GNSS signal compensation method based on double-branch neural network

Abstract

The application discloses a GNSS signal compensation method based on a double-branch neural network, relates to the technical field of integrated navigation, and is used for solving the problem of navigation accuracy reduction during long-time GNSS signal interruption, and comprises the following steps: collecting IMU angular velocity and specific force, combining an INS attitude to construct an input feature sequence; when GNSS is available, taking the feature sequence as input, taking velocity increments and position increments of integrated navigation calculation as labels, training a double-branch network, and respectively predicting the velocity increments and the position increments; when GNSS is interrupted, inputting the feature sequence into the network to obtain a predicted value, taking the last available integrated navigation velocity and position before interruption as initial values to accumulate and recursively calculate, and obtaining predicted velocity and predicted position as compensation output. The application improves the velocity and position prediction accuracy during long-time GNSS interruption by means of double-branch differential modeling and combination of TCN and Transformer to extract local-global features.

Description

Technical Field

[0001] This invention relates to the field of navigation technology, and more particularly to the field of integrated navigation data compensation technology, specifically a GNSS signal compensation method based on a dual-branch neural network. Background Technology

[0002] In complex environments such as urban canyons and tunnels, GNSS signals are prone to interruption. When the system relies solely on independent INS calculations, inertial errors accumulate rapidly with integration, leading to a sharp decline in positioning accuracy. Maintaining continuous and stable navigation calculations during GNSS outages is a key challenge in this field.

[0003] Existing solutions fall into two categories: one relies on additional hardware such as LiDAR and cameras to provide external constraints through multi-sensor fusion, but it is costly, computationally intensive, and complex to calibrate; the other focuses on algorithm improvement, such as kinematic constraint methods like nonholonomic constraints and zero-velocity updates, which do not require additional hardware and are low-cost, but their effectiveness is highly dependent on assumptions about the motion scenario and is difficult to adapt to complex maneuvers.

[0004] In recent years, data-driven AI approaches have emerged. Early methods employed feedforward models such as radial basis function networks and multilayer perceptrons, but these had limited training efficiency and did not utilize temporal information. Subsequently, temporal models such as LSTM, GRU, and Transformer were introduced, including CNN-LSTM, RF-LSTM, S-Transformer, and CNN-GRU, which achieved prediction compensation within interruption times of 20 to 62 seconds.

[0005] However, existing AI methods still have shortcomings: (1) The prediction time domain is relatively short, and the accuracy drops significantly after 30 to 60 seconds; (2) Using a unified network to predict velocity and position at the same time does not take into account the essential differences in dynamic characteristics and learning difficulty between velocity increment (single integration) and position increment (higher-order integration), which restricts the overall performance; (3) When RNN / LSTM processes long sequences, there is gradient decay, and the pure Transformer is weak in perceiving local transient features, and the two have insufficient collaborative modeling ability.

[0006] Therefore, there is an urgent need to develop a GNSS interruption compensation method that can simultaneously take into account local dynamic characteristics and global long-range dependence, and perform differentiated modeling of velocity increments and position increments, so as to break through the bottlenecks of existing methods in prediction time domain and accuracy, and meet the actual needs of high-precision continuous navigation in complex environments. Summary of the Invention

[0007] The purpose of this invention is to provide a GNSS signal compensation method based on a dual-branch neural network, in order to solve the problem that the existing technology is insufficient in its ability to jointly model the local dynamic characteristics and global long-range dependence of inertial measurement sequences, and is unable to effectively cope with the continuous high-precision navigation requirements under complex environments with long-term GNSS interruptions.

[0008] To address the above objectives, this invention provides a GNSS signal compensation method based on a dual-branch neural network, comprising: S1. A combined navigation system is constructed by integrating the inertial navigation system (INS) and the global navigation satellite system (GNSS). The system collects raw observation data output by the inertial measurement unit and attitude information calculated by the inertial navigation system based on the raw observation data in real time, and constructs an input feature sequence. S2. Monitor the availability of GNSS signals in real time. When GNSS signals are available, enter the training phase; when GNSS signals are interrupted, enter the prediction phase. S3. During the training phase, a dual-branch network containing a velocity branch and a position branch is constructed. The input feature sequence is used as input, and the velocity increment and position increment calculated by the integrated navigation system are used as supervision labels to train the dual-branch network. The velocity branch learns the mapping relationship between the input feature sequence and the velocity increment, and the position branch learns the mapping relationship between the input feature sequence and the position increment. S4. In the prediction stage, the input feature sequence is input into the dual-branch network trained in S3. The velocity branch outputs the predicted velocity increment, and the position branch outputs the predicted position increment. S5. Using the last combined navigation speed and position before the GNSS signal interruption as the initial values, the predicted speed increment and predicted position increment output by time step in S4 are accumulated respectively to obtain the predicted speed and predicted position, which are used as speed compensation and position compensation respectively, and the GNSS signal compensation is output.

[0009] The raw observation data includes three-axis angular velocity and three-axis specific force output by the inertial measurement unit; attitude information includes heading angle, pitch angle, and roll angle, which are mechanically arranged and calculated by the inertial navigation system; the input feature sequence is a multi-dimensional time-series feature matrix composed of three-axis angular velocity, three-axis specific force, and attitude information. The input feature sequence is: ; ; ; ; In the formula, Indicates the time step index. express The input feature sequence fed into the dual-branch network at each time step is equivalent to the input feature sequence. exist Sampling point data at time t, express The three-axis angular velocities at time t. , , They represent Projection onto the X, Y, and Z axes; express The three-axis ratio at any given time, , , They represent Projection onto the X, Y, and Z axes; express Attitude information matrix at time step, express The heading angle at any moment, express The pitch angle at any moment, express The roll angle at any given moment.

[0010] Both the velocity branch and the position branch are composed of a temporal convolutional network module and a Transformer module cascaded in sequence; The temporal convolutional network module is used to extract multi-scale local temporal features from the input feature sequence, and the Transformer module is used to model the global dependencies across time steps of the local temporal features output by the temporal convolutional network module.

[0011] The temporal convolutional network module consists of multiple stacked residual blocks, each of which includes a dilated causal convolutional layer, a batch normalization layer, a GELU activation function layer, and residual connections. Dilated causal convolution extracts multi-scale local temporal features by setting different dilation factors for different residual blocks: ; In the formula, express Local temporal characteristics at any given moment Indicates the input feature sequence. Represents the convolution kernel. Indicates the expansion factor. This indicates that the expansion factor is... convolution kernel For the input feature sequence After performing dilated causal convolution, in The characteristic response value output at time t, Indicates the kernel size. For convolution kernel index, Represents the input feature sequence exist The value at; Batch normalization layers are used to stabilize feature distribution and accelerate model convergence; GELU activation function layers are used to introduce nonlinear transformations; residual connections are used to add the input and output of the residual block element by element.

[0012] The Transformer module includes a multi-head self-attention mechanism, residual connections, layer normalization, and feedforward neural networks; Multi-head self-attention mechanism adaptively evaluates the correlation between different time positions through the interaction between query vector, key vector and value vector, and models time dependencies in parallel in different subspaces; residual connection is used to improve the information flow in deep network and alleviate gradient degradation; layer normalization is used to stabilize feature distribution and accelerate model convergence; feedforward neural network performs nonlinear transformation and feature enhancement at each time step; The output of the Transformer module in the velocity branch is mapped by the regression decoder to obtain the velocity increment prediction value, and the output of the Transformer module in the position branch is mapped by the regression decoder to obtain the position increment prediction value.

[0013] The velocity branch and the position branch use the same model structure. The temporal convolutional network module of each branch includes 6 residual blocks, each with 64 channels. The kernel size of the dilated causal convolution in each branch is 3, and the dilation factor is set in sequence. The output feature dimension is 3-dimensional; The hidden layer dimension of the Transformer in the velocity branch is smaller than that in the position branch. The hidden layer dimension of the Transformer in the velocity branch is 160, and the hidden layer dimension of the Transformer in the position branch is 320. The number of Transformer encoder layers in the velocity branch is less than that in the position branch. The velocity branch has 2 Transformer encoder layers, and the position branch has 3 Transformer encoder layers.

[0014] Supervision labels during training for: ; ; ; ; ; In the formula, Indicates the speed increment. Indicates the position increment. express Motion acceleration in the navigation coordinate system at any time This represents the attitude transformation matrix from the vehicle coordinate system to the navigation coordinate system. Indicates intermediate calculation parameters. This represents the projection of the Earth's rotation angular rate onto the navigation coordinate system. express The angular velocity of the navigation coordinate system relative to the Earth coordinate system at any given time. express The velocity vector in the navigation coordinate system at any given moment. This represents the gravitational acceleration vector in the navigation coordinate system.

[0015] During the training phase, the loss function is the sum of the mean squared error of the velocity increment and the mean squared error of the position increment: ; ; ; In the formula, Indicates the number of training samples. , They represent the first Predicted values ​​of velocity increment and position increment for each sample. , They are respectively , The corresponding supervision label.

[0016] During the training phase, a sliding window scheme is used to segment the IMU continuous time series samples. Each input sample window contains... The observation data is obtained from consecutive time steps, and the adjacent windows slide forward. One time step; This corresponds to a 2-second time length at an IMU sampling frequency of 100 Hz, with a window sliding step of 100 time steps, corresponding to a 1-second sample update interval.

[0017] During the prediction phase, when the duration of GNSS signal interruption exceeds the time length corresponding to a single input time window preset during the training phase, a recursive prediction strategy is adopted: the prediction output of the previous moment is used as a component of the input feature sequence of the next moment, and the velocity increment prediction value and position increment prediction value of subsequent moments are recursively generated until the GNSS signal is restored. The predicted speed is: ; The predicted location is: ; In the formula, Indicates the index of the predicted time. Indicates the first Prediction speed at each moment, Indicates the first Predicted location at each moment, This represents the initial value for velocity prediction. This represents the initial value for location prediction.

[0018] Compared with the prior art, the present invention has the following advantages:

[0019] This invention uses a dual-branch network architecture to model velocity increments and position increments differently, thereby better capturing their different characteristics in terms of temporal evolution and error propagation.

[0020] This invention employs a joint modeling strategy that uses the TCN module to extract multi-scale local temporal features and the Transformer module to model long-range dependencies, which can maintain high prediction accuracy even during a 60-second GNSS outage.

[0021] This invention relies solely on the existing IMU and GNSS receiver in the existing GNSS / INS integrated navigation system, without the need to introduce additional sensors such as lidar and cameras, thus avoiding the problems of high system cost, large computational load, and difficult sensor calibration caused by multi-sensor fusion.

[0022] In the prediction stage, this invention directly uses the recursively obtained predicted velocity and predicted position as navigation compensation outputs, avoiding the complex step of fusing deep learning prediction results with INS solution results through a Kalman filter, which is required in traditional methods. This reduces system complexity and improves real-time performance. Attached Figure Description

[0023] Figure 1 The overall flowchart of the GNSS signal compensation method based on a dual-branch neural network provided by the present invention;

[0024] Figure 2 This is a network architecture diagram of the DB-TTN model provided by the present invention;

[0025] Figure 3 for Figure 2 Network architecture diagram of the residual module;

[0026] Figure 4 The graph shows the variation of eastward velocity error over time using different methods.

[0027] Figure 5 The graph shows the variation of northbound velocity error over time using different methods.

[0028] Figure 6 The graph shows the variation of the azimuth velocity error over time for different methods.

[0029] Figure 7 The graph shows the changes in eastward position error over time using different methods.

[0030] Figure 8 The graph shows the changes in northward position error over time using different methods.

[0031] Figure 9 This is a graph showing the change of celestial position error over time using different methods. Detailed Implementation

[0032] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0033] GNSS signal compensation methods based on dual-branch neural networks include: S1. A combined navigation system is constructed by integrating the inertial navigation system (INS) and the global navigation satellite system (GNSS). The system collects raw observation data output by the inertial measurement unit and attitude information calculated by the inertial navigation system based on the raw observation data in real time, and constructs an input feature sequence. S2. Monitor the availability of GNSS signals in real time. When GNSS signals are available, enter the training phase; when GNSS signals are interrupted, enter the prediction phase. S3. During the training phase, a dual-branch network containing a velocity branch and a position branch is constructed. The input feature sequence is used as input, and the velocity increment and position increment calculated by the integrated navigation system are used as supervision labels to train the dual-branch network. The velocity branch learns the mapping relationship between the input feature sequence and the velocity increment, and the position branch learns the mapping relationship between the input feature sequence and the position increment. S4. In the prediction stage, the input feature sequence is input into the dual-branch network trained in S3. The velocity branch outputs the predicted velocity increment, and the position branch outputs the predicted position increment. S5. Using the last combined navigation speed and position before the GNSS signal interruption as the initial values, the predicted speed increment and predicted position increment output by time step in S4 are accumulated respectively to obtain the predicted speed and predicted position, which are used as speed compensation and position compensation respectively, and the GNSS signal compensation is output.

[0034] The raw observation data includes three-axis angular velocity and three-axis specific force output by the inertial measurement unit; attitude information includes heading angle, pitch angle, and roll angle, which are mechanically arranged and calculated by the inertial navigation system; the input feature sequence is a multi-dimensional time-series feature matrix composed of three-axis angular velocity, three-axis specific force, and attitude information. The input feature sequence is: ; ; ; ; In the formula, Indicates the time step index. express The input feature sequence fed into the dual-branch network at each time step is equivalent to the input feature sequence. exist Sampling point data at time t, express The three-axis angular velocities at time t. , , They represent Projection onto the X, Y, and Z axes; express The three-axis ratio at any given time, , , They represent Projection onto the X, Y, and Z axes; express Attitude information matrix at time step, express The heading angle at any moment, express The pitch angle at any moment, express The roll angle at any given moment.

[0035] Both the velocity branch and the position branch are composed of a temporal convolutional network module and a Transformer module cascaded in sequence; The temporal convolutional network module is used to extract multi-scale local temporal features from the input feature sequence, and the Transformer module is used to model the global dependencies across time steps of the local temporal features output by the temporal convolutional network module.

[0036] The temporal convolutional network module consists of multiple stacked residual blocks, each of which includes a dilated causal convolutional layer, a batch normalization layer, a GELU activation function layer, and residual connections. Dilated causal convolution extracts multi-scale local temporal features by setting different dilation factors for different residual blocks: ; In the formula, express Local temporal characteristics at any given moment Indicates the input feature sequence. Represents the convolution kernel. Indicates the expansion factor. This indicates that the expansion factor is... convolution kernel For the input feature sequence After performing dilated causal convolution, in The characteristic response value output at time t, Indicates the kernel size. For convolution kernel index, Represents the input feature sequence exist The value at; The Transformer module includes a multi-head self-attention mechanism, residual connections, layer normalization, and feedforward neural networks; Multi-head self-attention mechanism adaptively evaluates the correlation between different time positions through the interaction between query vector, key vector and value vector, and models time dependencies in parallel in different subspaces; residual connection is used to improve the information flow in deep network and alleviate gradient degradation; layer normalization is used to stabilize feature distribution and accelerate model convergence; feedforward neural network performs nonlinear transformation and feature enhancement at each time step; The output of the Transformer module in the velocity branch is mapped by the regression decoder to obtain the velocity increment prediction value, and the output of the Transformer module in the position branch is mapped by the regression decoder to obtain the position increment prediction value.

[0037] The velocity branch and the position branch use the same model structure. The temporal convolutional network module of each branch includes 6 residual blocks, each with 64 channels. The kernel size of the dilated causal convolution in each branch is 3, and the dilation factor is set in sequence. The output feature dimension is 3-dimensional; The hidden layer dimension of the Transformer in the velocity branch is smaller than that in the position branch. The hidden layer dimension of the Transformer in the velocity branch is 160, and the hidden layer dimension of the Transformer in the position branch is 320. The number of Transformer encoder layers in the velocity branch is less than that in the position branch. The velocity branch has 2 Transformer encoder layers, and the position branch has 3 Transformer encoder layers.

[0038] Supervision labels during training for: ; ; ; ; ; In the formula, Indicates the speed increment. Indicates the position increment. express Motion acceleration in the navigation coordinate system at any time This represents the attitude transformation matrix from the vehicle coordinate system to the navigation coordinate system. Indicates intermediate calculation parameters. This represents the projection of the Earth's rotation angular rate onto the navigation coordinate system. express The angular velocity of the navigation coordinate system relative to the Earth coordinate system at any given time. express The velocity vector in the navigation coordinate system at any given moment. This represents the gravitational acceleration vector in the navigation coordinate system.

[0039] During the training phase, the loss function is the sum of the mean squared error of the velocity increment and the mean squared error of the position increment: ; ; ; In the formula, Indicates the number of training samples. , They represent the first Predicted values ​​of velocity increment and position increment for each sample. , They are respectively , The corresponding supervision label.

[0040] During the training phase, a sliding window scheme is used to segment the IMU continuous time series samples. Each input sample window contains... The observation data is obtained from consecutive time steps, and the adjacent windows slide forward. One time step; This corresponds to a 2-second time length at an IMU sampling frequency of 100 Hz, with a window sliding step of 100 time steps, corresponding to a 1-second sample update interval.

[0041] During the prediction phase, when the duration of GNSS signal interruption exceeds the time length corresponding to a single input time window preset during the training phase, a recursive prediction strategy is adopted: the prediction output of the previous moment is used as a component of the input feature sequence of the next moment, and the velocity increment prediction value and position increment prediction value of subsequent moments are recursively generated until the GNSS signal is restored. The predicted speed is: ; The predicted location is: ; In the formula, Indicates the index of the predicted time. Indicates the first Prediction speed at each moment, Indicates the first Predicted location at each moment, This represents the initial value for velocity prediction. This represents the initial value for location prediction.

[0042] In S5, the last combined navigation velocity and position before GNSS signal interruption refers to the navigation velocity and position of the last valid GNSS / INS fusion output before the GNSS signal quality degraded to unusable levels. During recursive prediction, only the attitude angles predicted at the previous time step (updated via INS mechanical orchestration) or velocity / position increments are added to the input window as part of the historical state. The network output is a sequence with the same time step as the input, and the attitude angles during the prediction phase are updated in real time by independent INS mechanical orchestration.

[0043] The dilated causal convolutional layer expands the receptive field while maintaining temporal causality by setting different dilation factors for different residual blocks, and extracts multi-scale local temporal features. The dilated causal convolutional layer extracts local temporal features according to the following formula: The residual connection is used to add the input and output of the residual block element by element to improve gradient propagation and retain the original temporal information.

[0044] In position and velocity compensation tasks during GNSS signal interruptions, the input sequence contains angular velocity, specific force, and attitude information. These observations not only contain local dynamic features characterizing the instantaneous motion state but also long-range dependency information generated by the continuous evolution of vehicle motion and recursive updates of inertial state. TCN can effectively extract multi-scale local temporal features and accurately capture short-term dynamic changes and local correlations between adjacent epochs. In contrast, Transformer enhances the representation of long-term evolution patterns of velocity and position increments by modeling global dependencies across time steps through a self-attention mechanism. Velocity increments can be obtained by first-order integration of the velocity differential equation, while position increments are affected by the accumulation of higher-order integrals. Therefore, these two objectives differ fundamentally in terms of dynamic evolution, error propagation characteristics, and learning difficulty. To better meet different modeling needs, a dual-branch network architecture is constructed, in which velocity and position increments are learned separately. The detailed hyperparameter settings of the dual-branch network are shown in Table 1.

[0045] Table 1. Detailed hyperparameters of the two-branch network; .

[0046] The input of a two-branch network is a The feature matrix of , where The length of the time series is determined by the IMU sampling frequency and a predefined input time window. Input features are fed into the velocity branch and the location branch for training, respectively. Since these two branches have the same overall architecture and both consist of a TCN module and a Transformer module, differing only slightly in hyperparameter settings and network depth, the velocity increment prediction branch will be described in detail below as an example. In the velocity branch, the input sequence first extracts multi-scale local temporal features through the TCN module. This module consists of multiple stacked residual blocks, each containing dilated causal convolutions, batch normalization, a GELU activation function, and residual connections.

[0047] The dilation factor controls the spacing between adjacent sampling locations in the convolution operation. A larger dilation factor corresponds to a wider temporal coverage within a single convolutional layer, enabling the network to capture sequence dependencies over longer time scales. By assigning different dilation factors, the network can extract local dynamic patterns across multiple time scales. In the velocity branch, the TCN module employs five stacked residual blocks with dilation factors set to 1, 2, 4, 8, 16, and 32, respectively. The channel dimension of each residual block is set to 64, allowing temporal features to be projected into a unified high-level representation space. The progressive dilation strategy expands the receptive field layer by layer, effectively capturing short-range temporal fluctuations and long-range local dependencies. BatchNorm and GELU activation functions are used to improve training stability and enhance nonlinear representation capabilities, while residual connections facilitate gradient propagation and preserve original temporal information. This hierarchical temporal encoding scheme allows the network to progressively extract high-level local dynamic features from raw inertial observations, providing a more informative representation for subsequent Transformer modules to model global temporal dependencies.

[0048] Features processed by input embedding and positional encoding are fed into the Transformer module to further model global temporal dependencies across time steps. The self-attention mechanism in the Transformer adaptively evaluates the correlation between different time locations through the interaction between query vectors, key vectors, and value vectors, thus highlighting temporal features more valuable for velocity and positional increment prediction. Furthermore, a multi-head self-attention mechanism enhances the model's representational power by modeling temporal dependencies in parallel across different subspaces. The number of attention heads is set to 8 to balance representational power and computational efficiency. After self-attention computation, residual connections and layer normalization are applied sequentially. Residual connections improve information flow in the deep network and alleviate gradient degradation, while layer normalization stabilizes the feature distribution and accelerates model convergence. The resulting features are then fed into a positional feedforward network (FFN), which performs nonlinear transformations and feature augmentation at each time step. This operation further enhances the model's ability to represent high-level temporal patterns, which is crucial for learning the complex nonlinear mapping between habitual sequences and velocity and positional increments. The output of the feedforward neural network (FFN) is further processed through residual connections and layer normalization to enhance training stability and feature representation capabilities. Considering temporal modeling capabilities and computational cost, two Transformer encoder layers are stacked in the proposed network. Following the encoder, a lightweight regression decoder is introduced to map the encoded features, reducing model complexity while meeting the demands of real-time applications. This decoder omits computationally expensive components in the standard Transformer, such as multi-head attention and additive normalization, retaining only two feedforward sub-layers to perform pointwise regression. The velocity and position branches employ the same regression structure during the decoding phase and their outputs are fused in the final output phase. Through this design, the model can generate incremental predictions with relatively low computational overhead, and the final output shape is... This corresponds to the three-dimensional velocity increment and the three-dimensional position increment.

[0049] The navigation coordinate system is defined as a local East-North-Up (ENU) tangential coordinate system, with the body coordinate system having its origin at the vehicle's center of gravity, and its three axes pointing to the right, forward, and upward, respectively. Based on the principle of inertial mechanization, the INS recursively updates the navigation state using specific force measured by accelerometers and angular rate measured by gyroscopes. This update process is mainly controlled by three coupled continuous-time differential equations concerning attitude, velocity, and position: ; ; ; in, This represents the direction cosine matrix transformation vector from the main coordinate system to the navigation coordinate system. express The first derivative with respect to time. and The angular rate measured by the gyroscope and the specific force measured by the accelerometer are both represented in the vehicle coordinate system. This represents the Earth's angular velocity relative to an inertial frame of reference, expressed in navigation frames. This represents the projection of the Earth's rotational angular rate onto the navigation coordinate system. This represents the angular velocity of the navigation coordinate system relative to the Earth coordinate system, expressed in the navigation coordinate system. Represents the velocity vector in the navigation coordinate system. express The first derivative with respect to time is equivalent to the acceleration in the navigation coordinate system. for exist The value at time, Indicated by latitude ,longitude and height The position vector formed, express The first derivative with respect to time. It is the gravity vector in the navigation coordinate system. and These represent the radii of curvature of the meridian and the parallels of latitude, respectively. This represents the antisymmetric matrix associated with the cross product operation. latitude The secant function is mathematically defined as the reciprocal of the cosine function, i.e. To enable numerical implementation in practical navigation systems, the continuous-time state equations are discretized into recursive update equations for attitude, velocity, and position, and the corresponding discrete-time strapdown mechanized algorithm is derived in detail.

[0050] The DB-TTN model (a dual-branch network with velocity and position branches constructed using S3) is the core prediction model proposed in this invention. Its overall architecture employs a parallel dual-branch design, independently modeling the fundamental differences in dynamic evolution and error accumulation characteristics of velocity increments (single integrals) and position increments (double integrals). Both branches utilize a backbone structure of cascaded temporal convolutional network modules and Transformer modules. The temporal convolutional network module extracts multi-scale local temporal features of the input feature sequence by stacking multiple dilated causal convolutional residual blocks with different dilation factors, accurately capturing short-term dynamic changes in inertial measurement data and local correlations between adjacent moments. The Transformer module, through a multi-head self-attention mechanism, models the global dependencies of the local features output by the temporal convolutional network, effectively capturing long-term evolution patterns across time steps. The two modules work collaboratively, enabling the model to both keenly perceive transient maneuvers and grasp the continuous evolution trend of the navigation state over long periods. To accommodate the difference in modeling difficulty between velocity and position increments, the position branch employs a larger hidden layer dimension and more encoder layers to enhance its ability to represent the cumulative effects of higher-order integrals. When GNSS signals are available, the model uses the three-axis angular velocity, three-axis specific force output by the inertial measurement unit, and attitude information calculated by the inertial navigation system as input features, and the velocity and position increments calculated by the integrated navigation system as supervision labels for training. When GNSS signals are interrupted, the model maps the real-time acquired input feature sequence into time-by-time predicted velocity and position increment values, and uses the last valid integrated navigation velocity and position before the interruption as initial values ​​for cumulative recursion, ultimately outputting continuous velocity and position compensation results.

[0051] To evaluate the performance of the proposed DB-TTN model in compensating for velocity and position during GNSS outages, a series of systematic experiments were conducted based on real-world datasets. First, the DB-TTN model was trained using real data. Then, the model's performance was compared with four state-of-the-art methods (AT-LSTM, CNN-LSTM, CNN-GRU, and S-Transformer) to validate the effectiveness of the proposed method. Finally, ablation experiments were performed to further analyze the contributions of each component in the DB-TTN model.

[0052] To ensure fairness in the comparisons and reproducibility of the results, all experiments were conducted on the same hardware platform, and all methods were trained and evaluated using the same real dataset under the same experimental settings.

[0053] The dataset uses MEMS-IMU data, collected by the MPU6500 during actual vehicle operation, with a sampling frequency of 100Hz. Detailed hardware specifications are summarized in Table 2.

[0054] Table 2 IMU parameter settings; .

[0055] GNSS data was processed using differential positioning technology to obtain high-precision solution results at an output rate of 1Hz. The post-processed GNSS / INS integrated navigation solution results were used as high-precision ground reality reference values. A dataset with a total data acquisition duration of approximately 2080 seconds was used for model training and validation. To ensure strict independence between training, validation, and testing, data from 1 to 1300 seconds was used to train the DB-TTN model, while data from 1361 to 1560 seconds was used for model validation and parameter tuning. Furthermore, to simulate a GNSS outage scenario, GNSS velocity and position observation data from 1301 to 1360 seconds were deliberately removed, retaining only IMU data for independent mechanization. This 60-second interval includes straight-line motion and left-turn maneuvers under different speed conditions, thus providing a more challenging scenario for evaluating the position and velocity prediction performance of the proposed model during GNSS outages.

[0056] To comprehensively evaluate the prediction performance of the proposed DB-TTN model for velocity and position, four metrics were used: Root Mean Square Error (RMSE), Maximum Error (MAX), Correlation Coefficient (CC), and Index of Dispersion (SI). RMSE quantifies the overall prediction error level, reflecting the average deviation between the predicted results and the reference values. MAX characterizes the error in the worst-case scenario and can be used to assess the model's robustness under extreme conditions. CC measures the consistency and correlation between the predicted results and the reference values. SI reflects the relative dispersion of the prediction error in a normalized form, making it suitable for comparing performance at different magnitudes or scales. These four metrics provide a comprehensive evaluation of the model's performance from multiple perspectives, including overall accuracy, extreme error behavior, correlation consistency, relative dispersion, and statistical reliability.

[0057] ; ; ; ; In the formula, Indicates the number of training samples. and They represent the first Predicted and reference values ​​for each epoch (training batch). and These represent the average values ​​of the predicted sequence and the reference sequence, respectively.

[0058] To effectively train the proposed DB-TTN model, a training dataset was used to construct training samples. Since the IMU sampling frequency is 100Hz and the model's learning objective is the velocity and position increments between adjacent GNSS / INS solution cycles, a sliding window scheme was used to segment the time series. The input samples are set to a size of 100, with a step size of 100. Specifically, each input window contains observations from 200 consecutive time steps, corresponding to a 2-second time interval. Each time step contains 9 features: triaxial angular velocity, triaxial specific force, and 3D pose information. Adjacent windows slide forward 100 time steps, corresponding to a 1-second sample update interval. This sliding window design maintains the integrity of short-term dynamic information while balancing sample continuity and data utilization, effectively supporting the temporal characteristics of model learning speed and positional increments. The Adam optimizer is used to update network parameters. Adam automatically adjusts the learning rate of each parameter by adaptively estimating the first and second moments of the gradient, achieving fast convergence, stable training, and is well-suited for optimizing deep temporal networks. In the experiments, the initial learning rate and weight decay coefficients were both set to 100. , and The values ​​were set to 0.9 and 0.999 respectively. The batch size was set to 8. All hyperparameters were determined through grid search to ensure optimal performance on real datasets. Both branches in DB-TTN used the same training hyperparameter settings, with only branch-specific architecture parameters configured separately.

[0059] To verify the effectiveness of the proposed DB-TTN method in predicting speed and location using real-world road IMU data, comparative experiments were conducted with several state-of-the-art methods, including AT-LSTM, CNN-LSTM, CNN-GRU, and S-Transformer. RMSE, MAX, CC, and SI were used as evaluation metrics to comprehensively assess the prediction performance.

[0060] Table 3. Comparison of velocity prediction performance of different methods during a 60-second GNSS outage; ; Table 3 shows the RMSE, MAX, CC, and SI results of different methods for velocity prediction during a 60-second GNSS interruption. As shown in Table 3, for eastward velocity, DB-TTN's RMSE is 0.783 m / s, a reduction of 85.34% compared to PureINS' 5.341 m / s; MAX decreases from 8.746 m / s to 1.398 m / s, a reduction of 84.02%. Notably, DB-TTN's CC is 0.72, lower than PureINS, AT-LSTM, CNN-LSTM, and CNN-GRU. This may be because CC mainly reflects the linear consistency between the predicted result and the reference value in the overall trend of change, and is therefore more sensitive to the dynamic range and local fluctuations of the sample. Meanwhile, DB-TTN achieves the lowest SI value for eastward velocity prediction, at only 0.239, indicating the lowest error dispersion and more concentrated and stable overall prediction. Considering RMSE, MAX, CC, and SI, it can be concluded that DB-TTN still exhibits the best overall error control capability in eastward velocity prediction, and its accuracy and stability are higher compared with other comparative methods. For northward velocity, compared with pure INS, RMSE decreased from 2.198 m / s to 0.839 m / s, a reduction of 61.83%. The maximum velocity (MAX) decreased from 2.819 m / s to 1.962 m / s, a reduction of 30.40%; and the dispersion index (SI) decreased from 0.113 to 0.102. These results further validate the effectiveness of the proposed method in horizontal velocity compensation. In the upward velocity prediction task, compared with a pure inertial navigation system (INS), the root mean square error (RMSE) decreased from 1.434 m / s to 0.287 m / s, a reduction of 79.99%; the maximum velocity (MAX) decreased from 2.450 m / s to 0.620 m / s, a reduction of 74.69%; and the dispersion index (SI) decreased from 6.999 to 2.157. The S-Transformer exhibited the worst overall prediction performance, particularly in the eastward and upward velocity components, where a negative correlation coefficient was observed, indicating a significant deviation between the predicted trend and the reference trend. AT-LSTM performed relatively well in upward velocity prediction, but its errors in the eastward and northward directions remained relatively large. CNN-LSTM and CNN-GRU showed relatively balanced performance, capable of suppressing velocity error divergence to some extent, but still lagged behind DB-TTN in most evaluation metrics. In conclusion, under a 60-second GNSS interruption scenario, DB-TTN achieved more stable and accurate 3D velocity prediction, demonstrating a significant advantage in horizontal velocity compensation.

[0061] Table 4. Comparison of position prediction performance of different methods during a 60-second GNSS interruption; ; Table 4 shows the RMSE, MAX, CC, and SI results of different methods for position prediction during a 60-second GNSS outage. As shown in Table 4, for eastward positions, DB-TTN's RMSE is 6.690 meters, a 95.67% reduction compared to INS's 154.381 meters. Meanwhile, MAX decreases from 317.163 meters to 16.877 meters, a 94.68% reduction. The SI for eastward positions decreases from 0.029 to 0.002, a 94.79% reduction. Furthermore, CC is close to 1, and the sample points are highly concentrated and closely distributed near the diagonal, indicating strong consistency between the predicted position and the reference value. Considering all evaluation metrics, it is clear that the proposed method achieves significantly higher accuracy and better stability in eastward position prediction, with overall performance significantly superior to other comparative methods. DB-TTN also achieves the best error control performance in northward position prediction. Compared to pure INS, its RMSE decreased from 64.040 meters to 14.600 meters, a reduction of 77.20%; MAX decreased from 124.759 meters to 31.382 meters, a reduction of 74.85%; and SI decreased from 0.024 to 0.009, a reduction of 63.98%. These results further validate the effectiveness of the proposed method in horizontal position compensation. In the northward position prediction task, DB-TTN also further highlights its advantages in suppressing vertical position errors. Compared to the pure inertial navigation system (PureINS), its root mean square error (RMSE) decreased from 33.661 meters to 0.624 meters, a reduction of 98.15%; maximum error (MAX) decreased from 73.441 meters to 1.843 meters, a reduction of 97.49%; and direction consistency index (SI) decreased from 2.445 to 0.057, a reduction of 97.69%. Meanwhile, the consistency coefficients (CC) for northward and celestial directions reached 1.00 and 0.98, respectively, indicating a high degree of consistency between the predicted results and the reference values. In contrast, the other four methods all exhibited certain limitations in position prediction tasks. Pure inertial navigation systems showed rapid error divergence in all three directions. Specifically, in the eastward direction, its root mean square error (RMSE) and maximum error (MAX) reached 154.381 meters and 317.163 meters, respectively, indicating that independent inertial mechanization methods cannot maintain stable position calculations without GNSS constraints. S-Transformer performed the worst overall, especially in the northward direction, with its RMSE and MAX reaching 139.154 meters and 301.074 meters, respectively, significantly inferior to other methods. AT-LSTM performed relatively well in upward position prediction, but the errors in the eastward and northward directions remained large, and the negative correlation coefficient in the eastward direction indicated a significant deviation between the predicted trend and the reference trend.CNN-LSTM and CNN-GRU offer relatively balanced performance and can suppress positional error divergence to some extent, but they are still significantly inferior to DB-TTN in most metrics. In particular, for eastward position prediction, although CNN-GRU has a high CC value, its RMSE, MAX, and SI values ​​are still significantly higher than DB-TTN, indicating that the proposed method has stronger overall error control capabilities.

[0062] Figure 1 The overall flowchart of the GNSS signal compensation method based on a dual-branch neural network provided by this invention is as follows: Figure 1 As shown, when GNSS signals are available, the GNSS / INS integrated navigation system operates normally and enters the training phase. During this phase, the DB-TTN model operates at an angular velocity... Comparison and posture Using this as input, train it to predict velocity increments. and position increment When GNSS signals are unavailable, the integrated navigation system degrades to independent INS mode, and the system enters the prediction phase. First, using angular velocity... Comparison and posture As input, estimate the velocity increment. and position increment Then, the last available velocity obtained during the GNSS availability period. and location As the initial value, and based on the recursive acquisition of the predicted velocity and predicted location Finally, the predicted speed will be... and predicted location They are directly used as compensation speeds. and compensation position And without the need for INS export speed and location Further integration.

[0063] ; In the formula, The predicted position at time k is obtained by accumulating the model or position increments. Let be the predicted position at time k. This is the initial position when the GNSS interruption begins. This represents the position increment within the i-th time interval.

[0064] Figure 2 This is a network architecture diagram of the DB-TTN model provided by the present invention. Figure 3 for Figure 2 The network architecture diagram of the residual module is as follows: Figure 2 and Figure 3 As shown, the TCN module uses five stacked residual blocks, and its inflation factor is... The values ​​were set to 1, 2, 4, 8, 16, and 64 respectively, with a kernel size of 3 for each value. Each residual block has a channel dimension of 64, allowing temporal features to be projected into a unified high-level representation space. A progressive expansion strategy expands the receptive field layer by layer, effectively capturing short-range temporal fluctuations and long-range local dependencies. BatchNorm and GELU activation functions are used to improve training stability and enhance nonlinear representation capabilities, while residual connections facilitate gradient propagation and preserve original temporal information. This hierarchical temporal encoding scheme enables the network to progressively extract high-level local dynamic features from raw inertial observations, providing more informative representations for subsequent Transformer modules to model global temporal dependencies. Subsequently, features processed by input embedding and position encoding are fed into the Transformer module to further model global temporal dependencies across time steps. The self-attention mechanism in the Transformer adaptively evaluates the correlation between different temporal locations through the interaction between query vectors, key vectors, and value vectors, highlighting temporal features more valuable for velocity and position increment prediction. Furthermore, the multi-head self-attention mechanism enhances the model's representational capabilities by modeling temporal dependencies in parallel across different subspaces. Two Transformer encoder layers are stacked in the network. Following the encoder, a lightweight regression decoder is introduced to map the encoded features, reducing model complexity while meeting the demands of real-time applications. This decoder omits computationally intensive components found in standard Transformers, such as multi-head attention mechanisms and additive normalization operations, retaining only two feedforward sublayers to perform pointwise regression. The velocity and position branches employ the same regression structure during the decoding phase and their outputs are fused in the final output phase. This design enables the model to generate incremental predictions corresponding to 3D velocity and 3D position increments with relatively low computational overhead.

[0065] Figures 4 to 9 The changes in velocity and position error curves over time are shown for different methods.

[0066] like Figure 4As shown, pure INS (red curve) represents the error obtained by independent inertial calculation using only IMU data. Due to the lack of GNSS observation data to constrain the inertial calculation, the error accumulates rapidly and continues to diverge over time. S-Transformer (purple curve) has relatively poor prediction performance, even more severe than pure INS. AT-LSTM (blue curve) diverges slowly, but the error suddenly increases after 40 seconds, indicating that the method fails over time. CNN-LSTM (orange curve) shows a similar degree of error divergence to INS. CNN-GRU (black curve) has more balanced performance and can suppress velocity error divergence to some extent, second only to DB-TTN. In contrast, DB-TTN (green curve) shows the slowest velocity error growth, indicating that the proposed method can more effectively suppress error divergence during GNSS interruptions and obtain more accurate velocity and position predictions.

[0067] like Figure 5 As shown, during the 60s GNSS interruption, the pure inertial navigation error gradually accumulated over time, indicating that the velocity solution continuously drifted after integration of the inertial device error. The compensation effects of different deep learning methods varied significantly. The S-Transformer exhibited the largest error fluctuation, indicating its weak stability in predicting long-term changes in motion during this period. AT-LSTM and CNN-GRU suppressed error divergence to some extent, but the errors remained relatively large. CNN-LSTM could reduce the pure inertial navigation error in some periods, but the overall fluctuation was significant. In contrast, the DB-TTN method maintained a smaller northbound velocity error for most of the GNSS interruption period. The curve change was relatively stable in the early stages; although the error increased at the end of the interruption, it still showed good overall stability. The results indicate that the dual-branch structure, combined with the TCN's ability to extract local temporal features and the Transformer's ability to model long-term dependencies, can effectively suppress the continuous accumulation of northbound velocity errors during GNSS interruptions, improving the stability and reliability of velocity prediction.

[0068] like Figure 6 As shown, pure inertial navigation errors exhibit a continuous accumulation trend. Although the S-Transformer can suppress error divergence to some extent, it still exhibits significant unidirectional drift. AT-LSTM, CNN-LSTM, and DB-TTN all effectively improve the upward velocity estimation, making the overall error curve closer to zero. The error fluctuation and accumulation trend of CNN-GRU are relatively obvious. DB-TTN can track changes in upward velocity well and maintain relatively stable error characteristics, demonstrating good error suppression ability and prediction stability.

[0069] like Figure 7As shown, the pure inertial navigation error exhibits a continuous divergence trend, reflecting the continuous accumulation of inertial device errors after integration. Different deep learning methods all possess some error compensation capabilities, but AT-LSTM, CNN-GRU, and S-Transformer still show significant unidirectional drift, with CNN-LSTM also exhibiting increased error in later stages. DB-TTN keeps the error curve generally near zero with relatively small fluctuations, indicating that this method can effectively suppress position error accumulation and possesses better prediction stability and position compensation capabilities.

[0070] like Figure 8 As shown, pure inertial navigation error accumulates continuously with GNSS interruption. All the comparative models can correct the inertial navigation position to some extent, but AT-LSTM, CNN-LSTM, CNN-GRU, and S-Transformer still exhibit varying degrees of error drift, with S-Transformer showing a particularly pronounced divergence trend. DB-TTN can keep the northward position error near zero, and the curve is relatively stable overall, indicating that this method can more effectively learn the temporal variation of position error, suppress error accumulation, and improve the stability and reliability of northward position prediction during GNSS interruption.

[0071] like Figure 9 As shown, the pure inertial navigation error exhibits a clear and continuous divergence trend, indicating that the vertical position is easily affected by the accumulation of errors in inertial devices. All deep learning models can significantly suppress the growth of the astronomical position error, but CNN-LSTM and S-Transformer still show some unidirectional drift, and the errors of AT-LSTM and CNN-GRU gradually deviate from zero. The DB-TTN error curve is generally closer to zero and changes more smoothly, indicating that this method can effectively mitigate the accumulation of astronomical position errors and improve the accuracy and stability of vertical position prediction during GNSS interruptions.

[0072] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A GNSS signal compensation method based on a dual-branch neural network, characterized in that, include: S1. A combined navigation system is constructed by integrating the inertial navigation system (INS) and the global navigation satellite system (GNSS). The system collects raw observation data output by the inertial measurement unit and attitude information calculated by the inertial navigation system based on the raw observation data in real time, and constructs an input feature sequence. S2. Monitor the availability of GNSS signals in real time. When GNSS signals are available, enter the training phase; when GNSS signals are interrupted, enter the prediction phase. S3. During the training phase, a dual-branch network containing a velocity branch and a position branch is constructed. The input feature sequence is used as input, and the velocity increment and position increment calculated by the integrated navigation system are used as supervision labels to train the dual-branch network. The velocity branch learns the mapping relationship between the input feature sequence and the velocity increment, and the position branch learns the mapping relationship between the input feature sequence and the position increment. S4. In the prediction stage, the input feature sequence is input into the dual-branch network trained in S3. The velocity branch outputs the predicted velocity increment, and the position branch outputs the predicted position increment. S5. Using the last combined navigation speed and position before the GNSS signal interruption as the initial values, the predicted speed increment and predicted position increment output by time step in S4 are accumulated respectively to obtain the predicted speed and predicted position, which are used as speed compensation and position compensation respectively, and the GNSS signal compensation is output.

2. The GNSS signal compensation method based on a dual-branch neural network according to claim 1, characterized in that, The raw observation data includes three-axis angular velocity and three-axis specific force output by the inertial measurement unit; attitude information includes heading angle, pitch angle, and roll angle, which are mechanically arranged and calculated by the inertial navigation system; the input feature sequence is a multi-dimensional time-series feature matrix composed of three-axis angular velocity, three-axis specific force, and attitude information. The input feature sequence is: ； ； ； ； In the formula, Indicates the time step index. express The input feature sequence fed into the dual-branch network at each time step is equivalent to the input feature sequence. exist Sampling point data at time t, express The three-axis angular velocities at time t. , , They represent Projection onto the X, Y, and Z axes; express The three-axis ratio at any given time, , , They represent Projection onto the X, Y, and Z axes; express Attitude information matrix at time step, express The heading angle at any moment, express The pitch angle at any moment, express The roll angle at any given moment.

3. The GNSS signal compensation method based on a dual-branch neural network according to claim 2, characterized in that, Both the velocity branch and the position branch are composed of a temporal convolutional network module and a Transformer module cascaded in sequence; The temporal convolutional network module is used to extract multi-scale local temporal features from the input feature sequence, and the Transformer module is used to model the global dependencies across time steps of the local temporal features output by the temporal convolutional network module.

4. The GNSS signal compensation method based on a dual-branch neural network according to claim 3, characterized in that, The temporal convolutional network module consists of multiple stacked residual blocks, each of which includes a dilated causal convolutional layer, a batch normalization layer, a GELU activation function layer, and residual connections. Dilated causal convolution extracts multi-scale local temporal features by setting different dilation factors for different residual blocks: ； In the formula, express Local temporal characteristics at any given moment Indicates the input feature sequence. Represents the convolution kernel. Indicates the expansion factor. This indicates that the expansion factor is... convolution kernel For the input feature sequence After performing dilated causal convolution, in The characteristic response value output at time t, Indicates the kernel size. For convolution kernel index, Represents the input feature sequence exist The value at; Batch normalization layers are used to stabilize feature distribution and accelerate model convergence; GELU activation function layers are used to introduce nonlinear transformations; residual connections are used to add the input and output of the residual block element by element.

5. The GNSS signal compensation method based on a dual-branch neural network according to claim 4, characterized in that, The Transformer module includes a multi-head self-attention mechanism, residual connections, layer normalization, and feedforward neural networks; Multi-head self-attention mechanism adaptively evaluates the correlation between different time positions through the interaction between query vector, key vector and value vector, and models time dependencies in parallel in different subspaces; residual connection is used to improve the information flow in deep network and alleviate gradient degradation; layer normalization is used to stabilize feature distribution and accelerate model convergence; feedforward neural network performs nonlinear transformation and feature enhancement at each time step; The output of the Transformer module in the velocity branch is mapped by the regression decoder to obtain the velocity increment prediction value, and the output of the Transformer module in the position branch is mapped by the regression decoder to obtain the position increment prediction value.

6. The GNSS signal compensation method based on a dual-branch neural network according to claim 5, characterized in that, The velocity branch and the position branch use the same model structure. The temporal convolutional network module of each branch includes 6 residual blocks, each with 64 channels. The kernel size of the dilated causal convolution in each branch is 3, and the dilation factor is set in sequence. The output feature dimension is 3. The hidden layer dimension of the Transformer in the velocity branch is smaller than that in the position branch. The hidden layer dimension of the Transformer in the velocity branch is 160, and the hidden layer dimension of the Transformer in the position branch is 320. The number of Transformer encoder layers in the velocity branch is less than that in the position branch. The velocity branch has 2 Transformer encoder layers, and the position branch has 3 Transformer encoder layers.

7. The GNSS signal compensation method based on a dual-branch neural network according to claim 6, characterized in that, Supervision labels during training for: ； ； ； ； ； In the formula, Indicates the speed increment. Indicates the position increment. express Motion acceleration in the navigation coordinate system at any time This represents the attitude transformation matrix from the vehicle coordinate system to the navigation coordinate system. Indicates intermediate calculation parameters. This represents the projection of the Earth's rotation angular rate onto the navigation coordinate system. express The angular velocity of the navigation coordinate system relative to the Earth coordinate system at any given time. express The velocity vector in the navigation coordinate system at any given moment. This represents the gravitational acceleration vector in the navigation coordinate system.

8. The GNSS signal compensation method based on a dual-branch neural network according to claim 7, characterized in that, During the training phase, the loss function is the sum of the mean squared error of the velocity increment and the mean squared error of the position increment: ； ； ； In the formula, Indicates the number of training samples. , They represent the first Predicted values ​​of velocity increment and position increment for each sample. , They are respectively , The corresponding supervision label.

9. The GNSS signal compensation method based on a dual-branch neural network according to claim 8, characterized in that, During the training phase, a sliding window scheme is used to segment the IMU continuous time series samples. Each input sample window contains... The observation data is obtained from consecutive time steps, and the adjacent windows slide forward. One time step; This corresponds to a 2-second time length at an IMU sampling frequency of 100 Hz, with a window sliding step of 100 time steps, corresponding to a 1-second sample update interval.

10. The GNSS signal compensation method based on a dual-branch neural network according to claim 9, characterized in that, During the prediction phase, when the duration of GNSS signal interruption exceeds the time length corresponding to a single input time window preset during the training phase, a recursive prediction strategy is adopted: the prediction output of the previous moment is used as a component of the input feature sequence of the next moment, and the velocity increment prediction value and position increment prediction value of subsequent moments are recursively generated until the GNSS signal is restored. The predicted speed is: ； The predicted location is: ； In the formula, Indicates the index of the predicted time. Indicates the first Prediction speed at each moment Indicates the first Predicted location at each moment, This represents the initial value for velocity prediction. This represents the initial value for location prediction.

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