A Data Fusion Method and System for IMU Arrays Based on Physically Constrained Self-Supervised Learning

Abstract

This invention discloses a method and system for IMU array data fusion based on physically constrained self-supervised learning. The method acquires raw measurement data from multiple IMU arrays, and performs error calibration on the raw data by constructing independent multilayer perceptrons for each IMU to output calibration parameters such as zero bias and scale factor for gyroscopes and accelerometers. A physical loss function is constructed based on the consistency of rigid body kinematic angular velocities, enabling self-supervised network training without external ground truth. Then, dynamic weighted fusion coefficients are calculated based on the consistency differences in the calibrated angular velocities of each IMU, and the calibrated data is adaptively weighted and fused to output high-precision angular velocity and acceleration. This invention requires no ground truth labels, does not rely on precise mathematical models, and uses physical constraints to avoid non-physical estimations. Dynamic weighting can suppress the influence of noise and abnormal sensors, significantly improving fusion accuracy and stability. It is applicable to inertial measurement scenarios such as drones, robots, and autonomous driving.

Description

Technical Field

[0001] This invention relates to the field of sensor data processing technology, and specifically to a self-supervised IMU array data fusion method and system that integrates physical constraints. Background Technology

[0002] Inertial measurement units (IMUs) are sensors that measure the angular velocity and acceleration of objects, and are widely used in robotics, drones, autonomous driving, and other fields. Due to manufacturing limitations, a single low-cost MEMS-IMU suffers from significant noise and drift, leading to severe error accumulation after prolonged operation. By using multiple IMUs in an array and fusing their data, the advantages of multi-source data can be leveraged to improve overall measurement accuracy.

[0003] Currently, IMU array data fusion methods can be mainly divided into two categories:

[0004] 1. Traditional methods typically rely on precise mathematical models to describe sensor error characteristics (such as zero bias, scale factor, installation error, and noise statistics) and system kinematic equations. Representative algorithms include Kalman filtering and its variants (such as extended Kalman filtering and unscented Kalman filtering), weighted least squares, and maximum likelihood estimation. These methods establish state-space models and use observational data to optimally estimate the system state; their performance is highly dependent on model accuracy. In practical applications, sensor errors often vary with factors such as temperature, time, and vibration, and noise statistics are difficult to know accurately a priori, leading to model mismatch. When the model deviates significantly from the actual system, the fusion results will exhibit significant errors or even diverge.

[0005] 2. Deep learning-based methods directly learn the mapping relationship between measured values ​​and actual motion states. These methods use deep neural networks (such as convolutional neural networks, recurrent neural networks, or Transformers) to automatically extract features from large-scale labeled ground truth data. They can capture complex nonlinear patterns without requiring explicit sensor error models. Data-driven methods have achieved significant results in tasks such as visual inertial odometry and pedestrian dead reckoning, demonstrating strong fitting capabilities. However, their training process typically requires a large amount of high-quality ground truth data (such as pose data provided by high-precision motion capture systems or LiDAR), which is difficult to obtain in many real-world scenarios, and the ground truth labels themselves also contain errors. Furthermore, purely data-driven methods lack constraints on physical laws, and the model may learn spurious correlations that contradict kinematic laws, producing non-physical estimation results.

[0006] In summary, existing technologies generally suffer from drawbacks such as reliance on truth labels, reliance on accurate models, lack of physical constraints, and fixed fusion weights, making it impossible to achieve stable and high-precision IMU array data fusion in low-cost, no-external-truth, and strongly perturbed scenarios. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a data fusion method and system for IMU arrays based on physical constraint self-supervised learning. This aims to solve the problems of existing data-driven methods relying on a large number of ground truth labels and traditional methods relying on precise mathematical models, thereby improving the fusion accuracy.

[0008] To solve the above problems, the technical solution adopted by the present invention is as follows:

[0009] A data fusion method for IMU arrays based on physically constrained self-supervised learning includes:

[0010] Step S1: Acquire raw measurement data of the IMU array: Collect raw measurement data of an IMU array consisting of N inertial measurement units. The raw measurement data includes the three-dimensional raw angular velocities of each inertial measurement unit under the same time reference. and three-dimensional primitive acceleration And the complete time series, where N is an integer greater than or equal to 2, 1≤i≤N, and i is the unique serial number of the inertial measurement unit;

[0011] Step S2: Construct a multilayer perceptron network and output calibration parameters: Construct a multilayer perceptron network corresponding one-to-one with each inertial measurement unit (IMU). Input the raw timing measurement data of each IMU within a preset time window into the corresponding multilayer perceptron network. Output a 12-dimensional calibration parameter vector for the corresponding IMU through hierarchical operations of the network. The calibration parameters include the three-dimensional gyroscope zero bias corresponding one-to-one with the spatial dimension. 3D accelerometer zero bias 3D gyroscope scale factor and three-dimensional accelerometer scale factor ;

[0012] Step S3: Calibrate the raw measurement data: For the i-th inertial measurement unit, calibrate the corresponding raw measurement data according to the calibration parameters obtained in step S2 to obtain the three-dimensional calibration angular velocity of the inertial measurement unit. and three-dimensional calibration acceleration The calibration formula is:

[0013] .

[0014] Step S4: Construct the physical loss function and train the multilayer perceptron network: Construct the physical loss function L based on the consistency of rigid body kinematic angular velocity. phy With physical loss function L phy The self-supervised signal is used to train each multilayer perceptron network, enabling the three-dimensional calibration angular velocity of each inertial measurement unit. Towards consensus;

[0015] Step S5: Calculate the dynamic weighted fusion coefficients after network training is complete: For time t, calculate the dynamic weighted fusion coefficients based on the calibration angular velocities of each inertial measurement unit. Calibration angular velocity with other inertial measurement units The difference is used to calculate the dynamic weighted fusion coefficient β of each inertial measurement unit at time t. i (t), the sum of the dynamic weighted fusion coefficients of all inertial measurement units is 1, 1≤j≤N and j≠i, where j is the serial number of the inertial measurement unit;

[0016] Step S6: Weighted fusion to obtain fused data: Based on the dynamic weighted fusion coefficient β obtained in step S5 i (t), the calibration angular velocity of each inertial measurement unit. and calibration acceleration The weighted fusion was performed separately to obtain the fused angular velocity. and acceleration The fusion formula is:

[0017] ,

[0018] in, is the dynamic weighted fusion coefficient of the i-th inertial measurement unit.

[0019] To further optimize this process, in step S2, the multilayer perceptron network is constructed and trained in the following manner:

[0020] The network structure adopts a fully connected structure of input layer-hidden layer-output layer. The input layer has a dimension of T×6, where T is the preset time window length, and 6 corresponds to the three-dimensional primitive angular velocity and three-dimensional primitive acceleration. The hidden layer contains 32 neurons and uses the ReLU activation function. The output layer is a 12-dimensional linear output. Sliding window sampling is used for sample construction, with a window length of T and a step size of S, to generate time-aligned training samples. The optimizer is Adam, with an initial learning rate of 0.001. The training process uses backpropagation and gradient clipping, with a gradient clipping threshold of 1.0. The training of the multilayer perceptron network is completed when the total loss function stably converges.

[0021] Further optimization, in step S4, the physical loss function L phy The expression used to measure the difference in calibrated angular velocity between any two inertial measurement units is: .

[0022] Further optimization involves using a total loss function L in step S4 when training the multilayer perceptron network. loss To optimize, the total loss function L loss Data loss function L data The sum of the weighted physical loss function is expressed as:

[0023] ;

[0024] in The weighting factor for physical losses. ; Here is the data loss function, used to measure the difference between the calibration data of each inertial measurement unit and the fused data. Its expression is:

[0025] .

[0026] Further optimization involves the dynamic weighted fusion coefficient in step S5. The calculation process includes:

[0027] Step S51: Calculate the reliability of the i-th inertial measurement unit at time t. :

[0028] );

[0029] Wherein, λ is the sensitivity parameter, and its value range is 0≤λ≤1; Let be the calibration angular velocity of the i-th inertial measurement unit at time t;

[0030] Step S52: Calculate the dynamic weighted fusion coefficient based on credibility: Where K is the serial number of the inertial measurement unit, 1≤K≤N, c K (t) represents the reliability of the Kth inertial measurement unit at time t.

[0031] A data fusion system for IMU arrays based on physically constrained self-supervised learning includes:

[0032] The IMU array module consists of N inertial measurement units, used to synchronously acquire three-dimensional raw angular velocity, three-dimensional raw acceleration, and time series.

[0033] The parameter estimation module contains a multilayer perceptron network corresponding to each inertial measurement unit (IMU) and is used to output the calibration parameters of each IMU.

[0034] The data calibration module is used to perform zero bias and scale factor correction on the raw measurement data according to the calibration parameters, so as to obtain the calibration angular velocity and calibration acceleration.

[0035] The self-supervised training module is used to construct a physical loss function based on the consistency of rigid body kinematic angular velocity, and to train a multilayer perceptron network using the physical loss as a self-supervised signal.

[0036] The dynamic weighted calculation module is used to calculate the dynamic weighted fusion coefficient based on the consistency differences in the calibration angular velocities of each inertial measurement unit;

[0037] The data fusion module is used to perform weighted summation on the calibration data according to the dynamic weighted fusion coefficients and output the fused angular velocity and acceleration.

[0038] The system executes the aforementioned IMU array data fusion method based on physical constraint self-supervised learning.

[0039] In further optimization, the system also includes an embedded processing unit, which carries a solidified multilayer perceptron model to realize the integrated execution of real-time data acquisition, calibration, training and fusion, with a sampling frequency of 200Hz and a single-frame processing latency of ≤5ms.

[0040] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described method for IMU array data fusion based on physical constraint self-supervised learning.

[0041] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0042] 1. This invention constructs a physical loss function based on the consistency of rigid body kinematic angular velocity, embedding the physical laws of rigid body motion into the self-supervised learning process. The physical loss function is used as the self-supervised signal for network training. The training of multilayer perceptron networks can be completed without high-precision ground truth data, solving the technical problem of existing data-driven methods relying on a large amount of ground truth data, and reducing the cost and implementation difficulty of model training.

[0043] 2. This invention constrains the calibration angular velocities of each inertial measurement unit to be consistent through a physical loss function, forcing the network learning results to conform to the basic laws of rigid body kinematics. This avoids the defects of pure data-driven methods, which are prone to learning false correlations and producing non-physical estimation results, and improves the physical rationality and reliability of the data fusion results.

[0044] 3. This invention calculates a dynamic weighted fusion coefficient based on the real-time consistency of the calibrated angular velocity of each inertial measurement unit, thereby achieving adaptive adjustment of the fusion weight. The more reliable the measurement data of a unit, the higher the fusion weight it occupies. It can automatically identify and suppress the influence of abnormal, faulty or interfered sensors. Compared with the traditional equal-weighted average fusion method, the accuracy and stability of the fusion result are greatly improved.

[0045] 4. The present invention adopts a lightweight multilayer perceptron network structure that corresponds one-to-one with each inertial measurement unit. The network model is simple, the computational load is small, and the convergence speed is fast. It does not require complex deep network calculations and can meet the application scenarios with high real-time requirements such as robots, drones, and autonomous driving.

[0046] 5. This invention first corrects the original measurement data for zero bias and scale factor by using personalized calibration parameters output by the multilayer perceptron network, effectively eliminating the systematic error of the IMU; then, it performs dynamic weighted fusion on the calibrated data to further suppress the influence of random noise and abnormal data. Through the dual optimization strategy of calibration and fusion, the overall measurement accuracy of the IMU array is significantly improved. Attached Figure Description

[0047] Figure 1 This is a network model diagram of the IMU array data fusion method based on physical constraint self-supervised learning in an embodiment of the present invention;

[0048] Figure 2 This is a convergence curve of the loss function in an embodiment of the present invention;

[0049] Figure 3 This is a comparison chart of the cumulative distribution function of absolute trajectory error in embodiments of the present invention;

[0050] Figure 4 This is a comparison chart of the cumulative distribution function of the endpoint drift in the embodiments of the present invention. Detailed Implementation

[0051] The specific embodiments of the present invention are described below with reference to the accompanying drawings.

[0052] Example 1: In this example, the method is applied to the attitude control scenario of a quadcopter UAV. The IMU array is rigidly fixed to the UAV flight control platform, ensuring that all IMUs maintain no relative motion with the UAV fuselage, thus satisfying the uniformity condition of rigid body kinematic angular velocity. In other examples, this method can also be applied to practical scenarios such as autonomous driving and robotics.

[0053] See Figure 1 In conjunction with this embodiment, the IMU array data fusion method based on physical constraint self-supervised learning includes the following steps:

[0054] Step S1: Obtain raw measurement data from an array of N inertial measurement units (IMUs), the raw measurement data including the raw angular velocity and raw acceleration of each IMU.

[0055] In this embodiment, the dynamic test dataset of the IMU array publicly available from the Multi-Source Intelligent Navigation Laboratory of Wuhan University is used for verification. This dataset consists of an array of 16 IMUs fixed to a rigid platform, with a sampling frequency of 200Hz. Each IMU's data includes angular and velocity increments, with a total data duration of approximately 20 minutes, covering motion modes such as straight-line movement, turning, acceleration / deceleration, and stationary states, highly matching the flight conditions of the UAV. The angular and velocity increments are then converted into angular velocity and acceleration sequences.

[0056] Step S2: Construct a multilayer perceptron (MLP) network corresponding to each IMU. Each MLP network is used to output the calibration parameters of the corresponding IMU, including gyroscope error, accelerometer error, gyroscope scaling factor and accelerometer scaling factor.

[0057] In this embodiment, samples are constructed from the original data. A sliding window method is used, with a window length T=200 (corresponding to 1 second) and a step size S=100, resulting in a total of 6565 data samples. The first 60% is the training set (3939 samples), the middle 20% is the validation set (1313 samples), and the last 20% is the test set (1313 samples).

[0058] The structure of each MLP network is as follows: the input layer receives the raw measurement data of the corresponding IMU within a window, with an input dimension of T×6=1200; the hidden layer contains 32 neurons; and the output layer outputs a 12-dimensional vector. The 12-dimensional vector includes accelerometer error and gyroscope scale factor. Accelerometer scale factor.

[0059] In actual drone flights, the trained MLP model can be embedded into the flight control chip to achieve real-time online error calibration.

[0060] Step S3: Calibrate the corresponding raw measurement data according to the calibration parameters of each IMU to obtain the calibration angular velocity and calibration acceleration of each IMU: ,in, , These are the quasi-angular velocity and calibration acceleration of the i-th inertial measurement unit, respectively. , These are the original angular velocity and original acceleration of the i-th inertial measurement unit, respectively. , , , These represent the gyroscope error, accelerometer error, gyroscope scale factor, and accelerometer scale factor of the i-th inertial measurement unit, respectively. N is an integer greater than or equal to 2, 1≤i≤N, and i is the unique serial number of the inertial measurement unit.

[0061] This calibration process can effectively compensate for IMU bias and scale factor drift caused by UAV motor vibration and body shaking, thereby improving measurement stability.

[0062] Step S4: Construct a physical loss function based on the consistency of rigid body kinematic angular velocity, and use the physical loss function as a self-supervised signal to train each MLP network.

[0063] In this embodiment, in the rigid body coordinate system, the true angular velocities of any two IMUs in the IMU array are equal, a pattern perfectly consistent with the rigid body motion characteristics of the UAV. Based on this principle, a physical loss function is constructed to measure the difference between the calibrated angular velocities of any two inertial measurement units, and its expression is: ,

[0064] The total loss function is: ,in The weighting factor for physical losses. .

[0065] The expression for the data loss function is: .

[0066] The network was trained using the Adam optimizer with an initial learning rate of 0.001 and 100 training epochs. A gradient pruning strategy was employed, with a gradient pruning threshold of 1.0. Figure 2 As shown, the loss functions of both the training and validation sets decreased steadily, and the final loss of the training set converged to 0.000628, while the loss of the validation set converged to 0.002219. This indicates that the model has good convergence and generalization ability and can be stably applied to UAV attitude control.

[0067] Step S5: Calculate the dynamic weighted fusion coefficient for each IMU based on the difference between the calibrated angular velocity of each IMU and the calibrated angular velocity of other IMUs.

[0068] In this embodiment, the dynamic weighted fusion coefficient of the i-th inertial measurement unit at time t The calculation is performed as follows: First, the reliability of the i-th inertial measurement unit at time t is calculated. : ), where λ is the sensitivity parameter, and its value ranges from 0 to λ to 1; Let the calibration angular velocity of the i-th inertial measurement unit at time t be used as the sensitivity parameter. Then, the dynamic weighted fusion coefficient is calculated based on the confidence level. .

[0069] When a drone is experiencing strong vibrations or high maneuverability, this step can automatically reduce the weight of the disturbed IMU, thereby improving the system's robustness.

[0070] Step S6: Perform weighted fusion of the calibration data of each IMU according to the dynamic weighted fusion coefficient to obtain the fused angular velocity. and acceleration : ,in, is the dynamic weighted fusion coefficient of the i-th inertial measurement unit.

[0071] The fused high-precision angular velocity and acceleration are output to the UAV attitude calculation unit for roll, pitch and yaw angle calculation, thereby achieving stable attitude control of the UAV.

[0072] To verify the effectiveness of this invention, a trajectory error comparative analysis was performed on the test set. Two methods were selected for comparison: the first was single IMU data, i.e., using only the measurement data of a single IMU in the array; the second was the IMU array averaging method, i.e., the equal-weighted average of the measurement data of each IMU. Evaluation metrics included absolute trajectory error (ATE) and endpoint drift. The comparison results are shown in Table 1.

[0073] The average true distance traveled in the test set was 5.413 m, and the average displacement was 5.410 m. Figure 3 and Figure 4 As shown, the absolute trajectory error CDF curve and the endpoint drift CDF curve of the method described in this invention (red curve) are both located to the left of the single IMU (blue curve) and the average fusion method (green curve), indicating that its overall error distribution is better.

[0074] Table 1 Comparison of Trajectory Errors

[0075]

[0076] As shown in Table 1, the self-supervised IMU array data fusion network method with physical constraints proposed in this invention reduces ATE by 27% and endpoint drift by 23% compared with a single IMU. Compared with the average fusion method, ATE is reduced by 22% and endpoint drift is reduced by 18%, which verifies that the proposed method can effectively suppress sensor noise and outliers and improve the accuracy of position estimation after fusion.

[0077] In summary, the IMU array data fusion method based on physical constraint self-supervised learning proposed in this invention achieves self-supervised learning by constructing a rigid body kinematic angular velocity consistency physical loss function, which does not require external ground truth labels. At the same time, it adopts dynamic weighted fusion coefficients to adaptively adjust the fusion weights, which can effectively improve the accuracy of IMU array data fusion.

[0078] Example 2: A data fusion system for IMU arrays based on physically constrained self-supervised learning, comprising:

[0079] The IMU array module consists of N inertial measurement units, used to synchronously acquire three-dimensional raw angular velocity, three-dimensional raw acceleration, and time series.

[0080] The parameter estimation module contains a multilayer perceptron network corresponding to each inertial measurement unit (IMU) and is used to output the calibration parameters of each IMU.

[0081] The data calibration module is used to perform zero bias and scale factor correction on the raw measurement data according to the calibration parameters, so as to obtain the calibration angular velocity and calibration acceleration.

[0082] The self-supervised training module is used to construct a physical loss function based on the consistency of rigid body kinematic angular velocity, and to train a multilayer perceptron network using the physical loss as a self-supervised signal.

[0083] The dynamic weighted calculation module is used to calculate the dynamic weighted fusion coefficient based on the consistency differences in the calibration angular velocities of each inertial measurement unit;

[0084] The data fusion module is used to perform weighted summation on the calibration data according to the dynamic weighted fusion coefficients and output the fused angular velocity and acceleration.

[0085] An embedded processing unit is equipped with a solidified multilayer perceptron model, which is used to realize the integrated execution of real-time data acquisition, calibration, training and fusion.

[0086] The system executes the aforementioned IMU array data fusion method based on physical constraint self-supervised learning.

[0087] Example 3: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described IMU array data fusion method based on physical constraint self-supervised learning.

[0088] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A data fusion method for IMU arrays based on physically constrained self-supervised learning, characterized in that, include: Step S1: Acquire raw measurement data of the IMU array: Collect raw measurement data of an IMU array consisting of N inertial measurement units. The raw measurement data includes the three-dimensional raw angular velocities of each inertial measurement unit under the same time reference. and three-dimensional primitive acceleration And the complete time series, N is an integer greater than or equal to 2, 1≤i≤N, and i is the unique serial number of the inertial measurement unit; Step S2: Construct a multilayer perceptron network and output calibration parameters: Construct a multilayer perceptron network corresponding one-to-one with each inertial measurement unit (IMU). Input the raw timing measurement data of each IMU within a preset time window into the corresponding multilayer perceptron network. Output a 12-dimensional calibration parameter vector for the corresponding IMU through hierarchical operations of the network. The calibration parameters include the three-dimensional gyroscope zero bias corresponding one-to-one with the spatial dimension. 3D accelerometer zero bias 3D gyroscope scale factor and three-dimensional accelerometer scale factor ; Step S3: Calibrate the raw measurement data: For the i-th inertial measurement unit, calibrate the corresponding raw measurement data according to the calibration parameters obtained in step S2 to obtain the three-dimensional calibration angular velocity of the inertial measurement unit. and three-dimensional calibration acceleration The calibration formula is: ； Step S4: Construct the physical loss function and train the multilayer perceptron network: Construct the physical loss function L based on the consistency of rigid body kinematic angular velocity. phy With physical loss function L phy The self-supervised signal is used to train each multilayer perceptron network, enabling the three-dimensional calibration angular velocity of each inertial measurement unit. Towards consensus; Step S5: After network training is completed, calculate the dynamic weighted fusion coefficients: For time t, calculate the coefficients based on the calibration angular velocities of each inertial measurement unit. Calibration angular velocity with other inertial measurement units The difference is used to calculate the dynamic weighted fusion coefficient β of each inertial measurement unit at time t. i (t), the sum of the dynamic weighted fusion coefficients of all inertial measurement units is 1, 1≤j≤N and j≠i, where j is the serial number of the inertial measurement unit; Step S6: Weighted fusion to obtain fused data: Based on the dynamic weighted fusion coefficient β obtained in step S5 i (t), the calibration angular velocity of each inertial measurement unit. and calibration acceleration The weighted fusion was performed separately to obtain the fused angular velocity. and acceleration The fusion formula is: ,in, is the dynamic weighted fusion coefficient of the i-th inertial measurement unit.

2. The IMU array data fusion method based on physically constrained self-supervised learning according to claim 1, characterized in that, In step S2, the multilayer perceptron network is constructed and trained in the following manner: The network structure adopts a fully connected structure of input layer-hidden layer-output layer. The input layer has a dimension of T×6, where T is the preset time window length and 6 corresponds to the three-dimensional primitive angular velocity and three-dimensional primitive acceleration. The hidden layer contains 32 neurons and uses the ReLU activation function. The output layer is a 12-dimensional linear output. The sample construction adopts sliding window sampling with a window length of T and a step size of S to generate time-aligned training samples; The optimizer used is Adam, with an initial learning rate of 0.

001. The training process employs backpropagation and gradient clipping, with a gradient clipping threshold of 1.

0. The training of the multilayer perceptron network is completed when the total loss function stabilizes and converges.

3. The IMU array data fusion method based on physically constrained self-supervised learning according to claim 2, characterized in that, In step S4, the physical loss function L phy The expression used to measure the difference in calibrated angular velocity between any two inertial measurement units is: .

4. The IMU array data fusion method based on physically constrained self-supervised learning according to claim 3, characterized in that, In step S4, the multilayer perceptron network is trained using the total loss function L. loss To optimize, the total loss function L loss Data loss function L data The sum of the weighted physical loss function is expressed as: ； in, The weighting factor for physical losses. ; Here is the data loss function, used to measure the difference between the calibration data of each inertial measurement unit and the fused data. Its expression is: 。 5. The IMU array data fusion method based on physically constrained self-supervised learning according to claim 4, characterized in that, In step S5, the dynamic weighted fusion coefficient The calculation process includes: Step S51: Calculate the reliability of the i-th inertial measurement unit at time t. : )； Wherein, λ is the sensitivity parameter, and its value range is 0≤λ≤1; Let be the calibration angular velocity of the i-th inertial measurement unit at time t; Step S52: Calculate the dynamic weighted fusion coefficient based on credibility: Where K is the serial number of the inertial measurement unit, 1≤K≤N, c K (t) represents the reliability of the Kth inertial measurement unit at time t.

6. A data fusion system for IMU arrays based on physically constrained self-supervised learning, characterized in that, include: The IMU array module consists of N inertial measurement units, used to synchronously acquire three-dimensional raw angular velocity, three-dimensional raw acceleration, and time series. The parameter estimation module contains a multilayer perceptron network corresponding to each inertial measurement unit (IMU) and is used to output the calibration parameters of each IMU. The data calibration module is used to perform zero bias and scale factor correction on the raw measurement data according to the calibration parameters, so as to obtain the calibration angular velocity and calibration acceleration. The self-supervised training module is used to construct a physical loss function based on the consistency of rigid body kinematic angular velocity, and to train a multilayer perceptron network using the physical loss as a self-supervised signal. The dynamic weighted calculation module is used to calculate the dynamic weighted fusion coefficient based on the consistency differences in the calibration angular velocities of each inertial measurement unit; The data fusion module is used to perform weighted summation on the calibration data according to the dynamic weighted fusion coefficients and output the fused angular velocity and acceleration. The system executes the IMU array data fusion method based on physical constraint self-supervised learning as described in any one of claims 1 to 5.

7. The IMU array data fusion system based on physically constrained self-supervised learning according to claim 6, characterized in that, It also includes an embedded processing unit, which carries a solidified multilayer perceptron model to achieve integrated execution of real-time data acquisition, calibration, training and fusion.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the IMU array data fusion method based on physical constraint self-supervised learning as described in any one of claims 1 to 5.

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