A GNSS timing data prediction method and related equipment

Abstract

This invention relates to the field of navigation and timing technology, specifically to a GNSS timing data prediction method and related equipment. The method involves acquiring Roland timing data when GNSS timing data is invalid and preprocessing it. The preprocessed data is then input into a trained single-hidden-layer extreme learning machine model. This model calculates the hidden-layer output matrix by randomly initializing the input layer weight matrix and bias vector, and solves for the output weights using regularized least squares. The model outputs a normalized GNSS timing data prediction value, which is then denormalized to obtain the final GNSS timing prediction result. This method combines the high stability of the Roland system with the efficient computational power of the extreme learning machine to achieve accurate GNSS timing data prediction. It is suitable for enhancing the resilience of positioning, navigation, and timing systems in critical infrastructure scenarios, ensuring the continuous operation of the system even when GNSS signals are interfered with or fail.

Description

Technical Field

[0001] This invention relates to the field of navigation and timing technology, specifically to a GNSS timing data prediction method and related equipment. Background Technology

[0002] Global Navigation Satellite System (GNSS) has been widely used in many critical fields such as communications, power, and finance due to its superior nanosecond-level timing accuracy. However, in GNSS-denied environments such as urban canyons, indoor spaces, and areas with electromagnetic interference, GNSS signals are easily blocked or interfered with, leading to timing service interruptions and severely impacting the normal operation of related systems. The Loran (long-wave) navigation system, as a traditional land-based radio navigation technology, has significant advantages such as wide coverage and strong anti-interference capabilities, but its timing accuracy is relatively low, with a standard deviation typically greater than 60 ns, making it difficult to meet the requirements for high-precision time synchronization.

[0003] Existing technologies offer two main solutions: multi-source fusion methods, which improve timing performance by fusing data, but require complex hardware synchronization; and data-driven methods, which improve accuracy by establishing a mapping relationship between low-precision sensors and high-precision reference data. Extreme Learning Machine (ELM), as an improved algorithm for single-hidden-layer feedforward neural networks, shows promise in nonlinear mapping problems due to its fast training and strong generalization ability. Current solutions have shortcomings: multi-source fusion methods are costly, have poor real-time performance, and are difficult to adapt to practical applications; the application of ELM in timing data mapping has not been extensively explored, and its model generalization ability and robustness require further verification. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a GNSS timing data prediction method and related equipment to address the shortcomings of the prior art, thereby solving the technical problem of insufficient Roland timing accuracy and difficulty in meeting the high-precision timing requirements under GNSS denial environment.

[0005] The objective of this invention is achieved through the following technical solutions:

[0006] In a first aspect, the present invention provides a GNSS timing data prediction method, comprising:

[0007] Obtain Roland timing data when GNSS timing data is invalid, and preprocess the Roland timing data;

[0008] The preprocessed Roland timing data is input into the trained single-hidden-layer extreme learning machine model to obtain the normalized GNSS timing data prediction value. The GNSS timing data prediction value is restored by inverse normalization to obtain the final effective GNSS timing data prediction result.

[0009] The single-hidden-layer extreme learning machine model includes an input layer, a hidden layer, and an output layer. The input layer processes the Roland timing data into an input layer data matrix. The hidden layer performs mapping calculations on the input layer data matrix based on a predefined nonlinear mapping function to obtain a hidden layer output matrix. The output layer performs a linear combination of the hidden layer output matrix to obtain a normalized GNSS timing data prediction value.

[0010] As a further improvement of the present invention, the preprocessing process includes:

[0011] After averaging the Roland timing data, outlier correction was performed using the 3σ principle.

[0012] The corrected Roland timing data were normalized using the z-score normalization method.

[0013] As a further improvement of the present invention, the specific method for outlier correction is as follows:

[0014] Set the mean of the data after mean processing to be... The standard deviation is ;

[0015] When the mean-processed Roland timing data exceeds [ , If the range is not specified, then the Roland timing data will be replaced and corrected. Otherwise, no outlier correction will be performed.

[0016] As a further improvement of the present invention, the training process of the single hidden layer extreme learning machine model includes:

[0017] Acquire historical Roland timing data and corresponding valid GNSS timing data; perform mean processing and outlier correction processing on the historical Roland timing data and the corresponding valid GNSS timing data respectively; perform normalization processing on the valid GNSS timing data;

[0018] The corrected historical Roland timing data and the corresponding normalized effective GNSS timing data were used as the training set.

[0019] Construct a single-hidden-layer extreme learning machine model and determine the input layer dimension, the number of hidden layer neurons, and the output layer dimension.

[0020] Randomly initialize the input layer weight matrix and bias vector in a single hidden layer extreme learning machine model within a predetermined range;

[0021] Historical Roland timing data from the training set are input into a single-hidden-layer extreme learning machine model, and the hidden layer output matrix is ​​calculated using a nonlinear mapping function in the hidden layer; the nonlinear mapping function is the sigmoid activation function.

[0022] Based on the hidden layer output matrix and the normalized effective GNSS timing data, the output weights from the hidden layer to the output layer are updated using a regularized least squares algorithm. The output weights are used to determine the mapping relationship between the input layer data matrix after the hidden layer transformation and the corresponding normalized effective GNSS timing data. The single hidden layer extreme learning machine model is determined according to the input layer weight matrix, bias vector, and output weights.

[0023] As a further improvement of the present invention, the hidden layer output matrix is:

[0024]

[0025] In the formula, X is the hidden layer output matrix, and X is the input layer data matrix. The input layer weight matrix, This is the bias vector.

[0026] As a further improvement of the present invention, the output weights of the hidden layer to the output layer are updated using a regularized least squares algorithm. The calculation formula is:

[0027]

[0028] In the formula, To output weights, The output matrix of the hidden layer. Output matrix for hidden layer The transpose of the matrix, For regularization parameters, It is the identity matrix. This is the output of valid GNSS timing data.

[0029] As a further improvement of the present invention, the denormalization process includes:

[0030]

[0031] In the formula, To obtain the final effective GNSS timing data prediction results, These are the normalized predicted values ​​of GNSS timing data. The standard deviation of the GNSS timing data calculated from the training set. This is the mean value of GNSS timing data calculated from the training set.

[0032] Secondly, the present invention provides a GNSS timing data prediction system, comprising:

[0033] The data acquisition module is used to acquire Roland timing data when GNSS timing data is invalid;

[0034] The data preprocessing module, connected to the data acquisition module, is used to preprocess the Roland timing data;

[0035] The mapping module, connected to the data preprocessing module, is used to input the preprocessed Roland timing data into the trained single-hidden-layer extreme learning machine model to obtain the normalized GNSS timing data prediction value. The GNSS timing data prediction value is restored through inverse normalization processing to obtain the final GNSS timing data prediction result.

[0036] The single-hidden-layer extreme learning machine model includes an input layer, a hidden layer, and an output layer. The input layer processes the Roland timing data into an input layer data matrix. The hidden layer performs mapping calculations on the input layer data matrix based on a predefined nonlinear mapping function to obtain a hidden layer output matrix. The output layer performs a linear combination of the hidden layer output matrix to obtain a normalized GNSS timing data prediction value.

[0037] Thirdly, the present invention provides a computer-readable storage medium for storing one or more programs, the one or more programs including instructions that, when executed by a computing device, cause the computing device to perform the above-described GNSS timing data prediction method.

[0038] Fourthly, the present invention provides a computing device, comprising:

[0039] One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including methods for performing the GNSS timing data prediction method described above.

[0040] The beneficial effects of this invention are as follows: This invention provides a GNSS timing data prediction method, which obtains Roland timing data when GNSS timing data is invalid and preprocesses it, inputs the preprocessed Roland timing data into a trained single-hidden-layer extreme learning machine model to obtain normalized GNSS timing data prediction values, and then restores them to the final valid GNSS timing data prediction results through inverse normalization processing. This invention utilizes an input layer to process Rowland timing data into a structured input matrix. A hidden layer performs mapping calculations on the input data matrix based on a predefined nonlinear mapping function, generating a hidden layer output matrix. This achieves efficient capture of the nonlinear relationship between Rowland timing data and GNSS timing data. The output layer linearly combines the hidden layer output matrix to obtain a normalized GNSS timing data prediction value. Inverse normalization is then performed to restore the final GNSS timing data prediction result, ensuring accuracy while reducing computational complexity. In scenarios where GNSS timing data is invalid, this invention uses Rowland timing data with a single hidden layer extreme learning machine model to quickly and accurately predict GNSS timing data. Furthermore, compared to traditional linear models or complex multilayer networks, this invention achieves a better balance between prediction accuracy and computational efficiency. Experimental results show that this invention significantly reduces the standard deviation of Rowland timing data errors from 64.3812 ns to 3.6129 ns, approaching the accuracy level of GNSS timing data and greatly improving timing accuracy. Attached Figure Description

[0041] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0042] Figure 1 This is a schematic diagram of the GNSS timing data prediction method in an embodiment of the present invention;

[0043] Figure 2 This is a waveform comparison diagram of Roland timing data and GNSS timing data when both sources are active, inactive, and recovering.

[0044] Figure 3 This is a waveform comparison diagram of Roland's original timing data and GNSS's original timing data in an embodiment of the present invention;

[0045] Figure 4 This is a comparison chart of Roland's predicted values ​​and GNSS actual values ​​in an embodiment of the present invention;

[0046] Figure 5This is a schematic diagram of the structure of a computer device in an embodiment of the present invention. Detailed Implementation

[0047] To make the objectives and technical solutions of this invention clearer and easier to understand, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. The specific embodiments described herein are for illustrative purposes only and are not intended to limit the invention.

[0048] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings and specific embodiments. The described embodiments are only some embodiments of the present invention, and not all embodiments.

[0049] Example 1

[0050] This embodiment provides a GNSS timing data prediction method, such as Figure 1 As shown, the specific steps include: obtaining Rowland timing data when GNSS timing data is invalid, and preprocessing the Rowland timing data; inputting the preprocessed Rowland timing data into a trained single-hidden-layer extreme learning machine model, mapping the Rowland timing data according to the nonlinear mapping function between the Rowland timing data and the corresponding GNSS timing data to obtain the normalized GNSS timing data prediction value, and restoring the GNSS timing data prediction value through inverse normalization processing to obtain the final GNSS timing data prediction result.

[0051] In this embodiment, to address the technical problem of insufficient Rowland timing accuracy and difficulty in meeting high-precision timing requirements under GNSS denied environments, Rowland timing data is first acquired and preprocessed to optimize the data quality of the input model. The preprocessed Rowland timing data is then input into a trained single-hidden-layer extreme learning machine model. The input layer processes the Rowland timing data into a structured input form of a data matrix, while the hidden layer performs mapping calculations on the input layer data matrix based on a predefined nonlinear mapping function to generate the hidden layer output matrix. This achieves efficient capture of the nonlinear relationship between Rowland timing data and GNSS timing data. The output layer linearly combines the hidden layer output matrix to obtain the normalized GNSS timing data prediction value. Inverse normalization is then performed to restore the final GNSS timing data prediction result, thus reducing computational complexity while ensuring the accuracy of the prediction result. This embodiment effectively constructs a mapping from Rowland timing data to GNSS timing data, realizing the conversion from low-precision Rowland timing data to high-precision GNSS timing data. It provides a feasible solution for high-precision timing requirements in GNSS-denied environments. Furthermore, the random initialization of the input layer weight matrix and bias vector during the training of the single-hidden-layer extreme learning machine model, and the solution of the output weights using regularized least squares, helps ensure the efficiency and stability of model training, thereby ensuring the reliability of GNSS timing prediction results. In addition, the time-ordered GNSS timing data ultimately forms continuous timing data. The time-ordered GNSS timing data includes valid GNSS timing data and GNSS timing data predicted using this method.

[0052] It should be noted that the normalized GNSS timing data prediction value refers to the standardized prediction value directly output by the model, and this data is dimensionless. The GNSS timing data prediction value after denormalization, however, has corresponding dimensions and numerical meaning.

[0053] It should be noted that in this embodiment, GNSS timing data and Roland timing data are acquired in real time to determine the validity of the GNSS timing data. If the GNSS timing data is valid, the GNSS timing data prediction method of this embodiment is not required. Only when the GNSS timing data is invalid does it need to be predicted using the corresponding Roland timing data to replace the invalid GNSS timing data, ensuring data reliability. Invalid GNSS timing data refers to data exhibiting abnormalities such as sudden changes or missing values. Figure 2 As shown, the time difference curve data corresponding to GNSS timing data failure exhibits a clear characteristic of no fluctuation. For example... Figure 2As shown, the black area (marked with a "+") represents the original Roland data, and the gray curve represents the simulated continuous timing data fused from GNSS timing data. When both GNSS and Roland timing data are available, the Roland timing data exhibits extreme time difference fluctuations, while the simulated continuous timing data (fused from a single-hidden-layer extreme learning machine model) maintains a stable time difference near 0. This indicates that during dual-source fusion, the single-hidden-layer extreme learning machine model effectively learns the high precision of GNSS and the continuity of Roland, suppressing the fluctuations in the original data. When the GNSS timing data becomes invalid, the original Roland data fluctuates drastically, and the simulated continuous timing data displays an abnormal curve. When the GNSS timing data becomes available again, the simulated continuous timing data returns to stability.

[0054] The preprocessing in this embodiment further includes: first, averaging the acquired Rowland timing data to eliminate the DC component and prevent it from masking the true characteristics of the data; then, applying the 3σ principle to correct outliers in the averaged Rowland timing data, identifying and processing outliers that exceed reasonable limits, and reducing their interference with data quality; finally, normalizing the outlier-corrected Rowland timing data using z-score standardization to eliminate dimensional differences between different data points, ensuring a uniform data scale. Through the synergistic effect of averaging, 3σ outlier correction, and z-score standardization, the quality of the Rowland timing data is effectively optimized, interference factors are removed, and the consistency and reliability of the Rowland timing data input to subsequent models are ensured. This lays a solid data foundation for constructing a precise mapping relationship between Rowland timing data and GNSS timing data and improving the accuracy of GNSS timing data predictions.

[0055] Furthermore, the training process of the single hidden layer extreme learning machine model in this embodiment further includes: acquiring historical Rowland timing data and corresponding valid GNSS timing data; performing mean processing and outlier correction processing on the historical Rowland timing data and the corresponding valid GNSS timing data respectively; dividing the corrected historical Rowland timing data and the corresponding valid GNSS timing data into training set and test set according to a preset ratio; and normalizing the data in the training set and test set using the z-score normalization method. A single-hidden-layer extreme learning machine (SLM) model is constructed, and the dimensions of the input layer, the number of neurons in the hidden layer, and the dimension of the output layer are determined. The input layer weight matrix and bias vector are randomly initialized within a predetermined range. Historical Rowland timing data from the training set are input into the SLM model for training. The hidden layer output matrix is ​​calculated using the sigmoid activation function based on the input layer data matrix, input layer weight matrix, and bias vector. In this embodiment, the sigmoid activation function is used as a non-linear mapping function. Based on the hidden layer output matrix and the normalized effective GNSS timing data, a regularized least squares algorithm is used to update the output weights from the hidden layer to the output layer. The output weights are used to determine the mapping relationship between the input layer data matrix after the hidden layer transformation and the corresponding GNSS timing data. The predetermined range of the input layer weight matrix is ​​set to [-1, 1]. Single-hidden-layer extreme learning machine models do not require gradients or iterations during training. Therefore, in each training iteration, the input layer weight matrix and bias vector need to be randomly initialized, the output weights are recalculated based on the above process, and the input layer weight matrix, bias vector, and output weights are saved, thus completing the training process. When predicting GNSS timing data, the saved input layer weights, bias vectors, and output weights are used to calculate the predicted value.

[0056] Normalized historical Roland timing data from the test set is input into the trained single-hidden-layer extreme learning machine (SLM) model to obtain normalized GNSS timing data predictions. These predictions are then denormalized to restore the actual physical quantities, and the performance of the SLM model is evaluated using a preset error index. The processing steps of the SLM model are as follows: based on the input layer data matrix, input layer weight matrix, and bias vector, the hidden layer output matrix is ​​calculated using the sigmoid activation function; in this embodiment, the sigmoid activation function is used as a nonlinear mapping function. Based on the hidden layer output matrix, the output weights of the SLM model are solved using regularized least squares; these output weights are used to determine the mapping relationship between the input layer data matrix after the hidden layer transformation and the corresponding GNSS timing data.

[0057] In this embodiment, during model training, historical Rowland timing data and corresponding GNSS timing data are first acquired. Mean removal and outlier correction are performed on both types of data to eliminate DC components and remove interference from abnormal data. The corrected data are then divided into training and testing sets according to a preset ratio to provide data support for model training and performance verification. Subsequently, z-score normalization is used to normalize the data in the training and testing sets, eliminating differences in data units and unifying the data scale. Next, a single-hidden-layer extreme learning machine model is constructed, specifying that the input layer is historical Rowland timing data and the output layer is the corresponding valid GNSS timing data. The dimensions of the input layer, the number of neurons in the hidden layer, and the dimension of the output layer are determined, establishing a model structure with a mapping relationship. Within a predetermined range, the input layer weight matrix and bias vector are randomly initialized. The hidden layer output matrix is ​​calculated using the sigmoid activation function, and the output weights are solved using regularized least squares, thereby establishing the mapping relationship between historical Rowland timing data and corresponding valid GNSS timing data. Finally, normalized historical Rowland timing data from the test set was input into the trained model to obtain normalized GNSS timing data predictions. These predictions were then denormalized to restore the actual physical quantities. The model performance was evaluated using preset error metrics to verify the effectiveness of the mapping model. Through the synergistic effect of various technical features during training, the quality of the training data was effectively optimized, and a single-hidden-layer extreme learning machine model with a clear structure and stable mapping relationship was constructed. This achieved accurate mapping from historical Rowland timing data to corresponding GNSS timing data. Simultaneously, testing and evaluation ensured the reliability of the model's performance, laying a solid foundation for subsequently using this trained model to convert real-time Rowland timing data into GNSS timing data, thereby meeting the high-precision timing requirements in GNSS-denied environments.

[0058] Mean removal further includes:

[0059]

[0060]

[0061] In the formula, The mean-removed Roland timing data. This is the input layer data matrix, which is obtained from the original Rowland timing data (unit: ns). The mean of Roland's timed data. This represents the total length of the Roland timing data.

[0062] Similarly, the GNSS timing data mean removal process includes:

[0063]

[0064]

[0065] In the formula, This is the mean-removed GNSS timing data. For valid GNSS timing data (unit: ns). The mean of GNSS timing data. This represents the total length of GNSS timing data.

[0066] The specific method for outlier correction is as follows: Set the mean of the data after mean removal to be... The standard deviation is When the mean-processed Roland timing data exceeds [ , If the range is not specified, then the Roland timing data will be replaced and corrected. Otherwise, no outlier correction will be performed.

[0067] Furthermore, in this embodiment, the standard deviation of the Rowland timing data after mean processing is:

[0068]

[0069] In the formula, denoted as the standard deviation of Rowland's timing data.

[0070] Furthermore, the z-score standardization method specifically includes:

[0071]

[0072] In the formula, This refers to the normalized Rowland timing data, i.e., the standardized Rowland timing data.

[0073] It should be noted that the single-hidden-layer extreme learning machine model in this embodiment adopts a simple and efficient single-hidden-layer feedforward neural network structure. The input and output layers of the single-hidden-layer feedforward neural network structure have a dimension of 1, and the hidden layer includes several neurons.

[0074] The sigmoid activation function is used to process the linear combination of the input data and the input layer weight matrix to achieve a non-linear transformation. The hidden layer output matrix is:

[0075]

[0076] In the formula, The output matrix of the hidden layer. For the input layer data matrix, The input layer weight matrix, It serves as a bias vector to achieve nonlinear transformation of the data.

[0077] Furthermore, to avoid model overfitting, a regularization parameter is introduced, and the output weights of the single-hidden-layer extreme learning machine model are solved using the least squares method. The calculation formula is:

[0078]

[0079] In the formula, To output weights, The output matrix of the hidden layer. Output matrix for hidden layer The transpose of the matrix, For regularization parameters, It is the identity matrix. For the output GNSS timing data, For dimensions.

[0080] The denormalization process includes:

[0081]

[0082] In the formula, This is the GNSS timing prediction result after inverse normalization, i.e., the final effective GNSS timing data prediction result. These are the normalized predicted values ​​of GNSS timing data. The standard deviation of the GNSS timing data calculated from the training set. This is the mean value of GNSS timing data calculated from the training set.

[0083] Accurate prediction of Roland timing data to GNSS timing data is achieved using a single-hidden-layer extreme learning machine model, such as... Figure 3 As shown, the method in this embodiment significantly reduces the standard deviation of the Rowland timing data error from 64.3812 ns to 3.6129 ns, approaching the accuracy level of GNSS timing data. This greatly improves timing accuracy, effectively solves the high-precision timing requirements under GNSS denial environments, and provides a reliable guarantee for the normal operation of related systems. A comparison of Rowland prediction results with actual GNSS values ​​is provided. Figure 4 As shown. The standard deviation of the raw Roland data is 64.3812 ns, and the standard deviation of the Roland predicted value is 3.6129 ns, which is better than the standard deviation of the GNSS true value of 11.3402 ns. Figure 3 The gray lines represent GNSS timing data (i.e., raw satellite data).

[0084] Example 2

[0085] This embodiment provides a specific implementation method for GNSS timing data prediction. The steps of the specific embodiment are described below.

[0086] First, accurately acquire Roland timing data and GNSS timing data, and then perform mean removal and outlier correction on the Roland timing data and GNSS timing data.

[0087] Mean removal is used to eliminate the DC component in the data. The mean removal process in this embodiment is as follows:

[0088]

[0089]

[0090] In the formula, The mean-removed Roland timing data. This is the input layer data matrix, i.e., the original Rowland timing data (unit: ns). The mean of Roland's timed data. This represents the total length of the Roland timing data.

[0091] Similarly, the GNSS timing data averaging process includes:

[0092]

[0093]

[0094] In the formula, This is the mean-removed GNSS timing data. For valid GNSS timing data (unit: ns). The mean of GNSS timing data. This represents the total length of GNSS timing data.

[0095] The specific method for outlier correction is as follows: Outliers are identified and corrected using a strict 3σ principle, and the formula is:

[0096]

[0097] in,

[0098]

[0099] In the formula, This represents the standard deviation of Rowland's timing data after removing the mean.

[0100] Similarly, the outlier correction steps for GNSS timing data in this embodiment are as follows:

[0101]

[0102]

[0103] In the formula, This represents the standard deviation of the GNSS timing data after removing the mean.

[0104] The preprocessed data is scientifically divided into training, validation, and test sets, and the input and output data are standardized. In this embodiment, the data is randomly divided according to a set ratio (e.g., 50% for training, 15% for validation, and 35% for test) to ensure that the distribution of each subset is consistent, effectively avoid model overfitting, and improve the model's generalization ability.

[0105] The training, validation, and test sets all use the advanced z-score normalization method to eliminate the influence of dimensions. The formula is:

[0106]

[0107]

[0108] in, , These are the standardized input (i.e., Rowland timing data) and output (i.e., valid GNSS timing data), respectively, and the standardized parameters ( , , , The result is calculated from the training set and used for the standardization of the validation and test sets to ensure consistency in data processing.

[0109] A single-hidden-layer extreme learning machine model is constructed, with reasonable settings for the input layer dimension, the number of hidden layer neurons, the output layer dimension, and the regularization parameters. This embodiment employs a simple and efficient single-hidden-layer feedforward neural network structure. The input layer dimension is 1 (single feature input, i.e., Rowland timing data), the hidden layer contains L neurons (e.g., 100), and the output layer dimension is 1 (GNSS timing data), reducing model complexity and improving training efficiency.

[0110] Wherein, the input layer weight matrix Randomly generated within the range of [-1,1], precisely controlling the degree of influence of input data on hidden layer neurons.

[0111] bias vector Randomly generated within the range of [-1,1], the activation threshold of neurons in the hidden layer is effectively adjusted, enabling the single-hidden-layer extreme learning machine model to better fit the data.

[0112] A nonlinear transformation is achieved by processing the linear combination of input data and weights using the high-performance sigmoid activation function, as shown in the formula:

[0113]

[0114] in, The hidden layer output matrix (N is the number of training samples) is represented by the sigmoid function, which maps the linear combination result to the [0,1] interval, enhancing the non-linear expressive power of the model.

[0115] To avoid overfitting of the model, a regularization term is introduced. (e.g., 0.01), the output weights are solved using the least squares method. :

[0116]

[0117] in, To output weights, The output matrix of the hidden layer. Output matrix for hidden layer The transpose of is the identity matrix. For regularization parameters, It is the identity matrix. This provides the valid GNSS timing data for the output. Regularization terms enhance the invertibility of the matrix, improve the model's generalization ability, and enable the model to exhibit good predictive performance even on unknown data.

[0118] Roland timing data for the test set After standardization, the hidden layer output matrix is ​​calculated accurately. Then, the normalized prediction result is obtained by outputting the weights:

[0119]

[0120] in, These are the standardized GNSS timing data prediction values. The output matrix of the hidden layer. For output weights.

[0121] The predicted results are converted back to actual physical quantities (unit: ns) for practical application and evaluation. The inverse normalization process includes:

[0122]

[0123] In the formula, These are the predicted values ​​of GNSS timing data after inverse normalization processing. These are the normalized predicted values ​​of GNSS timing data. The standard deviation of the GNSS timing data calculated from the training set. This is the mean value of GNSS timing data calculated from the training set.

[0124] Finally, the Roland timing data from the test set is input into the trained model, which outputs GNSS timing data predictions. Multiple error metrics are then used to comprehensively evaluate the performance of the single-hidden-layer extreme learning machine model. In the evaluation step, Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and the standard deviation of the prediction error are used as evaluation metrics.

[0125] The mean squared error (MSE) accurately reflects the mean of the squared errors and is sensitive to outliers. The formula for MSE is:

[0126]

[0127] in, For the test set The presence of a few true GNSS values ​​highlights the model's performance in handling anomalies. The experimental result is 84.523105. , For the first The predicted GNSS timing data output for each test sample. This represents the total number of GNSS timing data samples in the test set.

[0128] The root mean square error (RMSE), being the square root of the mean square error (MSE), uses the same units as the original data, making it easy to intuitively understand the magnitude of the error. The formula for RMSE is:

[0129]

[0130] By taking the square root, the units of the MSE are restored to the same scale as the original data, making the magnitude of the error easier to understand and compare. The experimental result is 9.193645 ns.

[0131] The mean absolute error (MAE) is robust to outliers and can stably reflect the average deviation of predicted values. The formula for MAE is:

[0132]

[0133] Using absolute value calculations avoids the amplification effect of squaring on outliers, thus more stably reflecting the model's average prediction accuracy. The experimental result is 7.410173 ns.

[0134] The standard deviation of prediction error is used to accurately reflect the dispersion of the error. The smaller the value, the higher the stability of the model. The formula for the standard deviation of prediction error is:

[0135]

[0136] in, The standard deviation of the prediction error. For the first i The prediction error for each sample, where the prediction error is... , Let be the mean error, where , To test the sample size, the standard deviation of the prediction error was calculated to evaluate the model's predictive consistency across different samples, thus determining the model's stability and reliability. The experimental result was 9.176531. ns .

[0137] In summary, this embodiment utilizes a single-hidden-layer extreme learning machine model that eliminates the need for iterative training. Input weights and biases are randomly initialized, and output weights are directly calculated through matrix operations, significantly shortening training time and increasing training speed. This makes it highly suitable for real-time applications and meets the demands of domains requiring fast timing response times. Through rigorous outlier handling and regularization techniques, the model's adaptability to noisy data is effectively improved, ensuring stable performance even in complex environments. It provides consistent prediction results across different samples, offering reliable technical support for practical applications. Furthermore, the single-hidden-layer extreme learning machine model in this embodiment has few parameters, including only weights, biases, and normalization parameters, enabling lightweight deployment and easy embedding into navigation terminals or timing devices. This reduces system complexity and cost, demonstrating broad application prospects.

[0138] Example 3

[0139] Based on the GNSS timing data prediction method of Embodiment 1, this embodiment provides a GNSS timing data prediction system, which includes a data acquisition module, a data preprocessing module, and a mapping module connected by communication. Wherein:

[0140] The data acquisition module is used to acquire Roland timing data when GNSS timing data is invalid;

[0141] The data preprocessing module is used to preprocess Roland timing data;

[0142] The mapping module is used to input the preprocessed Roland timing data into the trained single-hidden-layer extreme learning machine model to obtain the normalized GNSS timing data prediction value. The GNSS timing data prediction value is restored through inverse normalization processing to obtain the final GNSS timing data prediction result.

[0143] The single-hidden-layer extreme learning machine model includes an input layer, a hidden layer, and an output layer. The input layer processes the Roland timing data into an input layer data matrix. The hidden layer performs mapping calculations on the input layer data matrix based on a predefined nonlinear mapping function to obtain the hidden layer output matrix. The output layer performs a linear combination of the hidden layer output matrix to obtain the normalized GNSS timing data prediction value.

[0144] The data preprocessing module performs the following steps: first, it performs mean processing on the acquired Rowland timing data to eliminate the DC component in the data and prevent the DC component from masking the true characteristics of the data; then, it applies the 3σ principle to correct outliers in the mean-processed Rowland timing data, identifying and processing outliers that exceed the reasonable range and reducing the interference of outliers on data quality; finally, it uses the z-score standardization method to normalize the outlier-corrected Rowland timing data, eliminating the dimensional differences between different data and giving the Rowland timing data a uniform data scale.

[0145] It also includes a model training module, which is used to perform the following steps:

[0146] Acquire historical Rowland timing data and corresponding valid GNSS timing data; perform mean processing and outlier correction on the historical Rowland timing data and corresponding GNSS timing data respectively; divide the corrected historical Rowland timing data and corresponding GNSS timing data into training set and test set according to a preset ratio; normalize the data in the training set and test set using the z-score normalization method; construct a single hidden layer extreme learning machine model, determine the input layer dimension, the number of hidden layer neurons, and the output layer dimension; randomly initialize the input layer weight matrix and bias vector in the single hidden layer extreme learning machine model within a predetermined range; input the historical Rowland timing data from the training set into the single hidden layer extreme learning machine model, and calculate the input layer weight matrix and bias vector according to the input layer data matrix and the input... The layer weight matrix and bias vector are used to calculate the hidden layer output matrix using the sigmoid activation function; the sigmoid activation function serves as a nonlinear mapping function; based on the output matrix of the hidden layer, the output weights from the hidden layer to the output layer in the single-hidden-layer extreme learning machine model are updated using regularized least squares; the output weights of the single-hidden-layer extreme learning machine model are used to determine the mapping relationship between the input layer data matrix after the hidden layer transformation and the corresponding GNSS timing data; the normalized historical Roland timing data in the test set is input into the trained single-hidden-layer extreme learning machine model to obtain normalized GNSS timing data prediction values; the GNSS timing data prediction values ​​are then denormalized to restore the actual physical quantities, and the model performance is evaluated using a preset error index.

[0147] Example 4

[0148] In another embodiment of the present invention, a computer-readable storage medium is provided as a storage component within a terminal device, the function of which is to store programs and data. It should be noted that the computer-readable storage medium here encompasses not only the built-in storage components of the terminal device but also extended storage components supported by the device. Essentially, it is a tangible medium capable of containing or storing programs that can be invoked by or in conjunction with an instruction execution system, device, or apparatus. This storage medium provides storage areas for the terminal's operating system and stores one or more instructions suitable for processor loading and execution, which can constitute one or more computer programs containing program code.

[0149] Specifically, examples of computer-readable storage media (a non-exclusive list) include: removable disks, hard disks, random access memory, read-only memory, erasable programmable read-only memory, optical fiber, portable optical disc read-only memory, optical storage devices, magnetic storage devices, or any reasonable combination of the above types.

[0150] This storage medium carries readable program code. The stored data signals can take many forms, including but not limited to electromagnetic signals, optical signals, or any reasonable combination of both. Furthermore, computer-readable storage medium can also refer to other readable media besides conventional readable storage media, capable of sending, propagating, or transmitting programs for use or operation by an instruction execution system, device, or apparatus. The program code on the storage medium can be transmitted via any suitable medium, including but not limited to wireless, wired, optical fiber, or any reasonable combination thereof.

[0151] The program code used to implement the operations of this invention can be written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C. The execution modes of the program code include: running entirely on the user's computing device, running partially on the user's device as a standalone software package, running partially in a distributed manner on both the user's device and a remote computing device, or running entirely on a remote computing device or server. When a remote computing device is involved, the device can be connected to the user's computing device via any type of network such as a local area network (LAN) or a wide area network (WAN), or connected to an external computing device via the Internet through an Internet service provider.

[0152] The processor is capable of loading and executing one or more instructions stored in a computer-readable storage medium to implement the corresponding steps of the GNSS timing data prediction method described in Example 1.

[0153] Example 5

[0154] Figure 5 This is a schematic diagram of a computer device provided according to an embodiment of the present invention.

[0155] Please see Figure 5 The terminal device is a computer device. The computer device 60 in this embodiment includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When the computer program 63 is executed by the processor 61, it implements the GNSS timing data prediction method in the embodiment. To avoid repetition, it will not be described in detail here.

[0156] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 5 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0157] The processor 61 may be a Central Processing Unit (CPU), or other general-purpose processors, graphics processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, quantum computing-based data processing logic units, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0158] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc., provided on the computer device 60.

[0159] Furthermore, memory 62 may include both internal storage units and external storage devices of the computer device 60. Memory 62 is used to store computer programs and other programs and data required by the computer device. Memory 62 can also be used to temporarily store data that has been output or will be output.

[0160] Any references to memory, database, or other media used in the embodiments provided in this application may include at least one of non-volatile and volatile memory. Non-volatile memory may include read-only memory (Read-Only Memory). Memory includes ROM, magnetic tape, floppy disk, flash memory, optical storage, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM can be in various forms, such as static random access memory (SRAM) or dynamic random access memory (DRAM).

[0161] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

Claims

1. A method for predicting GNSS timing data, characterized in that, include: Obtain Roland timing data when GNSS timing data is invalid, and preprocess the Roland timing data; The preprocessed Roland timing data is input into the trained single-hidden-layer extreme learning machine model to obtain the normalized GNSS timing data prediction value. The GNSS timing data prediction value is restored by inverse normalization to obtain the final effective GNSS timing data prediction result. The single-hidden-layer extreme learning machine model includes an input layer, a hidden layer, and an output layer; the input layer is used to process the Rowland timing data into an input layer data matrix; the hidden layer performs mapping calculations on the input layer data matrix based on a predefined nonlinear mapping function to obtain the hidden layer output matrix; The output layer linearly combines the output matrix of the hidden layer to obtain the normalized GNSS timing data prediction value. The training process of the single hidden layer extreme learning machine model includes: Acquire historical Roland timing data and corresponding valid GNSS timing data; perform mean processing and outlier correction processing on the historical Roland timing data and the corresponding valid GNSS timing data respectively; perform normalization processing on the valid GNSS timing data; The corrected historical Roland timing data and the corresponding normalized effective GNSS timing data were used as the training set. Construct a single-hidden-layer extreme learning machine model and determine the input layer dimension, the number of hidden layer neurons, and the output layer dimension. Randomly initialize the input layer weight matrix and bias vector in a single hidden layer extreme learning machine model within a predetermined range; Historical Roland timing data from the training set are input into a single-hidden-layer extreme learning machine model, and the hidden layer output matrix is ​​calculated using a nonlinear mapping function in the hidden layer; the nonlinear mapping function is the sigmoid activation function. Based on the hidden layer output matrix and the normalized effective GNSS timing data, the output weights from the hidden layer to the output layer are updated using a regularized least squares algorithm. The output weights are used to determine the mapping relationship between the input layer data matrix after the hidden layer transformation and the corresponding normalized effective GNSS timing data. The single hidden layer extreme learning machine model is determined according to the input layer weight matrix, bias vector, and output weights.

2. The GNSS timing data prediction method according to claim 1, characterized in that, The preprocessing process includes: After averaging the Roland timing data, outlier correction was performed using the 3σ principle. The corrected Roland timing data were normalized using the z-score normalization method.

3. The GNSS timing data prediction method according to claim 2, characterized in that, The specific method for correcting outliers is as follows: After averaging, the mean value in the Roland timing data is set to be... The standard deviation is ; When the mean-processed Roland timing data exceeds [ , If the range is not specified, then the Roland timing data will be replaced and corrected. Otherwise, no outlier correction will be performed.

4. The GNSS timing data prediction method according to claim 1, characterized in that, The hidden layer output matrix is: In the formula, The output matrix of the hidden layer. For the input layer data matrix, The input layer weight matrix, This is the bias vector.

5. The GNSS timing data prediction method according to claim 1, characterized in that, The output weights from the hidden layer to the output layer are updated using a regularized least squares algorithm. The calculation formula is: In the formula, To output weights, The output matrix of the hidden layer. Output matrix for hidden layer The transpose of the matrix, For regularization parameters, It is the identity matrix. For outputting valid GNSS timing data, For dimensions.

6. The GNSS timing data prediction method according to claim 1, characterized in that, The denormalization process includes: In the formula, To obtain the final effective GNSS timing data prediction results, These are the normalized predicted values ​​of GNSS timing data. The standard deviation of the GNSS timing data calculated from the training set. The mean of GNSS timing data calculated for the training set.

7. A GNSS timing data prediction system, characterized in that, include: The data acquisition module is used to acquire Roland timing data when GNSS timing data is invalid; The data preprocessing module, connected to the data acquisition module, is used to preprocess the Roland timing data; The mapping module, connected to the data preprocessing module, is used to input the preprocessed Roland timing data into the trained single-hidden-layer extreme learning machine model to obtain the normalized GNSS timing data prediction value. The GNSS timing data prediction value is restored through inverse normalization processing to obtain the final GNSS timing data prediction result. The single-hidden-layer extreme learning machine model includes an input layer, a hidden layer, and an output layer. The input layer is used to process the Roland timing data into an input layer data matrix. The hidden layer performs mapping calculations on the input layer data matrix based on a predefined nonlinear mapping function to obtain a hidden layer output matrix. The output layer performs a linear combination of the hidden layer output matrix to obtain a normalized GNSS timing data prediction value. The training process of the single hidden layer extreme learning machine model includes: Acquire historical Roland timing data and corresponding valid GNSS timing data; perform mean processing and outlier correction processing on the historical Roland timing data and the corresponding valid GNSS timing data respectively; perform normalization processing on the valid GNSS timing data; The corrected historical Roland timing data and the corresponding normalized effective GNSS timing data were used as the training set. Construct a single-hidden-layer extreme learning machine model and determine the input layer dimension, the number of hidden layer neurons, and the output layer dimension. Randomly initialize the input layer weight matrix and bias vector in a single hidden layer extreme learning machine model within a predetermined range; Historical Roland timing data from the training set are input into a single-hidden-layer extreme learning machine model, and the hidden layer output matrix is ​​calculated using a nonlinear mapping function in the hidden layer; the nonlinear mapping function is the sigmoid activation function. Based on the hidden layer output matrix and the normalized effective GNSS timing data, the output weights from the hidden layer to the output layer are updated using a regularized least squares algorithm. The output weights are used to determine the mapping relationship between the input layer data matrix after the hidden layer transformation and the corresponding normalized effective GNSS timing data. The single hidden layer extreme learning machine model is determined according to the input layer weight matrix, bias vector, and output weights.

8. A computer-readable storage medium for storing one or more programs, characterized in that, The one or more programs include instructions that, when executed by a computing device, cause the computing device to perform the GNSS timing data prediction method according to any one of claims 1 to 6.

9. A computing device, characterized in that, include: One or more processors, a memory, and one or more programs, wherein the one or more programs are stored in the memory and configured to be executed by the one or more processors, the one or more programs including methods for performing the GNSS timing data prediction method of any one of claims 1 to 6.

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