Inertial measurement unit (IMU) heading angle increment prediction combination navigation method and system based on neural network

Abstract

This invention discloses a neural network-based IMU heading angle increment prediction integrated navigation method and system. First, three-axis accelerometer and three-axis gyroscope data are collected and a training set is constructed. Then, standardization processing is performed. Next, a physically guided heading angle increment prediction network is constructed, and a combined loss function is used to train and optimize the network. Then, N frames of IMU data from before the current moment are input into the trained network to obtain the predicted heading angle increment value for the current moment. Finally, the difference between the predicted heading angle increment value for the current moment and the heading angle increment obtained by integration from the inertial navigation system is constructed as a pseudo-measurement residual, which is used to correct the heading angle error in the extended Kalman filter measurement update step. This invention utilizes a neural network to perform high-precision prediction of the heading angle increment in IMU data and integrates the prediction result as a pseudo-measurement into the extended Kalman filter framework to maintain and improve the positioning and attitude determination accuracy of the integrated navigation system during satellite lock-up periods.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation and integrated navigation technology, and more specifically, to a method for predicting the heading angle increment of an inertial measurement unit (IMU) based on a physics-informed neural network and its application in an inertial / satellite integrated navigation system. In particular, it relates to an IMU heading angle increment prediction integrated navigation method and system based on a neural network. Background Technology

[0002] Tight / loose combinations of Global Navigation Satellite Systems (GNSS) and Inertial Navigation Systems (INS) are widely used for precision navigation in vehicles, drones, and robots. In open environments, GNSS can continuously provide high-precision position and velocity measurements, effectively suppressing the cumulative errors of INS. However, in scenarios such as tunnels, underground passages, and dense urban buildings, GNSS signals are frequently interrupted, and the inertial navigation system can only maintain navigation output by relying on its own integral calculations.

[0003] The random walk, bias instability, and scaling factor error of a gyroscope accumulate rapidly over time without external measurement constraints, leading to divergence in attitude errors, especially heading errors. In vehicle driving scenarios, the impact of heading error on trajectory accuracy is particularly significant: even small heading deviations can produce significant lateral position deviations after integration over a period of time.

[0004] Existing methods for heading maintenance in GNSS denied scenarios mainly fall into the following categories: (1) Zero Speed ​​Correction (ZUPT) method: It is only effective when the vehicle is stationary and cannot deal with the heading drift problem when the vehicle is moving; (2) Non-holonomic constraint (NHC) method: It utilizes the kinematic constraints of the vehicle’s lateral and vertical velocities being close to zero, which has a certain effect on suppressing speed errors, but cannot directly constrain heading angle drift; (3) Odometer-assisted method: Odometers can provide forward velocity information and can improve horizontal position accuracy when used in conjunction with NHC, but they still cannot effectively correct heading angle deviation; (4) Map matching method: relies on high-precision maps and point clouds or image sensors, the system is complex and costly; (5) Traditional machine learning methods, such as support vector machines (SVM) and random forests, are difficult to effectively capture the complex dynamic features of IMU time series and have limited generalization ability; (6) Deep learning-based methods (such as LSTM, TCN, etc.): Existing works mostly predict velocity or displacement in an end-to-end manner, lack explicit utilization of physical priors, have weak physical interpretability of network output, and are not robust enough when data distribution drifts.

[0005] In summary, existing technologies have significant limitations in maintaining heading angle under GNSS signal obstruction conditions. Summary of the Invention

[0006] To overcome the shortcomings of the existing technology, this invention proposes an IMU heading angle increment prediction integrated navigation method based on a physically guided neural network. This method predicts short-term heading angle increments from IMU data using a specially designed neural network (HeadingDeltaNet), and embeds the predicted values ​​as pseudo-quantity measurements into an extended Kalman filter (EKF) integrated navigation framework to perform real-time correction of heading angle drift during periods of GNSS signal loss.

[0007] To achieve the above objectives, a first aspect of the present invention provides a neural network-based IMU heading angle increment prediction integrated navigation method, comprising: Collect data from a three-axis accelerometer and a three-axis gyroscope, extract the real heading angle increment at the corresponding moment from the reference navigation truth value as training labels, and construct a training set; Standardized IMU time series data were obtained based on the training set; A physically guided heading angle increment prediction network is constructed, which adopts a dual-branch architecture. The network is trained and optimized using standardized IMU time series data as input and heading angle increment as the prediction target. Using N frames of IMU data from before the current moment as input, after standardization preprocessing, the data is input into the trained network to obtain the predicted value of the heading angle increment at the current moment; The difference between the predicted heading angle increment at the current moment and the heading angle increment obtained by integration by the inertial navigation system is constructed as a pseudo-measurement residual, which is used to correct the heading angle error in the extended Kalman filter measurement update step.

[0008] In one implementation, standardized IMU time-series data is obtained based on the training set, including: Based on the mean and standard deviation of each IMU channel in the training set, the input data is standardized with zero mean and unit variance, and the predicted target heading angle increment is scaled up to obtain standardized IMU time series data.

[0009] In one implementation, the physics-guided heading angle increment prediction network includes a physics branch, a feature branch, a gyroscope zero-bias estimation head, a residual correction head, and an output module. The physics branch obtains the physical baseline prediction value of the heading angle increment based on three-axis gyroscope data. The feature branch acquires a global temporal feature representation using a combination of convolution and a Pre-LN Transformer encoder. The gyroscope zero-bias estimation head takes the time mean of the Transformer sequence features as input, estimates the current zero bias of the gyroscope's z-axis through a fully connected network, and performs zero-bias correction on the physical baseline prediction to obtain the zero-bias correction amount. The residual correction head takes the temporal feature representation, the physical baseline prediction value, and the original gyroscope z-axis angular velocity as joint input conditions, outputs a nonlinear residual correction amount through a fully connected network, and the output module obtains the heading angle increment prediction value based on the physical baseline prediction value, the zero-bias correction amount, and the nonlinear residual correction amount.

[0010] In one implementation, the physical branch is used to obtain a physical baseline prediction of the heading angle increment based on three-axis gyroscope data, including: Extract the z-axis angular velocity of the gyroscope from the last frame of the input sequence, restore it to the original physical space, multiply it by the sampling time step, and use it as the physical baseline prediction for the heading angle increment.

[0011] In one implementation, the feature branch is used to obtain a global temporal feature representation by combining convolution with a Pre-LN Transformer encoder, including: The original IMU data is concatenated with its first-order difference features along the channel dimension. Convolution operations are performed on the spliced ​​features using convolution stems; The convolutional features are encoded at learnable positions and then encoded using a Pre-LN Transformer encoder to obtain sequence features. Attention pooling is applied to the sequence features to obtain a global temporal feature representation.

[0012] In one implementation, the convolutional stem in the feature branch includes two one-dimensional convolutional networks, and the Pre-LN Transformer encoder includes at least two Transformer encoding layers, each layer employing a Pre-LN normalization structure, a multi-head self-attention mechanism, and a feedforward network; the attention pooling uses a learnable query vector to perform multi-head attention aggregation on the sequence features, outputting a fixed-dimensional global sequence representation.

[0013] In one implementation, the combined loss function includes smoothed L1 loss, Signed-log spatial mean square error, and relative error constraint.

[0014] In one implementation, the heading angle error is corrected in the extended Kalman filter measurement update step, including: When satellite navigation signals are normal, the extended Kalman filter uses GNSS position and velocity measurements to update the inertial navigation error state using standard measurements. When satellite signal obstruction is detected, it automatically switches to neural network-assisted mode, replacing GNSS measurements with pseudo-measurements of the heading angle increment predicted by the network, and continuously constrains and corrects the heading angle error within the EKF framework.

[0015] Based on the same inventive concept, a second aspect of this invention provides a neural network-based IMU heading angle incremental prediction integrated navigation system, comprising: The data acquisition module is used to collect data from the three-axis accelerometer and the three-axis gyroscope, extract the real heading angle increment at the corresponding moment from the reference navigation truth value as training labels, and construct a training set; The standardization processing module is used to obtain standardized IMU time series data based on the training set; The network training module is used to construct a physically guided heading angle increment prediction network. The physically guided heading angle increment prediction network adopts a dual-branch architecture. It takes standardized IMU time series data as input, heading angle increment as prediction target, and uses a combined loss function to train and optimize the network. The inference module takes N frames of IMU data from before the current time as input, performs standardized preprocessing, and then inputs it into the trained network to obtain the predicted value of the heading angle increment at the current time. The fusion module is used to construct a pseudo-measurement residual by the difference between the predicted heading angle increment at the current moment and the heading angle increment obtained by integration by the inertial navigation system, and to correct the heading angle error in the extended Kalman filter measurement update step.

[0016] Based on the same inventive concept, a third aspect of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the neural network-based IMU heading angle incremental prediction integrated navigation method described in the first aspect.

[0017] Compared with the prior art, the advantages and beneficial technical effects of the present invention are as follows: This invention discloses a neural network-based IMU heading angle increment prediction integrated navigation method. Using six-axis IMU data as input, it employs a dual-branch architecture: the physical branch explicitly encodes kinematic priors using the gyroscope z-axis angular velocity integral as a baseline; the feature branch extracts local dynamic features using convolutional stems, captures long-range temporal dependencies using a Pre-LN Transformer encoder, obtains a global sequence representation through learnable attention pooling, and outputs gyroscope zero-bias correction and nonlinear residual correction respectively; the final prediction is the baseline minus the zero-bias correction plus the residual correction. The difference between the current heading angle increment prediction and the heading angle increment obtained by the inertial navigation system integration is constructed as a pseudo-measurement residual. This residual is used to correct the heading angle error in the extended Kalman filter measurement update step, thereby maintaining and improving the positioning and attitude determination accuracy of the integrated navigation system during satellite lock-up periods.

[0018] Furthermore, during satellite signal masking, the network-predicted heading angle increment is embedded as a pseudo-quantity measurement into the EKF and fused with non-integrity constraints and odometer measurements to continuously suppress heading angle drift, effectively improving the positioning continuity and accuracy of the integrated navigation system in complex masking scenarios. Attached Figure Description

[0019] 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.

[0020] Figure 1 A flowchart of an IMU heading angle incremental prediction integrated navigation method based on neural networks is provided in this embodiment of the invention; Figure 2 This is a diagram of the HeadingDeltaNet network architecture in an embodiment of the present invention, showing the connection relationships between the physical branch, the feature branch (Conv Stem, Transformer encoder, attention pooling), the zero-bias estimation head, and the residual correction head. Figure 3 This is a comparison diagram of heading angle error in a tunnel scenario experiment in this embodiment of the invention, showing the comparison of heading angle error with and without neural network assistance; Figure 4 This is a comparison diagram of experimental trajectories in a tunnel scenario in an embodiment of the present invention, showing the positioning trajectory and error comparison under conditions of with and without neural network heading assistance; Figure 5 This is an overall framework diagram of the integrated navigation system in an embodiment of the present invention, showing the INS / GNSS / NN multi-source fusion EKF structure and the data flow between each module. Detailed Implementation

[0021] This invention addresses the navigation continuity problem of vehicle-mounted / airborne platforms in satellite signal obstruction scenarios (such as tunnels, underground parking lots, and areas with dense elevated bridges). It utilizes neural networks to perform high-precision prediction of heading angle increments in IMU data and integrates the prediction results as pseudo-quantity measurements into the extended Kalman filter (EKF) framework to maintain and improve the positioning and attitude determination accuracy of the integrated navigation system during satellite lock-up periods.

[0022] The core technical points of this invention include: (a) Physically Guided Heading Angle Increment Prediction Network (HeadingDeltaNet) The network takes IMU six-axis data (three-axis acceleration and three-axis gyroscope) in a 1-second window (25 frames, 25Hz sampling) as input and predicts the heading angle increment Δψ within 0.04 seconds of the current time, with a prediction range of 0.0001~0.01 rad.

[0023] The network adopts a two-branch architecture of "physical prior + residual learning": the physical branch uses the gyroscope z-axis angular velocity of the last frame multiplied by the time step as the baseline estimate (delta_psi_baseline = omega_z x dt), explicitly encoding the kinematic prior; the feature branch extracts local temporal features using convolutional stems (Conv Stem), combines a Pre-LN Transformer encoder (2 layers) to capture long-range temporal dependencies, and obtains the global sequence representation through learnable attention pooling; the gyroscope bias estimation head estimates the gyroscope z-axis bias from the entire sequence and corrects the baseline prediction; the residual correction head combines the global features, the baseline prediction value, and the original angular velocity to output a nonlinear residual correction value; the final output is the predicted value of the heading angle increment.

[0024] (ii) Combined loss function for small accuracy To address the characteristic that the heading angle increment spans approximately two orders of magnitude (0.0001~0.01 rad), a combined loss function is designed, comprising the following three components: Huber Loss (robust to outliers); Signed-log space MSE (balancing the accuracy of large and small values ​​on a logarithmic scale); and relative error constraint (explicitly requiring the prediction relative error in the small value region to meet the constraint).

[0025] (III) Fusion of heading angle increment pseudo-measurements in the EKF framework When satellite signals are available, EKF uses GNSS position and velocity measurements to correct the INS error status; when GNSS signals are missing and the system enters tunnel mode, the system uses the heading angle increment Δψ_pred predicted by the neural network as a pseudo-measurement to constrain the heading angle error δψ in the EKF measurement update step to prevent heading drift divergence.

[0026] (iv) Multi-constraint joint assisted navigation strategy By integrating neural network heading constraints with traditional methods such as non-integrity constraints (NHC), zero-speed correction (ZUPT), and odometry assistance within the EKF framework, complementary multi-source constraints are achieved, further improving navigation continuity and accuracy in complex scenarios.

[0027] Example 1 This embodiment provides a neural network-based IMU heading angle incremental prediction integrated navigation method. Please refer to [link to relevant documentation]. Figure 1 ,include: S1: Collect data from the three-axis accelerometer and the three-axis gyroscope, extract the real heading angle increment at the corresponding moment from the reference navigation truth value as training labels, and construct a training set.

[0028] Specifically, S1 is the data acquisition step. In practice, the inertial measurement unit (IMU) can collect data from the three-axis accelerometer and three-axis gyroscope at a fixed sampling frequency. The IMU time series samples with a length of N frames are constructed in a sliding window manner. Data when stationary is removed, and the real heading angle increment Δψ at the corresponding moment is extracted from the reference navigation truth value as a training label.

[0029] In specific implementation, during the data acquisition step, the IMU sampling frequency is 25Hz, the sliding window length is 25 frames corresponding to a 1-second time window, the prediction target is the heading angle increment within 0.04 seconds at the end of the window, and the prediction range covers the order of 0.0001 to 0.01 rad; the six channels of the IMU data are arranged in the order of [ax, ay, az, gx, gy, gz], the gyroscope z-axis channel index is 5, and the physical baseline calculation in the physical branch uses this channel data.

[0030] S2: Obtain standardized IMU time series data based on the training set.

[0031] Specifically, S2 is a standardized processing step, which can be implemented in the following way: Based on the mean and standard deviation of each IMU channel in the training set, the input data is standardized with zero mean and unit variance, and the predicted target heading angle increment is scaled up to obtain standardized IMU time series data.

[0032] S3: Construct a physically guided heading angle increment prediction network, which adopts a dual-branch architecture; using standardized IMU time series data as input and heading angle increment as the prediction target, the network is trained and optimized using a combined loss function.

[0033] Specifically, S3 is the network training step. First, a physically guided heading angle increment prediction network is built, and then a combined loss function is used to train and optimize the network.

[0034] Figure 2 This is a diagram of the HeadingDeltaNet network architecture in an embodiment of the present invention.

[0035] The physics-guided heading angle increment prediction network includes a physics branch, a feature branch, a gyroscope zero-bias estimation head, a residual correction head, and an output module. The physics branch obtains the physical baseline prediction value of the heading angle increment based on three-axis gyroscope data. The feature branch acquires a global temporal feature representation using a combination of convolution and a Pre-LN Transformer encoder. The gyroscope zero-bias estimation head takes the time mean of the Transformer sequence features as input, estimates the current zero bias of the gyroscope's z-axis through a fully connected network, and corrects the zero bias of the physical baseline prediction to obtain the zero-bias correction amount. The residual correction head takes the temporal feature representation, the physical baseline prediction value, and the original gyroscope z-axis angular velocity as joint input conditions, and outputs a nonlinear residual correction amount through a fully connected network. The output module obtains the heading angle increment prediction value based on the physical baseline prediction value, the zero-bias correction amount, and the nonlinear residual correction amount.

[0036] Specifically, the processing of the physics branch includes: Extract the z-axis angular velocity of the gyroscope from the last frame of the input sequence, restore it to the original physical space, multiply it by the sampling time step, and use it as the physical baseline prediction for the heading angle increment.

[0037] When the physics branch restores the gyroscope z-axis data from the normalized space to the original physical space, it uses the mean gz_mean and standard deviation gz_std of that channel, which are obtained only from the training set statistics, for inverse normalization to ensure consistency between the inference and training phases. The normalized parameters are saved together with the model weights and loaded for use when deploying inference.

[0038] The feature branch concatenates the original IMU data with its first-order difference features along the channel dimension, and then sequentially passes it through a convolutional stem (ConvStem), learnable positional encoding, a Pre-LN Transformer encoder, and learnable attention pooling to extract global temporal feature representations. The specific processing steps include: The original IMU data is concatenated with its first-order difference features along the channel dimension. Convolution operations are performed on the spliced ​​features using convolution stems; The convolutional features are encoded at learnable positions and then encoded using a Pre-LN Transformer encoder to obtain sequence features. Attention pooling is applied to the sequence features to obtain a global temporal feature representation.

[0039] In the specific implementation process, the convolutional stem in the feature branch includes two one-dimensional convolutional networks. The first convolutional kernel has a size of 5, and the second convolutional kernel has a size of 3. Both use the GELU activation function and employ the same padding method to keep the sequence length unchanged. The Pre-LN Transformer encoder contains at least two Transformer encoding layers. Each layer adopts a Pre-LN normalization structure, a multi-head self-attention mechanism, and a feedforward network. Attention pooling uses a learnable query vector to perform multi-head attention aggregation on the sequence features and outputs a fixed-dimensional global sequence representation.

[0040] The gyroscope bias estimation head (Bias Head) takes the vector (shape B×64) of the sequence features output by the Pre-LN Transformer encoder of the feature branch, which is averaged along the time dimension, as input. It then uses a fully connected network to estimate the current bias of the gyroscope's z-axis and corrects the physical baseline prediction for bias. The aforementioned time-averaged vector is a statistical summary of the global temporal feature representation of the feature branch. It is derived from the same Transformer output sequence as the pooling vector from the attention pooling output, but uses simple averaging instead of attention-weighted aggregation to obtain a more stable bias estimation input.

[0041] The output module obtains the heading angle increment prediction value based on the physical baseline prediction value, the zero bias correction, and the nonlinear residual correction. Specifically: Δψ_pred = baseline bias_correction + residual, Δψ_pred is the predicted value of the heading angle increment, baseline is the predicted value of the physical baseline, bias_correction is the zero bias correction, and residual is the nonlinear residual correction.

[0042] In particular, the weights and biases of the last layer of both the Bias Head and Residual Head are initialized to zero to ensure that the network training starts from the physical baseline in the early stages.

[0043] The combined loss function during training includes smoothed L1 loss, Signed-log space mean squared error, and relative error constraint.

[0044] Specifically, the combined loss includes the following three parts: (1) Huber loss (smoothing L1 loss): The prediction residual is penalized twice within the threshold β and linearly penalized when it exceeds the threshold, which improves the robustness to abnormal samples; (2) Signed-log spatial mean square error: The mean square error is calculated after applying a signed logarithmic transformation to the predicted value and the target value respectively. The calculation method is signed_log(x,ε)=sign(x)×log(1+|x| / ε), so that the loss balances the training accuracy of large and small values ​​on the logarithmic scale. In the formula, x is the predicted value or target value (i.e. the predicted value of the heading angle increment output by the network or the corresponding real heading angle increment target, the unit is the dimensionless value after scale magnification), sign(x) is the sign function of x (takes +1 when x>0, -1 when x<0, and 0 when x=0), ε is a smoothing constant to prevent division by zero. In this embodiment, ε=0.1 is used to control the sensitivity of the logarithmic transformation so that the gradient signal in the small value region is not overwhelmed by the large value.

[0045] (3) Relative error constraint: Calculate the mean square expectation of the ratio of the difference between the predicted value and the target value to the absolute value of the target value, and explicitly constrain the relative prediction error in the small value region.

[0046] The total loss is a weighted sum of the above three items, with the weighting coefficients determined by the performance of the validation set.

[0047] In the specific implementation process, the network training steps adopt the AdamW optimizer and a learning rate scheduling strategy of Warmup plus cosine annealing: in the early stage of training, a linear warm-up phase is performed to gradually increase the learning rate from zero to the initial value, and then cosine annealing is performed to the minimum value; at the same time, an early stopping mechanism is set up, with the validation set loss as the monitoring indicator. When the validation set loss has not improved for several consecutive rounds, training is stopped, and the model weights corresponding to the lowest validation set loss are saved as the final model.

[0048] S4: Using N frames of IMU data from before the current moment as input, after standardization preprocessing, input into the trained network to obtain the predicted value of the heading angle increment at the current moment.

[0049] Specifically, S4 is the reasoning step.

[0050] S5: Construct a pseudo-measurement residual by the difference between the predicted heading angle increment at the current moment and the heading angle increment obtained by integration of the inertial navigation system, and correct the heading angle error in the extended Kalman filter measurement update step.

[0051] Specifically, S5 is the EKF fusion step, which can be implemented in the following way: When satellite navigation signals are normal, the extended Kalman filter uses GNSS position and velocity measurements to update the inertial navigation error state using standard measurements. When satellite signal obstruction is detected, it automatically switches to neural network-assisted mode, replacing GNSS measurements with pseudo-measurements of the heading angle increment predicted by the network, and continuously constrains and corrects the heading angle error within the EKF framework.

[0052] Among them, the neural network-assisted mode, non-holonomic constraints (NHC), zero-speed correction (ZUPT), and odometer speed measurement are jointly integrated within the same EKF framework to achieve complementary multi-source constraints. The non-holonomic constraints utilize vehicle kinematics to constrain lateral and vertical speeds to zero, while the odometer measurement provides forward speed assistance. The three types of constraints, together with the heading angle pseudo-measurement, jointly suppress the accumulation of navigation errors during satellite signal obstruction.

[0053] The integrated navigation method provided by this invention can be applied to mobile platforms such as vehicles, drones, rail transit, and robots equipped with IMU and satellite navigation receivers. In scenarios where satellite signals are frequently interrupted, such as tunnels, underground parking lots, dense urban buildings, and overpasses, it provides continuous and reliable heading angle constraints for the integrated navigation system, maintaining the positioning and attitude determination accuracy of the navigation system during satellite lock-up periods.

[0054] Example 2 Based on the same inventive concept, this embodiment discloses a neural network-based IMU heading angle incremental prediction integrated navigation system, comprising: The data acquisition module is used to collect data from the three-axis accelerometer and the three-axis gyroscope, extract the real heading angle increment at the corresponding moment from the reference navigation truth value as training labels, and construct a training set; The standardization processing module is used to obtain standardized IMU time series data based on the training set; The network training module is used to construct a physically guided heading angle increment prediction network. The physically guided heading angle increment prediction network adopts a dual-branch architecture. It takes standardized IMU time series data as input, heading angle increment as prediction target, and uses a combined loss function to train and optimize the network. The inference module takes N frames of IMU data from before the current time as input, performs standardized preprocessing, and then inputs it into the trained network to obtain the predicted value of the heading angle increment at the current time. The fusion module is used to construct a pseudo-measurement residual by the difference between the predicted heading angle increment at the current moment and the heading angle increment obtained by integration by the inertial navigation system, and to correct the heading angle error in the extended Kalman filter measurement update step.

[0055] The system of the present invention will now be described in detail: I. System Overall Framework like Figure 5 As shown, the integrated navigation system of this invention consists of the following main modules: an IMU data acquisition and preprocessing module, a GNSS data receiving module, an odometry data acquisition module, a HeadingDeltaNet heading angle incremental prediction module, an Extended Kalman Filter (EKF) fusion module, and a navigation result output module. The IMU acquires data from the three-axis accelerometer and three-axis gyroscope at a sampling frequency of 25Hz. The GNSS module provides position and velocity measurements. The odometry provides forward velocity measurements. When GNSS signal is normal, the EKF uses GNSS measurements for updates; during GNSS signal obstruction, the system automatically switches to a neural network-assisted mode, using the HeadingDeltaNet prediction output as a pseudo-heading measurement, and continuously maintaining navigation accuracy by combining NHC constraints and odometry constraints.

[0056] II. Data Preparation The IMU collects six-axis data at a sampling rate of 25Hz, with the channel order as follows: [ax, ay, az, gx, gy, gz], where ax, ay, and az represent three-axis accelerations (m / s²), and gx, gy, and gz represent three-axis angular velocities (rad / s). The z-axis channel index of the gyroscope is 5. Training samples are constructed using a sliding window approach: each sample uses IMU six-axis data within a time window of length 25 (corresponding to 1 epoch) as input features, with a shape of (6, 25); the true heading angle increment Δψ within the last 0.04 seconds of the corresponding time window is used as the prediction target, calculated from the reference navigation ground truth. All samples are divided into training, validation, and test sets in a ratio of 80% / 10% / 10%. Standardized parameters are calculated only based on the training set, and these parameters are saved to a normalized file for use during inference.

[0057] III. HeadingDeltaNet Network Design like Figure 2 As shown, HeadingDeltaNet consists of the following components: (1) Input preprocessing: For the standardized input x (shape B×6×25), the first-order difference feature diff1 is calculated (zero padding is applied to the beginning), and concatenated with the original feature in the channel dimension to obtain 12-channel input features (shape B×12×25). The first-order difference feature explicitly encodes the dynamic rate of change of the IMU signal, which helps the network capture the angular velocity changes of fast motion.

[0058] (2) Physical branch: Extract the last frame of gyroscope z-axis data, restore it to the original physical space through normalization parameters, obtain the angular velocity (unit: rad / s), and calculate the physical baseline prediction value: baseline_scaled = gz_last_raw ×dt × output_scale, where dt is the IMU sampling time step, and at a sampling rate of 25Hz, dt = 1 / 25 = 0.04s; output_scale is the output scale amplification factor, with a value of 1000. Its function is to scale the heading angle increment (original magnitude is 0.0001~0.01 rad) proportionally to the numerical range of 0.1~10, so that the gradient of the loss function of the network during training is more stable and the gradient vanishes due to the target value being too small. Finally, the original physical unit (rad) can be restored by dividing the network output by output_scale during inference.

[0059] (3) Convolution Stem: Two one-dimensional convolutions. The kernel size of the first convolution is 5 (padding=2), and the kernel size of the second convolution is 3 (padding=1). Both layers use the GELU activation function, and the number of output channels is d_model=64. The sequence length remains unchanged at 25.

[0060] (4) Pre-LN Transformer encoder: It contains two Transformer coding layers, each containing a multi-head self-attention (4 heads), a feedforward network and a Pre-LN normalization structure, using GELU activation and Dropout (p=0.1).

[0061] (5) Learnable attention pooling: Multi-head attention aggregation of sequence features is performed using the learnable query vector (pool_query, shape 1×1×64) to obtain the global sequence representation pooled (shape B×64).

[0062] (6) Gyroscope Bias Head: The time mean of the Transformer sequence features, seq_mean, is used as input. The bias is estimated by two fully connected layers (64→32→1, GELU activation) and the bias correction is calculated as: bias_correction = bias_est × dt × output_scale. The weights and biases of the last layer of the Bias Head are initialized to zero.

[0063] (7) Residual Head: The pooled (64-dimensional), baseline_scaled, and gz_last_raw layers are concatenated to form a 66-dimensional conditional input. The residual is output through a three-layer fully connected layer (66→64→32→1, GELU activation, including Dropout). The weights and biases of the last layer of the Residual Head are initialized to zero.

[0064] (8) Final output: output_scaled = baseline_scaled bias_correction +residual, during inference, divide by output_scale to restore physical units.

[0065] IV. Loss Function Design This invention employs a three-factor combination loss: Huber Loss (smoothing L1 loss, β=1.0) robust to outliers; Signed-log space MSE (using the transformation signed_log(x,ε)=sign(x)×log(1+|x| / ε) to balance the accuracy of large values ​​on a logarithmic scale); and a relative error constraint to explicitly constrain small relative errors. The total loss is: L_total = L_huber + 0.3×L_log + 0.2×L_rel.

[0066] V. Training Strategies AdamW optimizer was used (initial learning rate 3×10). -4 Weight decay 1×10 -4 The learning rate is scheduled using Warmup + Cosine Annealing (linear warmup for the first 10 epochs, followed by cosine annealing), with a maximum training duration of 600 epochs. Early stopping is performed using validation set loss as the monitoring metric (patience=60), and the model weights with the lowest validation set loss are saved.

[0067] VI. EKF Integration and Tunnel-Aided Navigation The EKF state vector contains 16 error states: position error, velocity error, attitude error, gyroscope bias, and accelerometer bias. Regular measurement updates are performed when GNSS is available. When the system detects a GNSS signal interruption (triggered by a tunneling period), the system uses IMU data from one second prior to the current time as input, performs standardized preprocessing, and then inputs it into HeadingDeltaNet to obtain the predicted heading angle increment Δψ_pred. The difference between this and the heading angle increment obtained from INS integration is used as the pseudo-measurement residual, and the measurement equation is constructed as: z_heading = Δψ_pred Δψ_INS = H_heading × δx + v_heading, where EKF performs measurement updates to correct heading angle errors and suppress heading drift. Here, Δψ_pred is the predicted heading angle increment output by the HeadingDeltaNet network (in rad); Δψ_INS is the heading angle increment obtained by the inertial navigation system through gyroscope integration within the same time step (in rad); z_heading is the difference between the two, i.e., the pseudo-measurement residual, used to reflect the deviation between the INS heading integral and the neural network prediction; H_heading is the measurement matrix, a 1×16 row vector, with values ​​only appearing at the component positions corresponding to the heading angle error (column 9, corresponding to the state direction). The heading error δψ in the vector is 1, and all other elements are 0. Its function is to extract the heading angle error component from the 16-dimensional error state vector. δx is the 16-dimensional error state vector of EKF, which includes position error (3-dimensional), velocity error (3-dimensional), attitude error (3-dimensional, where the 9th dimension is the heading angle error δψ), gyroscope bias (3-dimensional), accelerometer bias (3-dimensional), and odometry error factor (1-dimensional). v_heading is the heading angle pseudo-measurement noise, which follows a zero-mean Gaussian distribution. Its variance is set according to the root mean square error (RMSE) of HeadingDeltaNet's prediction on the validation set to reflect the uncertainty of the network prediction. Simultaneously, NHC constraints (lateral and vertical velocities close to zero) and odometry velocity measurements are continuously updated as additional measurements, complementing the neural network heading constraints and comprehensively improving navigation performance in tunnel scenarios.

[0068] VII. Experimental Results The experimental platform uses a vehicle-mounted GNSS system equipped with an IMU and odometer. The test route includes complex road conditions such as tree-lined roads and urban canyons, with GNSS obstruction lasting approximately 120 seconds. Using a high-precision post-processed reference trajectory as the ground truth, the following schemes are compared: Scheme 1 (INS / GNSS / NHC / odometer, without neural network assistance) and Scheme 2 (this invention, with HeadingDeltaNet assistance).

[0069] like Figure 3 As shown, during the 120-second GNSS obstruction period, the cumulative heading angle error of Scheme 1 was 9.42°, resulting in a trajectory deviation of 18.14m; the heading angle error of Scheme 2 of the present invention was controlled within 1.68°, and the horizontal error was reduced to 1.40m, which is about 92.28% higher than that of Scheme 1.

[0070] Figure 4 The diagram shows a comparison of experimental trajectories in a tunnel scenario according to an embodiment of the present invention. It can be seen that the trajectory obtained by Scheme 2 of the present invention is closer to the actual trajectory.

[0071] In summary, the IMU heading angle incremental prediction integrated navigation method proposed in this invention, based on a physical guidance neural network, effectively suppresses the accumulation of heading angle errors in GNSS signal obstruction scenarios, significantly improves the positioning continuity and accuracy of the integrated navigation system, and has strong engineering application value.

[0072] Since the system in Embodiment 2 of this invention is the same system used in the neural network-based IMU heading angle incremental prediction integrated navigation method in Embodiment 1, those skilled in the art can understand the specific structure and variations of this system based on the method described in Embodiment 1 of this invention, and therefore will not be repeated here. All systems used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0073] Example 3 Based on the same inventive concept, the present invention also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in Embodiment 1.

[0074] Since the computer device described in Embodiment 3 of this invention is the electronic device used to implement the IMU heading angle incremental prediction integrated navigation method based on neural networks in Embodiment 1 of this invention, those skilled in the art can understand the specific structure and modifications of this electronic device based on the method described in Embodiment 1 of this invention, and therefore will not be described again here. All electronic devices used in the method of Embodiment 1 of this invention fall within the scope of protection of this invention.

[0075] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0076] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1A device that provides the functions specified in one or more boxes.

[0077] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various modifications and variations to the embodiments of the invention without departing from the spirit and scope of the invention. Thus, if these modifications and variations of the embodiments of the invention fall within the scope of the claims of the invention and their equivalents, the invention also intends to include these modifications and variations.

Claims

1. A neural network-based IMU heading angle incremental prediction integrated navigation method, characterized in that, include: Collect data from a three-axis accelerometer and a three-axis gyroscope, extract the real heading angle increment at the corresponding moment from the reference navigation truth value as training labels, and construct a training set; Standardized IMU time series data were obtained based on the training set; A physically guided heading angle increment prediction network is constructed, which adopts a dual-branch architecture. The network is trained and optimized using standardized IMU time series data as input and heading angle increment as the prediction target. Using N frames of IMU data from before the current moment as input, after standardization preprocessing, the data is input into the trained network to obtain the predicted value of the heading angle increment at the current moment; The difference between the predicted heading angle increment at the current moment and the heading angle increment obtained by integration by the inertial navigation system is constructed as a pseudo-measurement residual, which is used to correct the heading angle error in the extended Kalman filter measurement update step.

2. The IMU heading angle incremental prediction integrated navigation method based on neural networks as described in claim 1, characterized in that, Standardized IMU time-series data were obtained based on the training set, including: Based on the mean and standard deviation of each IMU channel in the training set, the input data is standardized with zero mean and unit variance, and the predicted target heading angle increment is scaled up to obtain standardized IMU time series data.

3. The IMU heading angle incremental prediction integrated navigation method based on neural networks as described in claim 1, characterized in that, The physics-guided heading angle increment prediction network includes a physics branch, a feature branch, a gyroscope zero-bias estimation head, a residual correction head, and an output module. The physics branch obtains the physical baseline prediction value of the heading angle increment based on three-axis gyroscope data. The feature branch acquires a global temporal feature representation using a combination of convolution and a Pre-LN Transformer encoder. The gyroscope zero-bias estimation head takes the time mean of the Transformer sequence features as input, estimates the current zero bias of the gyroscope's z-axis through a fully connected network, and corrects the zero bias of the physical baseline prediction to obtain the zero-bias correction amount. The residual correction head takes the temporal feature representation, the physical baseline prediction value, and the original gyroscope z-axis angular velocity as joint input conditions, and outputs a nonlinear residual correction amount through a fully connected network. The output module obtains the heading angle increment prediction value based on the physical baseline prediction value, the zero-bias correction amount, and the nonlinear residual correction amount.

4. The IMU heading angle incremental prediction integrated navigation method based on neural networks as described in claim 3, characterized in that, The physics branch is used to obtain the physical baseline prediction value of the heading angle increment based on the three-axis gyroscope data, including: Extract the z-axis angular velocity of the gyroscope from the last frame of the input sequence, restore it to the original physical space, multiply it by the sampling time step, and use it as the physical baseline prediction for the heading angle increment.

5. The IMU heading angle incremental prediction integrated navigation method based on neural networks as described in claim 3, characterized in that, The feature branch is used to obtain global temporal feature representations by combining convolution with a Pre-LN Transformer encoder, including: The original IMU data is concatenated with its first-order difference features along the channel dimension. Convolution operations are performed on the spliced ​​features using convolution stems; The convolutional features are encoded at learnable positions and then encoded using a Pre-LN Transformer encoder to obtain sequence features. Attention pooling is applied to the sequence features to obtain a global temporal feature representation.

6. The IMU heading angle incremental prediction integrated navigation method based on neural networks as described in claim 5, characterized in that, The convolutional stem in the feature branch includes two one-dimensional convolutional networks. The Pre-LN Transformer encoder contains at least two Transformer encoding layers, each layer employing a Pre-LN normalization structure, a multi-head self-attention mechanism, and a feedforward network. The attention pooling uses a learnable query vector to perform multi-head attention aggregation on the sequence features, outputting a fixed-dimensional global sequence representation.

7. The IMU heading angle incremental prediction integrated navigation method based on neural networks as described in claim 5, characterized in that, The combined loss function includes smoothed L1 loss, Signed-log space mean square error, and relative error constraint.

8. The neural network-based IMU heading angle incremental prediction integrated navigation method as described in claim 1, characterized in that, The heading angle error is corrected in the extended Kalman filter measurement update step, including: When satellite navigation signals are normal, the extended Kalman filter uses GNSS position and velocity measurements to update the inertial navigation error state using standard measurements. When satellite signal obstruction is detected, it automatically switches to neural network-assisted mode, replacing GNSS measurements with pseudo-measurements of the heading angle increment predicted by the network, and continuously constrains and corrects the heading angle error within the EKF framework.

9. A neural network-based IMU heading angle incremental prediction integrated navigation system, characterized in that, include: The data acquisition module is used to collect data from the three-axis accelerometer and the three-axis gyroscope, extract the real heading angle increment at the corresponding moment from the reference navigation truth value as training labels, and construct a training set; The standardization processing module is used to obtain standardized IMU time series data based on the training set; The network training module is used to construct a physically guided heading angle increment prediction network. The physically guided heading angle increment prediction network adopts a dual-branch architecture. It takes standardized IMU time series data as input, heading angle increment as prediction target, and uses a combined loss function to train and optimize the network. The inference module takes N frames of IMU data from before the current time as input, performs standardized preprocessing, and then inputs it into the trained network to obtain the predicted value of the heading angle increment at the current time. The EKF fusion module is used to construct a pseudo-measurement residual by comparing the predicted heading angle increment at the current moment with the heading angle increment obtained by integration from the inertial navigation system, and to correct the heading angle error in the extended Kalman filter measurement update step.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the neural network-based IMU heading angle incremental prediction integrated navigation method as described in any one of claims 1 to 8.

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