model for training in each training cycle, so that the tropospheric delay prediction model learns the mapping relationship between the residual term including the trend term and the time;

[0088] Inputting the validation set into the trained tropospheric delay prediction model, and calculating the root mean square error of the corresponding training cycle based on the output result of the tropospheric delay prediction model and the corresponding parameters of the validation set;

[0089] If the change in the value of the root mean square error of a preset number of consecutive training cycles is less than a preset threshold, the training process is terminated and the trained tropospheric delay prediction model is output.

[0090] It can be understood that the embodiment of the present application uses the root mean square error as an evaluation indicator of model convergence. By monitoring the changing trends of the training loss and the validation loss, the convergence of the tropospheric delay prediction model can be effectively judged.

[0091] In some embodiments, in the initial stage of training, the learning rate is set to 0.001, and the learning rate is decayed by 50% after every three training cycles (epochs) to ensure that the model can learn quickly in the early stage and gradually approach the global optimal solution.

[0092] Furthermore, to prevent the model from falling into a local optimum or overfitting, during model training, if the RMSE of the validation set does not show a significant downward trend over multiple consecutive training cycles, for example, after seven training cycles, the model is considered to have reached convergence and training is terminated. This setting not only effectively prevents overfitting but also ensures that the model's performance is fully optimized on the validation set, improving the model's generalization ability.

[0093] The tropospheric delay prediction model provided in the embodiments of the present application can accurately reflect the changing trend of the tropospheric delay. When the tropospheric delay undergoes a sudden change, it can timely track the change of the tropospheric delay and accurately predict the value of the tropospheric delay.

[0094] The following are device embodiments of the present application, which can be used to implement the method embodiments of the present application. For details not disclosed in the device embodiments of the present application, please refer to the method embodiments of the present application.

[0095] See next Figure 3 , is a schematic diagram of the structure of a deep learning-based tropospheric delay prediction device provided by an exemplary embodiment of the present application. The device can be implemented as all or part of a terminal through software, hardware, or a combination of both, and can also be integrated into a server as an independent module. The deep learning-based tropospheric delay prediction device in the embodiment of the present application can be applied to a terminal or the cloud. The device 30 includes a data input module 301, a data processing module 302, and a prediction module 303, wherein:

[0096] The data input module 301 is used to obtain the tropospheric delay time series of the historical period and input the tropospheric delay time series into the trained tropospheric delay prediction model;

[0097] The data processing module 302 is used to decompose the tropospheric delay time series of the historical period into a periodic sequence and a residual sequence including a trend term through Fourier analysis, and to fit the periodic sequence;

[0098] The prediction module 303 is configured to perform prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and output the residual sequence containing the trend term within the prediction period;

[0099] The prediction module 303 is further configured to combine the residual sequence containing the trend term within the prediction period with the fitted periodic sequence, and output a tropospheric delay time series within the prediction period.

[0100] It should be noted that the apparatus 30 provided in the above embodiment, when executing the deep learning-based tropospheric delay prediction method, is only illustrated by the division of the above functional modules. In actual applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device can be divided into different functional modules to complete all or part of the functions described above. In addition, the apparatus provided in the above embodiment and the embodiment of the deep learning-based tropospheric delay prediction method are based on the same concept. The implementation process is detailed in the method embodiment and will not be repeated here.

[0101] An embodiment of the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the method of any of the above embodiments are implemented.

[0102] See Figure 4 , is a structural block diagram of an electronic device provided in an embodiment of the present application.

[0103] like Figure 4 As shown, the electronic device 400 includes a processor 401 and a memory 402 .

[0104] In the embodiment of the present application, the processor 401 is the control center of the computer system and can be the processor of a physical machine or the processor of a virtual machine. The processor 401 may include one or more processing cores, such as a 4-core processor, an 8-core processor, etc. The processor 401 can be implemented in the form of at least one hardware selected from the group consisting of a DSP (Digital Signal Processing), an FPGA (Field-Programmable Gate Array), and a PLA (Programmable Logic Array).

[0105] The processor 401 may also include a main processor and a coprocessor. The main processor is a processor for processing data in the awake state, also known as a CPU (Central Processing Unit); the coprocessor is a low-power processor for processing data in the standby state.

[0106] The memory 402 may include one or more computer-readable storage media, which may be non-transitory. The memory 402 may also include high-speed random access memory and non-volatile memory, such as one or more disk storage devices and flash memory storage devices. In some embodiments of the present application, the non-transitory computer-readable storage medium in the memory 402 is used to store at least one instruction, which is used to be executed by the processor 401 to implement the method in the embodiment of the present application.

[0107] In some embodiments, the electronic device 400 further includes: a peripheral device interface 403 and at least one peripheral device 404. The processor 401, the memory 402, and the peripheral device interface 403 can be connected via a bus or signal lines. Each peripheral device 404 can be connected to the peripheral device interface 403 via a bus, signal lines, or a circuit board. Specifically, the peripheral devices 404 include: a display screen, a camera, and an audio circuit. The peripheral device interface 403 can be used to connect at least one I / O (Input / Output)-related peripheral device to the processor 401 and the memory 402.

[0108] In some embodiments of the present application, the processor 401, the memory 402, and the peripheral device interface 403 are integrated on the same chip or circuit board; in some other embodiments of the present application, any one or two of the processor 401, the memory 402, and the peripheral device interface 403 may be implemented on separate chips or circuit boards. This embodiment of the present application is not specifically limited to this.

[0109] The electronic device structure block diagram shown in the embodiment of the present application does not constitute a limitation on the electronic device 400. The electronic device 400 may include more or fewer components than shown in the figure, or combine certain components, or adopt a different component arrangement.

[0110] The present application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method of any of the aforementioned embodiments. The computer-readable storage medium may include, but is not limited to, any type of disk, including a floppy disk, an optical disk, a DVD, a CD-ROM, a microdrive, a magneto-optical disk, a ROM, a RAM, an EPROM, an EEPROM, a DRAM, a VRAM, a flash memory device, a magnetic card or an optical card, a nanosystem (including a molecular memory IC), or any type of medium or device suitable for storing instructions and / or data.

[0111] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the above technical solution, in essence, or the part that contributes to the relevant technology, can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0112] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A tropospheric delay prediction method based on deep learning, characterized in that: include: Obtaining a tropospheric delay time series for a historical period, and inputting the tropospheric delay time series into a trained tropospheric delay prediction model; Decomposing the tropospheric delay time series of the historical period into a periodic series and a residual series including a trend term by Fourier analysis, and fitting the periodic series; Performing prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and outputting the residual sequence containing the trend term within the prediction period; Combining the residual sequence containing the trend term within the forecast period with the fitted periodic sequence to output a tropospheric delay time series within the forecast period; The step of performing prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term and outputting the residual sequence containing the trend term within the prediction period includes: Inputting the residual sequence including the trend term into the convolution layer of the trained tropospheric delay prediction model, extracting data features through the convolution layer, performing a dimension swap operation to swap the time feature dimension and the variable feature dimension of the data features, and outputting a feature vector after the dimension swap; Inputting the dimension-swapped feature vector into the attention mechanism layer of the trained tropospheric delay prediction model to obtain an attention matrix output by the attention mechanism layer; Inputting the attention matrix into the linear layer of the trained tropospheric delay prediction model, performing prediction based on the attention matrix, and outputting trend features and residual features at each moment in the prediction period; The time dimensions and variable dimensions of the trend features and residual features at each moment in the prediction period are exchanged, and a residual sequence containing trend items in the prediction period is output.

2. The method for predicting tropospheric delay based on deep learning according to claim 1, characterized in that: After outputting the zenith tropospheric delay data within the prediction period, the method further includes: performing positioning based on the tropospheric delay time series within the prediction period; The zenith tropospheric delay at each moment is input into the pseudorange point positioning observation equation or the precise point positioning observation equation, and the positioning result at the corresponding moment is output.

3. The method for predicting tropospheric delay based on deep learning according to claim 1, characterized in that: After decomposing the tropospheric delay time series of the historical period into a periodic series and a residual series including a trend term by Fourier analysis, the method further includes: Normalizing each residual value in the residual sequence containing the trend term to obtain normalized data; performing the step of predicting by using the tropospheric delay prediction model in combination with the residual sequence including the trend term based on the standardized normalized data, and outputting a prediction result; Performing an inverse normalization process corresponding to the normalization process on the prediction result, and outputting a residual sequence containing a trend term within the prediction period.

4. The method for predicting tropospheric delay based on deep learning according to claim 1, characterized in that: The obtaining of the tropospheric delay time series of the historical period includes: Dividing the historical period into a time series consisting of multiple moments according to a preset time interval, and obtaining historical tropospheric delay data at each moment; Determining a time to be interpolated for which historical tropospheric delay data is missing, and performing interpolation calculation based on historical tropospheric delay data at times adjacent to the time to be interpolated to obtain the historical tropospheric delay data at the time to be interpolated; Output the tropospheric delay time series for the historical period.

5. The method according to claim 1, characterized in that The training process of the tropospheric delay prediction model includes: Generate a training set and a validation set based on a tropospheric delay time series collected by at least one observation device within a preset time period; Inputting the training set into the tropospheric delay prediction model for training in each training cycle, so that the tropospheric delay prediction model learns the mapping relationship between the residual term including the trend term and the time; Inputting the validation set into the trained tropospheric delay prediction model, and calculating the root mean square error of the corresponding training cycle based on the output result of the tropospheric delay prediction model and the corresponding parameters of the validation set; If the change in the value of the root mean square error of a preset number of consecutive training cycles is less than a preset threshold, the training process is terminated and the trained tropospheric delay prediction model is output.

6. A tropospheric delay prediction device based on deep learning, characterized in that: include: A data input module is used to obtain a tropospheric delay time series of a historical period and input the tropospheric delay time series into a trained tropospheric delay prediction model; a data processing module, configured to decompose the tropospheric delay time series of the historical period into a periodic sequence and a residual sequence including a trend term through Fourier analysis, and to fit the periodic sequence; A prediction module, configured to perform prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and output a residual sequence containing the trend term within a prediction period; The prediction module is further configured to combine the residual sequence containing the trend term within the prediction period with the fitted periodic sequence to output a tropospheric delay time series within the prediction period; The prediction module performs prediction by combining the tropospheric delay prediction model with the residual sequence containing the trend term, and outputs the residual sequence containing the trend term within the prediction period, including: Inputting the residual sequence including the trend term into the convolution layer of the trained tropospheric delay prediction model, extracting data features through the convolution layer, performing a dimension swap operation to swap the time feature dimension and the variable feature dimension of the data features, and outputting a feature vector after the dimension swap; Inputting the dimension-swapped feature vector into the attention mechanism layer of the trained tropospheric delay prediction model to obtain an attention matrix output by the attention mechanism layer; Inputting the attention matrix into the linear layer of the trained tropospheric delay prediction model, performing prediction based on the attention matrix, and outputting trend features and residual features at each moment in the prediction period; The time dimensions and variable dimensions of the trend features and residual features at each moment in the prediction period are exchanged, and a residual sequence containing trend items in the prediction period is output.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the steps of the method according to any one of claims 1 to 5 are implemented.

8. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 5 are implemented.

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