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

Abstract

The embodiment of the invention discloses a troposphere delay prediction method and device based on deep learning, equipment and a medium, and relates to the technical field of navigation positioning, and the method comprises the steps: obtaining a troposphere delay time sequence of a historical time period, and inputting a trained troposphere delay prediction model; decomposing the troposphere delay time sequence of the historical time period into a periodic sequence and a residual sequence containing a trend term through Fourier analysis; and performing prediction by combining a troposphere delay prediction model with the residual sequence containing the trend term, outputting the residual sequence containing the trend term in a prediction time period, adding the residual sequence with the fitted periodic sequence, and outputting a zenith troposphere delay sequence in the prediction time period. According to the embodiment of the invention, a high-precision troposphere delay prediction result can be output while the calculation complexity is reduced, and real-time and accurate zenith troposphere delay can be provided for positioning in a complex and changeable environment, so that the calculation efficiency of positioning can be improved.

Description

Technical Field

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

[0002] Zenith tropospheric delay (ZTD) is one of the key factors affecting GNSS (Global Navigation Satellite System, GNSS) high-precision positioning. By calculating the accurate ZTD and eliminating the error caused by ZTD, it is beneficial to improve the positioning accuracy.

[0003] At present, the zenith tropospheric delay can be calculated through the tropospheric model, and the calculated zenith tropospheric delay can be used to correct the error during the positioning process. However, the accuracy of most tropospheric models is limited, and most models need to be predicted based on historical data to obtain the long-term trend of the zenith tropospheric delay. However, such models do not take into account the rapidly changing atmospheric conditions, and it is difficult to reflect the short-term changes in the tropospheric delay. When making predictions in different regions, the prediction accuracy fluctuates greatly. For example, in some areas where the zenith wet delay (ZWD) is greatly affected by water vapor, the accuracy of these empirical models will decrease, thereby limiting the rapid solution of real-time precise single-point positioning and the accuracy of ZTD inversion of water vapor.

[0004] In addition, some tropospheric models can also introduce a large number of external parameters to improve the prediction accuracy of the model. 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, which makes it difficult to provide real-time and accurate zenith tropospheric delay for positioning in a complex and changing environment, affecting the timeliness of high-precision positioning. Summary of the invention

[0006] The embodiments of the present application provide a method, device, equipment and medium for predicting tropospheric delay based on deep learning, so as to solve the defects of the above-mentioned related technologies. The technical solution is 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] Acquire a tropospheric delay time series for a historical period, and input 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] Predicting 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 the 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 pseudo-range 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 standardized normalized data;

[0017] Based on the standardized normalized data, the step of predicting by using the tropospheric delay prediction model in combination with the residual sequence containing the trend term is performed, and a prediction result is output;

[0018] The prediction results are subjected to an inverse normalization process corresponding to the normalization process, and a residual sequence containing a trend term within the prediction period is output.

[0019] In an optional solution of the first aspect, the predicting 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:

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

[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 of the historical period includes:

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

[0026] Determine a time to be interpolated for missing historical tropospheric delay data, and perform interpolation calculation based on historical tropospheric delay data at adjacent times 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 of 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 period according to 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 for 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, used for obtaining a tropospheric delay time series in a historical period, and inputting the tropospheric delay time series into a trained tropospheric delay prediction model;

[0035] A data processing module, used for 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;

[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 also used to combine the residual sequence containing the trend term within the prediction period with the fitted periodic sequence, and output the 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 implementation methods of the first aspect is implemented.

[0039] In a fourth aspect, the present application also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the method provided by the first aspect of the embodiment of the present application or any one of the implementations of the first aspect.

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

[0041] The embodiments of the present application provide a tropospheric delay prediction method, apparatus, device and medium based on deep learning. The periodic sequence in the tropospheric delay time series is separated by Fourier analysis, and only the residual sequence containing the trend term is input into the trained tropospheric delay prediction model. The correspondence between the residual and the time learned by the model can capture the residual and trend corresponding to the future time even in the case of sudden changes in the environment. It is only necessary to predict the residual and the trend and combine them with the overfitted periodic term to obtain the predicted tropospheric delay. While reducing the computational complexity, the embodiments 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 a complex and changeable environment, thereby improving the positioning solution efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] In order to more clearly illustrate the technical solutions in the present application or related technologies, the drawings required for use in the embodiments or related technical descriptions are briefly introduced below. 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 creative work.

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

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

[0045] Figure 3 It is a structural schematic 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 schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0047] In order to make the purpose, technical solutions and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below in conjunction with the drawings in this application. Obviously, the described embodiments are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work 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 the present application and the above drawings are intended to cover non-exclusive inclusions. For example, a process, method, system, product or device including a series of steps or modules is not limited to the listed steps or modules, but may optionally include steps or modules that are not listed, or may optionally include other steps or modules that are inherent to these processes, methods, products or devices.

[0049] It should be noted that the terms "first\second" involved in the present application are only used to distinguish similar objects, and do not represent a specific order for the objects. It is understandable that "first\second" can be interchanged with a specific order or sequence where permitted. It should be understood that the objects distinguished by "first\second" can be interchanged where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those 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 an embodiment of the present application. For details, please refer to Figure 1 , Figure 1 FIG. 1 is a flow chart of a method for predicting tropospheric delay based on deep learning provided in an embodiment of the present application. Figure 1 As shown, the method comprises the following steps:

[0052] S101, obtaining a tropospheric delay time series in 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 the predicted tropospheric delay sequence is obtained 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] Exemplarily, 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 represents 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 of the pseudorange equation, and e is the satellite altitude angle.

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

[0061] Exemplarily, it can be used in Precise Point Positioning (PPP), and the zenith tropospheric delay sequence within the prediction period obtained by the above tropospheric delay prediction model is used as an external virtual observation value to constrain the calculation of the tropospheric delay parameters of the Precise Point Positioning. 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 observations of the ionosphere-free combination, respectively. 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) correction, phase winding and solid Earth tides have been corrected using existing models.

[0065] Specifically, the accuracy of the tropospheric delay prediction model can be determined by comparing the values ​​predicted by the tropospheric delay prediction model with the values ​​collected by the multiple tropospheric delay stations through real-time tropospheric delay data collected by multiple tropospheric delay stations and real-time positioning parameters collected by multiple positioning stations. The values ​​predicted by the tropospheric delay prediction model can be used for positioning, and the positioning results can be 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 time 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 station may not obtain or save the tropospheric delay data at each moment, or the preset time interval is less than the sampling interval of the tropospheric delay station. The time to be interpolated for the missing historical tropospheric delay data 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) of the tropospheric delay value changing with time can be obtained.

[0071] Specifically, in S104, the tropospheric delay prediction model predicts based on the input residual sequence, obtains the residual sequence of the prediction period, and combines it with the tropospheric delay period function obtained after fitting. It can be understood that the residual term at each moment is obtained according to the predicted residual sequence, and the periodic term at the corresponding moment can be obtained through the tropospheric delay period function. The residual term and the periodic term are directly added to obtain the tropospheric delay at the corresponding moment. Combined with the tropospheric delays predicted at each moment, the tropospheric delay time series within the prediction period can be 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 A flowchart 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, and the decomposed periodic terms are 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 convolution layer, the data features are extracted by the convolution 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 exchange 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 the attention score, and then performs a weighted average of these attention scores to generate a new feature representation. This mechanism enables the model to focus on different time points in the sequence at the same time, improving the ability to model complex time 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 similarities of Q and K are 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. Each element in the input vector is converted into a probability value through the Softmax function. The similarity matrix is ​​further Softmaxed to obtain the weight distribution of each query vector and all key vectors. Then, these weights are multiplied with 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 at 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 containing 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 time and / or time period can be predicted by the trained tropospheric delay prediction model, and then the tropospheric delay at a given time 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 period according to 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 for 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 verification 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] At the same time, in order to prevent the model from falling into local optimality or overfitting, during the model training process, if the RMSE of the validation set does not show a significant downward trend in multiple consecutive training cycles, such as 7 training cycles, the model is considered to have reached a convergence state and the training process is terminated. This setting can not only effectively prevent overfitting, but also ensure that the performance of the model is fully optimized on the validation set, improving the generalization ability of the model.

[0093] The tropospheric delay prediction model provided in the embodiment of the present application can accurately reflect the changing trend of the tropospheric delay. When there is a sudden change in the tropospheric delay, 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 execute 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 tropospheric delay prediction device based on deep learning 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 on a server as an independent module. The tropospheric delay prediction device based on deep learning in the embodiment of the present application can be applied to a terminal or a 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 used 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 the tropospheric delay time series within the prediction period.

[0100] It should be noted that when the device 30 provided in the above embodiment executes the tropospheric delay prediction method based on deep learning, only the division of the above functional modules is used as an example. In practical applications, the above functions can be assigned to different functional modules as needed, that is, the internal structure of the device is divided into different functional modules to complete all or part of the functions described above. In addition, the device provided in the above embodiment and the embodiment of the tropospheric delay prediction method based on deep learning belong to the same concept, and its implementation process is detailed in the method embodiment, which 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, wherein the processor implements the steps of any of the above-mentioned method embodiments when executing the program.

[0102] See also Figure 4 , which 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, which can be a processor of a physical machine or a 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 may be implemented in at least one hardware form of DSP (Digital Signal Processing), FPGA (Field-Programmable Gate Array), and 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 called 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 a high-speed random access memory, and a non-volatile memory, such as one or more disk storage devices, 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 a signal line. Each peripheral device 404 can be connected to the peripheral device interface 403 via a bus, a signal line or a circuit board. Specifically, the peripheral device 404 includes: a display screen, a camera and an audio circuit. The peripheral device interface 403 can be used to connect at least one peripheral device related to I / O (Input / Output) 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 can be implemented on a separate chip or circuit board. This embodiment of the present application does not specifically limit 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 embodiment of the present application also provides a computer-readable storage medium, on which a computer program is stored, and when the program is executed by a processor, the steps of the method of any of the above embodiments are implemented. 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 micro drive, and 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 implementation methods, those skilled in the art can clearly understand that each implementation method can be implemented by means of software plus a necessary general hardware platform, and of course, by hardware. Based on this understanding, the above technical solution can be essentially or in other words, the part that contributes to the relevant technology can be embodied in the form of a software product, which can be stored in a computer-readable storage medium, such as ROM / RAM, a disk, an optical disk, etc., including a number of instructions for 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 some parts of the embodiment.

[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 it. 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: Acquire a tropospheric delay time series for a historical period, and input 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; Predicting 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; The residual sequence containing the trend term within the prediction period is combined with the fitted periodic sequence to output the tropospheric delay time series within the prediction period.

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 pseudo-range 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 zenith tropospheric delay data into a periodic sequence and a residual sequence containing a trend term by Fourier analysis, the method further includes: Normalizing each residual value in the residual sequence containing the trend term to obtain standardized normalized data; Based on the standardized normalized data, the step of predicting by using the tropospheric delay prediction model in combination with the residual sequence containing the trend term is performed, and a prediction result is output; The prediction results are subjected to an inverse normalization process corresponding to the normalization process, and a residual sequence containing a trend term within the prediction period is output.

4. A tropospheric delay prediction method based on deep learning according to claim 1 or 3, characterized in that: 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 comprises: Inputting the residual sequence containing the trend term into the convolution layer of the trained tropospheric delay prediction model, extracting data features through the convolution layer, performing a dimension exchange operation to exchange the time feature dimension and the variable feature dimension of the data feature, and outputting a feature vector after the dimension exchange; 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.

5. The method for predicting tropospheric delay based on deep learning according to claim 1, characterized in that: The step of obtaining the tropospheric delay time series of the historical period includes: Dividing the historical period into a time series consisting of a plurality of moments according to a preset time interval, and obtaining historical tropospheric delay data at each moment; Determine a time to be interpolated for missing historical tropospheric delay data, and perform interpolation calculation based on historical tropospheric delay data at adjacent times 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 of the historical period.

6. 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 period according to 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 for 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.

7. A tropospheric delay prediction device based on deep learning, characterized in that: include: A data input module, used for obtaining a tropospheric delay time series in a historical period, and inputting the tropospheric delay time series into a trained tropospheric delay prediction model; A data processing module, used for 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; A prediction module, 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 a prediction period; The prediction module is also used to combine the residual sequence containing the trend term within the prediction period with the fitted periodic sequence, and output the tropospheric delay time series within the prediction period.

8. 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 6 are implemented.

9. 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 6 are implemented.

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