Micro-electro-mechanical system inertial measurement unit signal denoising method based on domain adaptation

Abstract

The application discloses a micro-electro-mechanical system inertial measurement unit signal denoising method based on domain adaptation, belongs to the technical field of navigation and positioning, and is used for micro-electro-mechanical system inertial measurement unit navigation, and comprises the following steps: preparing source domain data and target domain data for pretreatment, constructing a multi-scale convolutional Transformer network model, using the source domain data for model training, obtaining an inertial measurement unit signal denoising model, inputting the pretreated target domain data into the denoising model to generate pseudo labels and performing weak supervision fine-tuning, and outputting denoised inertial measurement unit navigation data by inertial navigation mechanical arrangement. Through the inertial measurement unit denoising network based on the multi-scale convolutional Transformer, the common nonlinear and non-stationary noise in the low-cost micro-electro-mechanical system inertial measurement unit signal is effectively inhibited, the domain adaptation strategy is introduced to realize robust cross-domain denoising, the clean label is not needed, the divergence delay is prolonged, and the overall navigation precision is improved.

Description

TECHNICAL FIELD

[0001] The application discloses a micro-electro-mechanical system inertial measurement unit signal denoising method based on domain adaptation, and belongs to the technical field of navigation and positioning. BACKGROUND

[0002] In recent years, the rapid development of deep learning and computing resources has driven breakthroughs in various fields such as computer vision, natural language processing, and autonomous driving. Existing methods for inertial measurement unit signal denoising based on deep learning include using a neural network based on a hollow convolution to utilize spatial features in sequence inertial measurement unit data, which improves the accuracy of attitude estimation; using a hybrid data-driven and model information denoising method to improve the reliability of low-cost inertial measurement units in maritime navigation tasks; and using airborne visual data to correct inertial measurement unit measurements, thereby improving trajectory accuracy without the need for external equipment. However, all of these methods rely on a supervised learning framework, which requires a large amount of high-quality labeled data. In practice, the cost of collecting ground truth navigation data and noise-free inertial measurement unit reference data is high, which severely limits the scalability of these methods. Methods that adopt a self-supervised inertial measurement unit denoising framework do not require external ground truth poses or clean inertial measurement unit signals, and extract temporal and structural information from noisy sequences by jointly training three auxiliary tasks: masked inertial measurement unit modeling, inertial measurement unit denoising modeling, and future inertial measurement unit prediction. Although this self-supervised paradigm exhibits effective noise suppression capabilities under practical conditions, it still has problems such as training instability, indirect supervision targets, and limited generalization ability in different application scenarios. In summary, current deep learning-based inertial measurement unit denoising methods are still severely limited by the need for high-quality labeled data and insufficient generalization ability in complex real-world scenarios. SUMMARY

[0003] The purpose of the present application is to provide a micro-electro-mechanical system inertial measurement unit signal denoising method based on domain adaptation to solve the problem of severe dependence on high-quality labeled data and insufficient generalization ability in complex real-world scenarios in the prior art.

[0004] The micro-electro-mechanical system inertial measurement unit signal denoising method based on domain adaptation comprises the following steps:

[0005] S1, source domain data and target domain data are prepared and preprocessed, the source domain data is a simulated micro-electro-mechanical system inertial measurement unit dataset, containing noisy original measurement values and corresponding noise-free reference labels ; the target domain data is a micro-electro-mechanical system inertial measurement unit measured dataset, containing noisy measurement values without reference labels ;

[0006] S2, input the pretreated source domain data into a multi-scale convolutional Transformer network, the multi-scale convolutional Transformer network is an untrained inertial measurement unit signal denoising model, and the inertial measurement unit signal denoising model is trained in a supervised manner to obtain the inertial measurement unit signal denoising model;

[0007] S3, input the pretreated into the inertial measurement unit signal denoising model to generate the pseudo label ;

[0008] S4, input and into the inertial navigation mechanical arrangement module, including inputting and into the inertial measurement unit signal denoising model, adopting a weak supervision strategy to obtain the denoised inertial measurement unit signal , performing inertial navigation mechanical arrangement on , and outputting the denoised micro-electromechanical system inertial measurement unit navigation data.

[0009] S1 includes S1.1, source domain data is generated according to a micro-electromechanical system inertial measurement unit error model, and the micro-electromechanical system inertial measurement unit error model is as follows:

[0010] ;

[0011] ;

[0012] In the formula, is a measured angular velocity vector of the gyroscope, is a true angular velocity vector of the gyroscope, is a measured specific force vector of the accelerometer, is a true specific force vector of the accelerometer, is a proportional factor error matrix of the gyroscope, is a proportional factor error matrix of the accelerometer, is an installation error matrix of the gyroscope, is an installation error matrix of the accelerometer, is a constant or time-varying offset in the gyroscope output, is a constant or time-varying offset in the accelerometer output, is random walk noise in the gyroscope measurement, is random walk noise in the accelerometer measurement; , , and are defined as follows:

[0013] ;

[0014] ;

[0015] ;

[0016] ;

[0017] wherein, , , are the scale factor errors of the gyroscope in the axis, , , are the scale factor errors of the accelerometer in the axis, is the cross-coupling error of the gyroscope axis sensitive component on the axis measurement, is the cross-coupling error of the gyroscope axis sensitive component on the axis measurement, is the cross-coupling error of the gyroscope axis sensitive component on the axis measurement, is the cross-coupling error of the gyroscope axis sensitive component on the axis measurement, is the cross-coupling error of the gyroscope axis sensitive component on the axis measurement, is the cross-coupling error of the gyroscope axis sensitive component on the axis measurement, is the cross-coupling error of the accelerometer axis sensitive component on the axis measurement, is the cross-coupling error of the accelerometer axis sensitive component on the axis measurement, is the cross-coupling error of the accelerometer axis sensitive component on the axis measurement, is the cross-coupling error of the accelerometer axis sensitive component on the axis measurement, is the cross-coupling error of the accelerometer axis sensitive component on the axis measurement, is the cross-coupling error of the accelerometer The axis-sensitive component is in Cross-coupling error on axis measurement.

[0018] S1 includes S1.2, preprocessing the source domain data and the target domain data, including preprocessing the gyroscope data into a standardized form with zero mean and unit variance, and normalizing the accelerometer data according to the physical measurement range to The range is within, the sliding window and the step are set according to the inertial measurement unit sampling frequency, and the dimension of the preprocessed data is , The batch size is The time window is The three-axis gyroscope The axis measurement value and the accelerometer The axis measurement value.

[0019] S2 includes constructing a multi-scale convolutional Transformer network, inputting the preprocessed source domain data for neural network training, combining adaptive gradient update and weight decay regularization using the AdamW optimizer, drawing a loss curve to verify the neural network error performance after training, outputting the denoised inertial measurement unit signal if the loss curve converges to the minimum value, generating an inertial measurement unit signal denoising model, and returning to neural network training if the loss curve does not converge to the minimum value; the multi-scale convolutional Transformer network includes a multi-scale convolutional module and a shallow Transformer module.

[0020] The multi-scale convolutional module step is: inputting the preprocessed source domain data or the preprocessed target domain data, using 4 parallel one-dimensional convolution layer branches for processing, each layer generating a feature map with a size of Connecting the feature maps along the channel dimension, using a fully connected layer with a weight matrix to apply linear projection, obtaining an embedded feature tensor with a shape of .

[0021] The shallow Transformer module step is: inputting , adding position encoding to along the time dimension to provide sequence order information, obtaining an embedded sequence , , The input is fed into encoder layer 1, which employs a multi-head self-attention mechanism to model the dependencies between different time positions in parallel. The self-attention mechanism processing result is input into the residual connection and normalization layer, and then through the position feedforward network. At each time step, the feedforward network performs nonlinear transformation and feature enhancement. The output of the feedforward network is then passed through the residual connection and normalization layer, and then input into encoder layer 2. Encoder layer 2 follows the same steps as encoder layer 1. The output of encoder layer 2 is then passed to the decoder layer, which uses two feedforward sub-layers to perform pointwise regression. The final output shape is... The denoised signal from the inertial measurement unit.

[0022] The mean squared error (MSE) is used as the loss function to evaluate the training performance of the multi-scale convolutional Transformer network on the source domain data. The MSE loss function is calculated as follows:

[0023] ;

[0024] In the formula, Let the mean squared error loss function be . For batch indexing, , For time window indexing, , For gyroscopes and accelerometers Index of shaft measurement values , For steps Time The first sample The denoising value of each component The corresponding noise-free labels are used; the loss curve is plotted, and when the loss curve converges to the minimum value, the inertial measurement unit signal denoising model is obtained.

[0025] S3 includes inputting the standardized and normalized target domain data into the inertial measurement unit signal denoising model to generate... .

[0026] S4 includes, S4.1, and will and Input inertial navigation mechanical orchestration module, including... and Input the inertial measurement unit (IMU) signal denoising model, employ a weakly supervised strategy, and reduce the number of iterations and the learning rate of the IMU signal denoising model to a set threshold, outputting... .

[0027] S4 includes, S4.2, and will Input two branches, the first branch will Transform to the navigation coordinate system, second branch pair The posture estimation is performed, the second branch result is input into the first branch for fusion, the acceleration is corrected according to the fusion result of the two branches, a gravity model and a Coriolis force correction, then the corrected acceleration is integrated once to obtain the denoised velocity information output by the inertial measurement unit, and the corrected acceleration is integrated twice to obtain the denoised position information output by the inertial measurement unit.

[0028] Compared with the prior art, the inertial measurement unit denoising network based on the multi-scale convolutional Transformer network has the following beneficial effects: the inertial measurement unit denoising network based on the multi-scale convolutional Transformer network effectively suppresses the common nonlinear and non-stationary noise in the low-cost micro-electromechanical system inertial measurement unit signal, introduces a domain adaptive strategy, realizes robust cross-domain denoising without relying on clean labels, prolongs the divergence delay, and improves the overall navigation precision. BRIEF DESCRIPTION OF DRAWINGS

[0029] Figure 1 is a technical flowchart of the present application;

[0030] Figure 2 is a multi-scale convolutional Transformer network structure and an inertial navigation mechanical arrangement module structure diagram of the present application;

[0031] Figure 3 is a simulated driving trajectory schematic diagram;

[0032] Figure 4 is a loss curve schematic diagram of a training set and a verification set;

[0033] Figure 5 is a simulated trajectory schematic diagram of a test data set;

[0034] Figure 6 is an east direction velocity error comparison diagram of original data and the method achievement of the present application;

[0035] Figure 7 is a north direction velocity error comparison diagram of original data and the method achievement of the present application;

[0036] Figure 8 is a vertical direction velocity error comparison diagram of original data and the method achievement of the present application;

[0037] Figure 9 is an east direction position error comparison diagram of original data and the method achievement of the present application;

[0038] Figure 10 is a north direction position error comparison diagram of original data and the method achievement of the present application;

[0039] Figure 11 is a vertical direction position error comparison diagram of original data and the method achievement of the present application;

[0040] Figure 12 is a comparison chart of east direction velocity error of the method result of the present application and the method result of other methods;

[0041] Figure 13 is a comparison chart of north direction velocity error of the method result of the present application and the method result of other methods;

[0042] Figure 14 is a comparison chart of vertical direction velocity error of the method result of the present application and the method result of other methods;

[0043] Figure 15 is a comparison chart of east direction position error of the method result of the present application and the method result of other methods;

[0044] Figure 16 is a comparison chart of north direction position error of the method result of the present application and the method result of other methods;

[0045] Figure 17 is a comparison chart of vertical direction position error of the method result of the present application and the method result of other methods. DETAILED DESCRIPTION

[0046] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0047] The method for denoising micro-electro-mechanical system inertial measurement unit signals based on domain adaptation comprises the following steps:

[0048] S1, source domain data and target domain data are prepared and preprocessed, the source domain data is a simulated micro-electro-mechanical system inertial measurement unit data set, containing original measurement values with noise and corresponding noise-free reference labels ; the target domain data is a micro-electro-mechanical system inertial measurement unit measured data set, containing measurement values with noise without reference labels ;

[0049] S2, the preprocessed source domain data is input into a multi-scale convolutional Transformer network, the multi-scale convolutional Transformer network is an untrained inertial measurement unit signal denoising model, which is trained in a supervised manner to obtain an inertial measurement unit signal denoising model;

[0050] S3, the preprocessed is input into the inertial measurement unit signal denoising model to generate pseudo labels ;

[0051] S4, the and input inertial navigation mechanical arrangement module, including and input inertial measurement unit signal denoising model, using a weak supervision strategy, to obtain denoised inertial measurement unit signal , the inertial navigation mechanical arrangement, output denoised micro-electro-mechanical system inertial measurement unit navigation data.

[0052] S1 includes, S1.1, source domain data is generated according to micro-electro-mechanical system inertial measurement unit error model, micro-electro-mechanical system inertial measurement unit error model is:

[0053] ;

[0054] ;

[0055] In the formula, is the measured angular velocity vector of the gyroscope, is the true angular velocity vector of the gyroscope, is the measured specific force vector of the accelerometer, is the true specific force vector of the accelerometer, is the proportional factor error matrix of the gyroscope, is the proportional factor error matrix of the accelerometer, is the installation error matrix of the gyroscope, is the installation error matrix of the accelerometer, is the constant or time-varying offset in the gyroscope output, is the constant or time-varying offset in the accelerometer output, is the random walk noise in the gyroscope measurement, is the random walk noise in the accelerometer measurement; , , and The matrix definitions are as follows:

[0056] ;

[0057] ;

[0058] ;

[0059] ;

[0060] In the formula, , , respectively, are the scale factor errors of the accelerometer in the

[0061] S1 includes, S1.2, pre-processing the source domain data and the target domain data, including pre-processing the gyroscope data into a standardized form with zero mean and unit variance, normalizing the accelerometer data to the range of according to the physical measurement range, setting a sliding window and a step according to the inertial measurement unit sampling frequency, the dimension of the pre-processed data is ,​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​ batch size, time window, corresponding three-axis gyroscope axis measurement values and accelerometers axis measurement values.

[0062] S2 comprises constructing a multi-scale convolutional Transformer network, inputting the pre-processed source domain data for neural network training, combining adaptive gradient update and weight decay regularization by using an AdamW optimizer, drawing a loss curve to verify the neural network error performance after training, outputting the denoised inertial measurement unit signal if the loss curve converges to a minimum value, generating an inertial measurement unit signal denoising model, and returning to neural network training if the loss curve does not converge to a minimum value; the multi-scale convolutional Transformer network comprises a multi-scale convolutional module and a shallow Transformer module.

[0063] The multi-scale convolutional module step is: inputting the pre-processed source domain data or the pre-processed target domain data, using 4 parallel one-dimensional convolution layer branches for processing, each layer generating a feature map with a size of connecting the feature maps along the channel dimension, using a fully connected layer with a weight matrix to apply linear projection, obtaining an embedded feature tensor with a shape of .

[0064] The shallow Transformer module step is: inputting , adding position encoding to along the time dimension to provide sequence order information, obtaining an embedded sequence , inputting to encoder layer 1, the encoder layer uses a multi-head self-attention mechanism to model the dependency between different time positions in parallel, the self-attention mechanism processing result is input to a residual connection and a normalization layer, then passing through a positional feedforward network, each time step of the feedforward network performs a nonlinear transformation and feature enhancement, the output result of the feedforward network is then input to a residual connection and a normalization layer, and then input to encoder layer 2, the encoder layer 2 has the same step as the encoder layer 1, and the output of the encoder layer 2 is transmitted to a decoder layer, the decoder layer uses two feedforward sublayers to perform point-by-point regression, and finally outputs an inertial measurement unit denoised signal with a shape of .

[0065] The mean square error is used as a loss function to evaluate the training performance of the multi-scale convolutional Transformer network on the source domain data, and the mean square error loss function is calculated as follows:

[0066] ;

[0067] wherein, is a mean square error loss function, is a batch index, , is a time window index, , is an index of the gyroscope and accelerometer measurements in axis, , is a denoised value of the i-th component of the j-th sample at step , , is a corresponding noise-free label; a loss curve is drawn, and when the loss curve converges to a minimum value, an inertial measurement unit signal denoising model is obtained. S3 includes inputting the normalized and standardized target domain data into the inertial measurement unit signal denoising model to generate

[0068] .

[0069] S4 includes S4.1, inputting and into the inertial navigation mechanical orchestration module, including inputting and into the inertial measurement unit signal denoising model, adopting a weak supervision strategy, and reducing the iteration number and learning rate of the inertial measurement unit signal denoising model to a set threshold, and outputting .

[0070] S4 includes S4.2, inputting into two branches, the first branch converts to a navigation coordinate system, and the second branch performs attitude estimation on , inputs the second branch result into the first branch for fusion, corrects the acceleration according to the fusion results of the two branches, a gravity model and a Coriolis force correction, then performs a first integration on the corrected acceleration to obtain denoised velocity information output by the inertial measurement unit, and performs a second integration on the corrected acceleration to obtain denoised position information output by the inertial measurement unit.

[0071] In order to evaluate the effectiveness of the method of the present application in the low-cost micro-electromechanical system inertial measurement unit signal denoising, systematic experiments were conducted in the source domain and the target domain. As Figure 1 ​As shown, first, the source domain data and the target domain data are prepared, in the source domain experiment, the original inertial measurement unit signal sequence obtained by simulation is used as the source domain data to train the multi-scale convolutional Transformer network, to generate an inertial measurement unit signal denoising model, in the target domain evaluation, the target domain data is input into the inertial measurement unit signal denoising model to generate pseudo labels, the target domain data and the corresponding pseudo labels are used for weakly supervised training, and the denoising result is input into the inertial navigation system for mechanical arrangement, and the denoised micro-electro-mechanical system inertial measurement unit navigation data is output. Finally, the wavelet threshold processing and the method of the application are comprehensively compared and analyzed, all evaluations are carried out under consistent experimental conditions, in order to ensure the rigor and fairness of the comparative analysis, the data used in the source domain and the target domain are designed to have consistent structures.

[0072] The multi-scale convolutional Transformer network structure and the inertial navigation mechanical arrangement module structure are as shown in Figure 2 As shown, the steps S3 and S4 are included, the inertial measurement unit (IMU) original data is input into the multi-scale convolutional module, the data is divided according to the gyroscope data and the accelerometer data, the data dimension is set to , 4 parallel one-dimensional convolution layers are input, the kernel size (k) is 3, 5, 7 and 3 respectively, and the channel number is 64, the feature map processed by the one-dimensional convolution layer is connected along the channel with a dimension of , and then connected along the channel with a dimension of , to obtain an embedded feature tensor with a shape of ; the is input into the shallow Transformer module, the position encoding is added to the along the time dimension to provide sequence order information, to obtain an embedded sequence , the is input into the encoder layer 1, the encoder layer adopts a multi-head self-attention mechanism to model the dependency between different time positions in parallel, the self-attention mechanism processing result is input into the residual connection and the normalization layer, and then through the position feedforward network, each time step of the feedforward network performs nonlinear transformation and feature enhancement, the output result of the feedforward network is then input into the residual connection and the normalization layer, and then input into the encoder layer 2, the encoder layer 2 has the same steps as the encoder layer 1, the output of the encoder layer 2 is transmitted to the decoder layer, the decoder performs point-by-point regression through two feedforward sublayers, the channel dimensions of the two feedforward sublayers are and respectively, and finally outputs ; the and the are input into the inertial measurement unit signal denoising model, a weak supervision strategy is adopted, the iteration number and the learning rate of the inertial measurement unit signal denoising model are reduced to a set threshold, and the output is​ , including gyroscope data and accelerometer data, input two branches, the first branch converts to a navigation coordinate system, and the second branch performs attitude estimation, inputs the second branch result into the first branch for fusion, combines the two branch fusion results, a gravity model and a Coriolis force correction to correct the acceleration, then performs a first integration on the corrected acceleration to obtain denoised inertial measurement unit velocity information, and performs a second integration on the corrected acceleration to obtain denoised inertial measurement unit position information.

[0073] To ensure consistency in computational performance and repeatability in experiments, all evaluations (including those performed in simulated source domains and real target domains) were performed on the same hardware platform.

[0074] To systematically evaluate the denoising ability of the method, the source domain experiment first trains a multi-scale convolutional Transformer network using simulated inertial measurement unit data, thereby obtaining an inertial measurement unit signal denoising model, which lays the foundation for subsequent real experiments in the target domain.

[0075] (1) Dataset: To better simulate the error characteristics of low-cost micro-electromechanical system inertial measurement unit devices in actual scenarios, the present invention configures a simulated inertial measurement unit model using the specifications listed in Table 1:

[0076] Table 1, simulation parameter settings

[0077] ;

[0078] These parameters are intentionally set slightly lower than those of typical commercial micro-electromechanical system inertial measurement units, in order to introduce more obvious noise and error levels during simulation. This conservative configuration helps to ensure that the method is verified under more challenging conditions than actual hardware. As shown in Figure 3 , a simulated driving trajectory (blue line in Figure 3 ) is constructed, starting from the initial position marked by the red star, with coordinates . The trajectory has a duration of 1267 seconds and a sampling rate of 100 Hz, simulating urban driving conditions, including acceleration, deceleration, turning, uphill and downhill, etc. By combining a series of representative motion patterns observed in actual applications, this setting helps to rigorously evaluate the effectiveness of the model in handling complex non-stationary inertial measurement unit noise.

[0079] To train the multi-scale convolutional Transformer network on the source domain, 70% of the simulated inertial measurement unit dataset (from 1 to 887 seconds) is designated as the training set for model parameter optimization, and the remaining 30% (from 888 to 1267 seconds) is used as the validation set to monitor the training effect and guide hyperparameter tuning and architecture adjustment. In addition, hundreds of seconds of simulated inertial measurement unit data are generated as an independent test set to evaluate the model's generalization ability to previously unseen data; before training, the original inertial measurement unit measurements are preprocessed to improve learning stability and convergence. Specifically, the gyroscope data (angular velocity) is standardized to have a zero mean and unit variance to mitigate the effects of cross-axis scale differences. On the other hand, the accelerometer data (specific force) is normalized to the range, thus preserving the relative amplitude information. This hybrid preprocessing strategy ensures that both sensor modalities can effectively participate in network training while avoiding the influence of high-amplitude signals. During model training, considering the inertial measurement unit sampling frequency of 100 Hz, the original data is segmented using a sliding window of length 100, resulting in an input sample of size 100x6, where 6 represents the measurements of the three-axis gyroscope and accelerometer. To improve training efficiency and the stability of sequence modeling, the stride is also set to 100 to ensure sufficient temporal coverage and feature diversity between samples, thereby helping to extract consistent and robust temporal features. The AdamW optimizer is adopted, combining adaptive gradient updates with weight decay regularization to accelerate convergence while effectively alleviating overfitting. The initial learning rate and weight decay coefficient are set to 0.0001, and respectively, and are configured as 0.9 and 0.999, respectively. During training, the learning rate is adaptively decayed according to a predefined schedule within the first 150 traversal periods, further improving convergence stability and model generalization ability. The batch size is 16, and all hyperparameters are determined through grid search to ensure optimal performance on the source domain dataset.

[0080] Figure 4 The evolution of the training and validation loss curves of the multi-scale convolutional Transformer network is shown over multiple training periods. Both loss curves show a consistent and significant downward trend, eventually converging to a minimum value of about 0.0021 around the 40th period, indicating that the model has achieved satisfactory training performance at this stage. In addition, the training and validation losses remain closely aligned throughout the process, with minimal fluctuations and no significant differences. This consistency indicates that the model has achieved stable convergence during source domain training and has not shown signs of overfitting, which also reflects the model's strong generalization ability and robustness when applied to unknown data.

[0081] (2) Performance evaluation metrics: To comprehensively evaluate the denoising performance of the multi-scale convolutional Transformer network, three widely used quantitative metrics are adopted: mean absolute error (MAE) , root mean square error (RMSE) , and signal-to-noise ratio (SNR) . The mean absolute error measures the average absolute deviation between the denoised signal and the true signal, making it robust to outliers; the root mean square error penalizes larger deviations more severely by squaring the residuals, making it a more sensitive indicator of denoising accuracy; the signal-to-noise ratio is a standard metric in signal processing that quantifies the ratio of signal power to noise power, reflecting the degree of preservation of the underlying signal relative to the residual noise. These metrics are calculated by comparing the denoised output of the low-cost MEMS IMU with the noise-free reference signal, as follows:

[0082] ;

[0083] ;

[0084] ;

[0085] where is the measured or denoised signal, is the corresponding noise-free reference.

[0086] Lower mean absolute error and root mean square error values imply smaller estimation errors, while higher signal-to-noise ratios indicate more effective noise suppression and higher fidelity of signal reconstruction, making these metrics comprehensive and objective in evaluating the denoising performance of gyroscope and accelerometer outputs. However, relying solely on signal-level metrics such as mean absolute error, root mean square error, and signal-to-noise ratio is insufficient to comprehensively assess the actual impact of denoising on navigation performance. In inertial navigation systems, velocity and position are calculated by time-integrating the gyroscope and accelerometer outputs, a process that is highly sensitive to spatial and temporal consistency between different sensor axes. Even if single-axis denoising appears effective, any disruption to the inherent inter-axis relationships can introduce cumulative errors during the integration process, ultimately degrading navigation accuracy. Therefore, in addition to evaluating signal-level denoising quality, it is necessary to examine whether the denoised inertial measurement unit signals contribute to improved velocity and position estimation in subsequent navigation tasks.

[0087] To this end, the maximum absolute error is introduced as a supplementary performance metric to evaluate the worst-case deviation of the navigation output:

[0088] ;

[0089] Unlike the mean absolute error and the root mean square error, which quantify the average performance, the maximum absolute error focuses on the most extreme error, and thus is particularly important for applications where safety and reliability are of utmost importance. This is particularly important in scenarios such as autonomous driving or air navigation, where a momentary large deviation in speed or position can have serious consequences. Therefore, the introduction of the maximum absolute error can provide a more rigorous and comprehensive evaluation of the actual effect of the denoising algorithm.

[0090] (3) Inertial measurement unit denoising experimental results: the experiment was performed on a 100s test data set, and the corresponding trajectory is shown in FIG. 2, where the blue line represents the trajectory and the red star marks the initial position. Table 2 and Table 3 provide a comprehensive quantitative comparison of the average absolute error, root mean square error, and signal-to-noise ratio of the gyroscope and accelerometer along the three axes: Figure 5

[0091] Table 2, Performance indicators of denoised inertial measurement unit data (gyroscope)

[0092]

[0093] Table 3, Performance indicators of denoised inertial measurement unit data (accelerometer)

[0094]

[0095] For the gyroscope, the multi-scale convolutional Transformer network reduced the average absolute error and the root mean square error of the X-axis by 97.9% and 97.6%, respectively, and simultaneously improved the signal-to-noise ratio from -1.01 dB to 31.96 dB (a gain of 33 dB); similar trends were observed for the Y-axis and the Z-axis, with signal-to-noise ratios improved by 32.8 dB and 26.4 dB, respectively; for the accelerometer, the average absolute error and the root mean square error of the X-axis were reduced by 88.7% and 85.7%, respectively, and the signal-to-noise ratio was improved by 16.9 dB; the signal-to-noise ratios of the Y-axis and the Z-axis were improved by 1.6 dB and 10.6 dB, respectively. The above data demonstrate the effectiveness of the method in suppressing noise and preserving the essential signal characteristics.

[0096] (4) Navigation estimation experimental results: the denoised inertial measurement unit signal output was processed through a strapdown inertial mechanization system to estimate the velocity and position, thereby quantitatively evaluating the impact of denoising on navigation accuracy, according to Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 It can be seen that the error divergence of the method is slow, indicating that it can effectively suppress the noise of the inertial measurement unit, and the detailed quantitative results are shown in Table 4 and Table 5:

[0097] ​​​​​​​​Table 4. Velocity estimation error of the first 20s and 40s of denoised IMU data

[0098] ;

[0099] Table 5. Position estimation error of the first 20s and 40s of denoised IMU data

[0100] ;

[0101] Table 4 summarizes the velocity error performance of the proposed method along the east, north and vertical directions (i.e., the longitudinal axis of the local ENU coordinate system) for the 20s and 40s inertial navigation duration. For the 20s test case, the velocity error derived from the original IMU data without denoising is relatively large: the average absolute error values in the east, north and vertical directions are 1.951 m / s, 0.551 m / s and 0.620 m / s, respectively, the corresponding maximum absolute errors reach 5.112 m / s, 2.289 m / s and 1.090 m / s, respectively, and the root mean square errors are 2.453 m / s, 0.847 m / s and 0.699 m / s, respectively. After applying the multi-scale convolutional Transformer network to the source domain denoising, the average absolute error, maximum absolute error and root mean square error in the three directions are significantly reduced, among which the root mean square error values are reduced by 88.7%, 44.1% and 54.1%, respectively, proving the effectiveness of the proposed method in short-term inertial navigation scenarios. Even in the longer integration period of 40s, the denoising benefit is still significant. For example, in the east direction, the average absolute error decreases from 6.744 m / s (original IMU) to 1.001 m / s (a decrease of 85.2%), the maximum absolute error decreases from 20.037 m / s to 3.637 m / s, and the root mean square error decreases from 8.850 m / s to 1.439 m / s, all of which decrease by more than 80%; in the north direction, the average absolute error, maximum absolute error and root mean square error decrease from 4.074 m / s, 14.291 m / s and 5.941 m / s to 0.705 m / s, 1.914 m / s and 0.933 m / s, respectively; in the vertical direction, the average absolute error decreases from 1.036 m / s to 0.258 m / s, the maximum absolute error decreases from 1.805 m / s to 0.485 m / s, and the root mean square error decreases from 1.153 m / s to 0.285 m / s, with an increase of 75.1%, 73.1% and 75.3%, respectively. Overall, the multi-scale convolutional Transformer network exhibits strong robustness and consistent denoising performance in different times and directions. Although the vertical velocity error fluctuates due to the influence of gravity acceleration, the continuous suppression of the proposed method on the vertical velocity error in a longer integration interval highlights the potential of the proposed method to improve navigation accuracy in practical inertial navigation applications.

[0102] Table 5 demonstrates the position error performance of the method of the present application in the East, North and Vertical directions for 20s and 40s integration periods. The raw inertial measurement unit data without denoising exhibits significant accumulated errors. For example, in the 20s test, the root mean square error of the raw inertial measurement unit in the East direction is 15.756 meters, with a maximum absolute error of 38.940 meters, while the root mean square errors in the North and Vertical directions are 2.604 meters and 5.745 meters, respectively, indicating a significant degradation in navigation accuracy. In contrast, after applying the method of the present application, the position error is significantly reduced, specifically, in the 20s scenario, the root mean square error in the East direction is reduced from 15.756 meters to 1.312 meters (a reduction of about 91.7%), the root mean square error in the North direction is reduced from 2.604 meters to 1.624 meters, and the root mean square error in altitude is improved from 5.745 meters to 3.676 meters, demonstrating the effectiveness of the method of the present application. For the longer 40s integration period, the accumulated errors of the raw inertial measurement unit data become more pronounced, with the root mean square error in the East direction rising to 103.922 meters, and the method of the present application reduces this error to 14.013 meters, reflecting an improvement of 86.5%. Similarly, the root mean square error in the North direction is reduced from 55.682 meters to 14.678 meters, and the root mean square error in altitude is reduced from 19.428 meters to 5.984 meters, corresponding to relative reductions of 73.6% and 69.2%, respectively. These results confirm that the method of the present application significantly suppresses the accumulated drift of position estimates over different integration durations, thereby improving the robustness and long-term accuracy of inertial navigation using low-cost microelectromechanical system inertial measurement units.

[0103] In summary, the multi-scale convolutional Transformer network trained on source domain simulated data can effectively denoise the raw inertial measurement unit signals while avoiding overfitting, and importantly, the denoising process preserves the inherent spatial correlation and temporal consistency between the axes of the inertial measurement unit, thereby ensuring the structural integrity of the inertial measurements, which makes the downstream velocity and position estimates more accurate, thereby improving the overall reliability of the navigation system.

[0104] Unlike the source domain where clear IMU labels can be obtained through simulation, the target domain uses real-world IMU measurement data, which cannot obtain high-precision reference data due to the lack of advanced reference sensors. Therefore, a domain adaptation strategy is needed to ensure effective training in such an environment. Specifically, the IMU signal denoising model trained on the source domain is first applied to the original IMU measurement data in the target domain in inference mode to generate the corresponding denoised output. Although these outputs are not supervised by real labels, they can be used as pseudo labels because the model has learned to recover structured signals from noisy inputs. These pseudo labels are then used in a weakly supervised fine-tuning process to enable the network to better fit the statistical characteristics and noise patterns of the target domain data. During the fine-tuning phase, the network architecture remains consistent with the source domain training, with only two hyperparameters adjusted: the number of iterations is reduced to 3, and the learning rate is set to By preserving the original model architecture and its learned feature extraction capabilities, the risk of performance instability due to excessive modifications is effectively reduced; at the same time, the use of shorter training time and smaller learning rate helps to prevent overfitting on limited pseudo-labeled target domain data. This strategy ensures more stable parameter updates and enables better adaptation to the statistical characteristics and noise patterns of the target domain, resulting in significantly improved denoising performance and generalization ability on real IMU measurement data. This enhanced adaptability further enhances the model's denoising capabilities and improves navigation performance in real-world conditions. At the same time, a comprehensive comparative analysis of three state-of-the-art methods is conducted, including wavelet thresholding, visual soft calibration, and shallow Transformer.

[0105] (1) Dataset: The real road dataset used in the invention, the IMU sensor used for data collection is a low-cost six-axis sensor with a sampling rate of 100 Hz. GNSS data is collected using differential positioning technology with an output frequency of 1 Hz. To establish an accurate ground truth reference, the combined navigation results of the satellite-inertial integrated positioning system are post-processed, and the total data collection time is 2298 seconds. The detailed hardware specifications are shown in Table 6:

[0106] Table 6, IMU configuration

[0107] ;

[0108] (2) Performance evaluation index: three evaluation indexes, mean absolute error, maximum absolute error and root mean square error, are used to evaluate the navigation performance. In order to ensure the consistency and comparability of the source domain and the target domain, the same set of indexes is used in the target domain experiment. Since the target domain involves real-world measurements, there is no noise-free inertial measurement unit signal, so it is not possible to directly evaluate the denoised inertial measurement unit data. Therefore, the effectiveness of the denoising process is indirectly evaluated by examining the time-domain waveform characteristics of the denoising process and its impact on the downstream navigation performance (speed and position estimation accuracy).

[0109] (3) Navigation estimation experiment results: In order to comprehensively evaluate the performance of each denoising method, three error indexes are used: mean absolute error, maximum absolute error and root mean square error. Figure 12 、 Figure 13 、 Figure 14 、 Figure 15 、 Figure 16 and Figure 17 The speed and position estimation errors of different methods are compared intuitively. The results show that the error divergence of the method of the present application is the slowest, indicating that it has excellent performance in effectively suppressing inertial measurement unit noise. The detailed quantitative results are shown in Tables 7 and 8:

[0110] Table 7, speed estimation error of denoised inertial measurement unit data for the first 5s, 10s, 30s and 60s

[0111] ;

[0112] Table 8, position estimation error of denoised inertial measurement unit data for the first 5s, 10s, 30s, 60s

[0113] ;

[0114] Table 7 shows the comparison of velocity estimation error of raw IMU data and four denoising methods in east, north and vertical directions at integration intervals of 5s, 10s, 30s and 60s. Overall, the accumulated error of raw IMU data grows rapidly with the increase of integration time, especially showing serious drift and instability in the north and vertical directions; the average absolute error, maximum absolute error and root mean square error of the method of the present application are better than those of other methods in all time intervals and spatial directions; in the short-term 5s interval, although the error of the raw data is still moderate, the method of the present application has achieved robust denoising: the root mean square error in the east direction is reduced from 7.537 m / s to 6.910 m / s, the root mean square error in the north direction is reduced from 3.308 m / s to 1.307 m / s, and the vertical root mean square error is reduced from 0.462 m / s to 0.150 m / s, which is more than 67% reduction in the vertical component, which significantly improves the reliability of the initial velocity estimation of navigation. In the medium-term of 10s and 30s, when the inertial drift accelerates, the method of the present application effectively suppresses the error propagation. For example, in 30s, the root mean square error in the north direction is reduced from 16.382 m / s to 1.224 m / s (92.5% reduction), and the root mean square error in the altitude is reduced from 2.047 m / s to 0.401 m / s (80% reduction). In contrast, the improvement effect of visual soft calibration and shallow Transformer is more limited, especially in the high dynamic axis; the wavelet threshold denoising ability is weaker, and the error is only slightly lower than the raw data. When evaluated in 60s, the error of the raw data grows more sharply, the root mean square error in the north direction reaches 33.990 m / s, and the maximum absolute error exceeds 62 m / s, resulting in unreliable navigation results, in contrast, the method of the present application achieves significant error suppression, reducing the root mean square error in the north direction to 3.094 m / s (90.9% improvement), and reducing the root mean square error in the east direction and the altitude direction to 6.926 m / s and 1.025 m / s (more than 50% improvement in both directions). In addition, the method of the present application also effectively suppresses the average absolute error of velocity in three directions, thereby reducing the overall error amplitude and improving the robustness of the navigation solution.

[0115] Table 8 compares the position estimation errors in three directions within the same time interval. The position errors exhibit a clear nonlinear accumulation characteristic, with severe drift in the north and vertical directions. At 5 seconds, although the errors are relatively small, the inventive method has already shown a clear advantage, significantly reducing the root mean square error in the north direction from 7.605 meters to 2.725 meters and in the vertical direction from 1.036 meters to 0.626 meters, thereby providing a more accurate position baseline. As the motion duration extends to 10 seconds and 30 seconds, the position errors accumulate more quickly, but the inventive method consistently exhibits superior error suppression capability. At 30 seconds, the root mean square error in the north direction is reduced from 204.837 meters to 24.102 meters (more than 88% reduction), and in the vertical direction from 26.491 meters to 2.169 meters (more than 90% reduction). Other methods have limited gain and limited effect in the case of rapid error growth, especially in the dynamic axes. When the motion duration reaches 60 seconds, the original inertial measurement unit position error rises sharply (root mean square error in the north direction: 785.873 meters, maximum absolute error: more than 1700 meters), severely affecting the actual usability. The inventive method significantly reduces these errors, reducing the root mean square error in the north direction to 64.125 meters and the maximum absolute error to 151.867 meters (about 92% and 91% reduction, respectively), and observing the same significant improvement in the east and vertical directions. In addition, the inventive method performs well in the average absolute error of position in all three directions.

[0116] The evaluation of navigation error is limited to the first 60 seconds of inertial integration, which is due to the inevitable accumulation of drift and system error in low-cost micro-electromechanical system inertial measurement units during long-term operation. Although the inventive method effectively reduces short-term and medium-term errors, residual bias and long-term drift still have a significant impact on navigation accuracy as the integration time increases, and ultimately can lead to the failure of inertial navigation. Therefore, limiting the analysis to a 60-second window not only objectively evaluates the ability of each method to suppress error growth in the early stages of integration, but also minimizes the interference of non-algorithmic factors such as long-term drift. In summary, the inventive method exhibits comprehensive, stable, and superior performance in all integration intervals and spatial directions of velocity and position estimation, significantly improving short-term estimation accuracy while effectively suppressing long-term inertial drift, meeting the stringent requirements of high-precision practical navigation applications.

[0117] The above examples are only used for illustrating the technical solutions of the present application, and are not intended to limit the present application. Although the present application has been described in detail with reference to the foregoing examples, it should be understood by those skilled in the art that the technical solutions recorded in the foregoing examples can be modified, or some or all of the technical features can be replaced by equivalent replacements, and these modifications or replacements 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 application.

Claims

1. A method for denoising micro-electro-mechanical system inertial measurement unit signals based on domain adaptation, characterized in that, Comprise: S1, prepare source domain data and target domain data, and pre-process, the source domain data is a simulated micro-electro-mechanical system inertial measurement unit dataset, containing original measurement values with noise and corresponding noise-free reference labels ; the target domain data is a micro-electro-mechanical system inertial measurement unit measured dataset, containing measurement values with noise without reference labels ; S2, input the pretreated source domain data into the multiscale convolutional Transformer network, the multiscale convolutional Transformer network is an untrained inertial measurement unit signal denoising model, which is trained in a supervised manner to obtain an inertial measurement unit signal denoising model; the multiscale convolutional Transformer network comprises a multiscale convolutional module and a shallow Transformer module; The multi-scale convolution module step is: input the pre-processed source domain data or the pre-processed target domain data, adopt 4 parallel one-dimensional convolution layer branches for processing, each layer generates a feature map with a size of , connect the feature maps along the channel dimension, apply linear projection using a fully connected layer with a weight matrix , and obtain an embedding feature tensor with a shape of ; The shallow Transformer module step is: input , position encoding is added along the time dimension , providing sequence order information, obtaining embedded sequence , , input to the encoder layer 1, the encoder layer uses a multi-head self-attention mechanism to model the dependency between different time positions in parallel, the self-attention mechanism processing result is input to the residual connection and normalization layer, and then passes through the position feedforward network, each time step of the feedforward network performs a nonlinear transformation and feature enhancement, and the output result of the feedforward network is input to the residual connection and normalization layer again, and then input to the encoder layer 2, the encoder layer 2 is consistent with the encoder layer 1 step, and the output of the encoder layer 2 is transmitted to the decoder layer, the decoder layer uses two feedforward sublayers to perform point-by-point regression, and finally outputs the inertial measurement unit denoised signal with a shape of ; S3, the pretreated input inertial measurement unit signal denoising model, generate pseudo label ; S4, the method further comprises and inputting an inertial navigation mechanical arrangement module, comprising and inputting an inertial measurement unit signal denoising model, adopting a weak supervision strategy to obtain denoised inertial measurement unit signals , performing inertial navigation mechanical arrangement on , and outputting denoised micro-electro-mechanical system inertial measurement unit navigation data; Will And Input inertial navigation mechanical arrangement module, including With Input inertial measurement unit signal denoising model, using weak supervision strategy, and reducing the iteration number and learning rate of the inertial measurement unit signal denoising model to a set threshold, output ; Will input two branches, the first branch will convert to the navigation coordinate system, and the second branch will perform attitude estimation, input the second branch result into the first branch for fusion, correct the acceleration according to the fusion result of the two branches, the gravity model and the correction of the Coriolis force, then integrate the corrected acceleration once to obtain the speed information of the output of the inertial measurement unit after denoising, and integrate the corrected acceleration twice to obtain the position information of the output of the inertial measurement unit after denoising.

2. The domain adaptation based micro-electromechanical system inertial measurement unit signal denoising method according to claim 1, characterized in that, S1 comprises S1.1, the source domain data is generated according to the micro-electro-mechanical system inertial measurement unit error model, and the micro-electro-mechanical system inertial measurement unit error model is: ； ； where is the measured angular rate vector of the gyroscope, is the true angular rate vector of the gyroscope, is the measured specific force vector of the accelerometer, is the true specific force vector of the accelerometer, is the scale factor error matrix of the gyroscope, is the scale factor error matrix of the accelerometer, is the misalignment error matrix of the gyroscope, is the misalignment error matrix of the accelerometer, is the constant or time-varying bias in the gyroscope output, is the constant or time-varying bias in the accelerometer output, is the random walk noise in the gyroscope measurement, is the random walk noise in the accelerometer measurement; , , and The matrix definitions are as follows: ； ； ； ； wherein , , are the scale factor errors of the gyroscope in the axis, respectively, , , are the scale factor errors of the accelerometer in the axis, respectively, is the cross-coupling error of the gyroscope sensitive component in the axis measurement on the axis, is the cross-coupling error of the gyroscope sensitive component in the axis measurement on the axis, is the cross-coupling error of the gyroscope sensitive component in the axis measurement on the axis, is the cross-coupling error of the gyroscope sensitive component in the axis measurement on the axis, is the cross-coupling error of the gyroscope sensitive component in the axis measurement on the axis, is the cross-coupling error of the accelerometer sensitive component in the axis measurement on the axis, is the cross-coupling error of the accelerometer sensitive component in the axis measurement on the axis, is the cross-coupling error of the accelerometer sensitive component in the axis measurement on the axis, is the cross-coupling error of the accelerometer sensitive component in the axis measurement on the axis.

3. The domain adaptation based micro-electromechanical system inertial measurement unit signal denoising method according to claim 2, characterized in that, S1 comprises, S1.2, pre-processing the source domain data and the target domain data, including pre-processing the gyroscope data into a standardized form with zero mean and unit variance, normalizing the accelerometer data to a range of 0 to 1 according to the inertial measurement unit sampling frequency, the pre-processed data dimension is , as the batch size, as the time window, corresponding to three-axis gyroscope axis measurements and accelerometer axis measurements.

4. The domain adaptation based micro-electromechanical system inertial measurement unit signal denoising method according to claim 3, characterized in that, S2 comprises constructing a multiscale convolutional Transformer network, inputting pretreated source domain data for neural network training, combining adaptive gradient update with weight decay regularization by using an AdamW optimizer, drawing a loss curve to verify the neural network error performance after training, outputting the denoised inertial measurement unit signal if the loss curve converges to a minimum value, generating an inertial measurement unit signal denoising model, and returning to neural network training if the loss curve does not converge to a minimum value.

5. The domain adaptation based micro-electromechanical system inertial measurement unit signal denoising method according to claim 4, characterized in that, The mean square error is used as a loss function to evaluate the training performance of the multiscale convolutional Transformer network on the source domain data, and the mean square error loss function is calculated as follows: ； In the formula, Let the mean squared error loss function be . For batch indexing, , For time window indexing, , For gyroscopes and accelerometers Index of shaft measurement values , For steps Time The first sample The denoising value of each component The corresponding noise-free labels are used; the loss curve is plotted, and when the loss curve converges to the minimum value, the inertial measurement unit signal denoising model is obtained.

6. The domain adaptation based micro-electromechanical system inertial measurement unit signal denoising method according to claim 4, characterized in that, S3 comprises inputting the standardized and normalized target domain data into an inertial measurement unit signal denoising model to generate .

Images