Inertial positioning method based on data enhancement

By performing data augmentation of inertial navigation data and introducing attention mechanisms into the LSTM network, the prediction problems caused by the differences in data set requirements and task in inertial navigation are solved, and higher navigation accuracy and robustness are achieved.

CN119573711AInactive Publication Date: 2025-03-07CHINA NUCLEAR POWER ENGINEERING COMPANY LTD
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Patent Information

Application Number
CN202411628004.4
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2024-11-14
Publication Date
2025-03-07
Estimated Expiration
Not applicable · inactive patent

AI Technical Summary

Technical Problem

The prior art requires more annotated data sets for training in inertial navigation, and if the training task and the test task are too different, the prediction results of the model will be poor.

Method used

Using the inertial positioning method based on data enhancement, the data is subjected to strong enhancement and weak enhancement processing by acquiring inertial sensor data and normalizing and timing segmentation. Then, an attention mechanism is introduced into the LSTM network, an inertial positioning network model is built, and the model is trained using enhanced data.

Benefits of technology

It improves the accuracy of the inertial navigation system, does not need to rely on external information, and simply completes tasks, and overcomes the accuracy and generality of traditional transfer learning. Through the design of data enhancement and consistency loss terms, the network is better robust to noise and sensor degradation.

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Abstract

The invention discloses an inertial positioning method based on data enhancement, which belongs to the field of inertial positioning, and comprises the following steps: acquiring initial inertial data, normalizing the initial inertial data, and performing time sequence segmentation processing on the normalized initial inertial data to obtain inertial training data; respectively performing strong enhancement and weak enhancement on the inertial training data to obtain strong enhancement training data and weak enhancement training data; constructing an inertial positioning network model for inertial positioning; training the inertial positioning network model by using the inertial training data, the strong enhancement training data and the weak enhancement training data to obtain a trained inertial positioning network model; and acquiring inertial data of an inertial sensor IMU, and inputting the trained inertial positioning network model to obtain an inertial positioning result. According to the method, the problem that the prediction result of the model is poor due to the fact that the existing method needs more marked data sets for training and the difference between the training task and the testing task is too large is solved.
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Description

Technical Field

[0001] The invention belongs to the field of inertial positioning, and in particular relates to an inertial positioning method based on data enhancement. Background Art

[0002] With the rapid progress of society, the demand for navigation technology continues to grow, both in the military and civilian fields. However, in environments such as indoors, underground, in tunnels and forests, the penetration of satellite signals is limited, which makes it difficult for satellite navigation systems to operate effectively. The inertial navigation system is a technology that is independent of external signals and is not easily interfered by external conditions. It can achieve autonomous navigation by measuring inertial signals only through built-in inertial sensors, overcoming the shortcomings of satellite navigation and having unique advantages in the absence of satellite navigation.

[0003] Traditional inertial navigation systems use inertial sensor modules to measure the motion parameters of pedestrians or vehicles, and then obtain position information through navigation solutions. Inertial sensors are usually composed of three orthogonal accelerometers and three orthogonal gyroscopes, etc., which provide measured acceleration and angular acceleration. The inertial navigation system performs a second integration on these measurements to obtain the navigation trajectory. The accuracy and efficiency of this navigation solution are affected by the duration of the mission and the quality of the sensor module. High-quality inertial sensor modules can reduce the impact of noise and provide more accurate navigation solutions over a long period of time, while low-cost sensor modules may cause errors and noise to accumulate faster and fail to complete long-term positioning tasks.

[0004] The existing solutions to the accumulated noise and error generally rely on accurate external auxiliary sensors or external signal assistance, such as GNSS signals transmitted by the global navigation satellite system and Doppler speedometers that can provide accurate speed, so as to alleviate the error. Inertial sensors and external auxiliary information are fused in nonlinear filters, such as extended Kalman filters and non-central Kalman filters. Such a combination can reduce the uncertainty of the model and the noise covariance in the measurement process, avoiding the accumulation of errors in the inertial navigation algorithm.

[0005] shortcoming:

[0006] Some external auxiliary signals, such as millimeter-wave radar signals and laser signals, require high equipment requirements, are expensive and not easy to carry, and cannot fully meet the needs of use. GNSS signals are not suitable for all scenarios. When navigating indoors or in tunnels, GNSS signals may not fully meet the needs of use.

[0007] With the continuous advancement of neural network architecture, neural networks are increasingly being used in inertial navigation tasks. By designing a convolutional neural network model, it is also possible to predict the output through the input measured by the inertial simulator and complete the inertial navigation task. Through transfer learning, a model trained on one inertial navigation task can be applied to other inertial navigation tasks, saving the time and resources required for training.

[0008] shortcoming:

[0009] However, general transfer learning requires more labeled data sets for training. At the same time, if the training task and the test task are too different, the model's prediction results may be poor. Summary of the invention

[0010] In view of the above-mentioned deficiencies in the prior art, the present invention provides an inertial positioning method based on data enhancement, which solves the problem that the existing methods require more labeled data sets for training, and if the training task and the test task are too different, it will lead to poor prediction results of the model.

[0011] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is: an inertial positioning method based on data enhancement, comprising the following steps:

[0012] Acquire data collected by an inertial sensor IMU, and perform alignment based on data measured by a magnetometer, wherein the collected data is initial inertial data;

[0013] Normalizing the initial inertial data, and performing time series segmentation processing on the normalized initial inertial data to obtain inertial training data;

[0014] Perform strong enhancement and weak enhancement on the inertial training data respectively to obtain strong enhancement training data and weak enhancement training data;

[0015] Introduce the attention mechanism into the LSTM network and build an inertial positioning network model for inertial positioning;

[0016] The inertial positioning network model is trained using the inertial training data, the strong enhancement training data and the weak enhancement training data to obtain a trained inertial positioning network model;

[0017] The inertial data of the inertial sensor IMU is acquired in real time and input into the trained inertial positioning network model to obtain the inertial positioning result.

[0018] Furthermore, the expression of the inertia training data is:

[0019] X i =D[iN,(i+1)N-1]

[0020] Among them, X i is the i-th inertial training data; D[] is the initial inertial data frame function; i is the data number, which is a non-negative integer; N is the data frame length.

[0021] Furthermore, the inertial training data is strongly enhanced and weakly enhanced respectively to obtain strongly enhanced training data and weakly enhanced training data, specifically:

[0022] Noise is added to the acceleration and angular velocity data of the inertial training data to obtain weakly enhanced training data; for the inertial training data, a portion of data is randomly selected, deleted and scrambled to obtain strongly enhanced training data; the expression of the weakly enhanced training data is:

[0023] X i,aug =D aug [iN,(i+1)N-1]

[0024] D aug (t)=D(t)+ò(t)

[0025]

[0026] Among them, X i,aug is the weakly enhanced training data obtained based on the i-th inertial training data; D aug [] is the frame function of the weakly enhanced data sequence; i is the data number, which is a non-negative integer; N is the data frame length; D aug (t) is the time series of weakly enhanced data; D(t) is the time series of inertial training data; ò(t) is the Gaussian noise introduced at time t; is the variance of Gaussian noise; N(·) is the distribution function.

[0027] Furthermore, the inertial positioning network model includes several groups of inertial positioning prediction units and output units based on time series parallelism; the inertial positioning prediction unit includes a first LSTM network layer, a second LSTM network layer, an attention mechanism and an FC fully connected layer connected in sequence; the first LSTM network layer is connected to the attention mechanism; the first LSTM network layer of the inertial positioning prediction unit for inputting the i-th time series data is connected to the first LSTM network layer of the inertial positioning prediction unit for inputting the i+1-th time series data; the second LSTM network layer of the inertial positioning prediction unit for inputting the i-th time series data is connected to the second LSTM network layer of the inertial positioning prediction unit for inputting the i+1-th time series data; the FC fully connected layer of each inertial positioning prediction unit is connected to the output unit; the time series data includes inertial training data, weak enhancement data and strong enhancement data.

[0028] Furthermore, the inertial positioning network model is trained using the inertial training data, the strong enhancement training data and the weak enhancement training data to obtain a trained inertial positioning network model, specifically:

[0029] Inputting the inertial training data into the first inertial positioning network model to obtain the inertial prediction result;

[0030] Input the weakly enhanced training data into the second inertial positioning network model to obtain the weakly enhanced inertial prediction result;

[0031] Inputting the strongly enhanced training data into the third inertial positioning network model to obtain the strongly enhanced inertial prediction results;

[0032] The inertial prediction results are compared with the weakly enhanced inertial prediction results and the strongly enhanced inertial prediction results to obtain the weakly enhanced consistency loss and the strongly enhanced consistency loss;

[0033] The weak enhancement consistency loss, the strong enhancement consistency loss, the loss function of the first inertial positioning network model, the loss function of the second inertial positioning network model and the loss function of the third inertial positioning network model are summed to obtain the supervised loss; the inertial positioning network model is trained based on the supervised loss to obtain a trained inertial positioning network model; the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model have the same network structure as the inertial positioning network model; the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model have the same network parameters.

[0034] Furthermore, the loss functions of the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model are all mean square errors between the predicted results and the actual results.

[0035] Furthermore, the supervision loss is expressed as:

[0036] L loss =L sup +L aug_weak +L aug_strong +λL consistency,weak +βL consistency,strong

[0037]

[0038] Among them, L loss To monitor the loss; L sup is the loss function of the first inertial positioning network model; L aug_weak is the loss function of the second inertial positioning network model; L aug_strong is the loss function of the third inertial positioning network model; λ is the weight of the weakly enhanced consistency loss; Lconsistency,weak is the weakly enhanced consistency loss; β is the weight of the strongly enhanced consistency loss; L consistency,strong is the strong enhanced consistency loss; i is the data number, which is a non-negative integer; n is the upper limit of the data number; is the weakly enhanced inertial prediction result of the weakly enhanced training data obtained based on the i-th inertial training data; is the inertia prediction result of the i-th inertia training data; is the strong enhancement inertia prediction result of the i'th strong enhancement training data; m is the upper limit of the strong enhancement training data number; i' is the data number, which is a non-negative integer; is the inertia prediction result of the inertia training data corresponding to the i'th strongly enhanced training data.

[0039] The beneficial effects of the present invention are as follows: while being able to improve the accuracy of the inertial navigation system, the present invention does not need to rely on external information and can complete the task more easily. At the same time, the solution can overcome the problems of traditional transfer learning, such as low accuracy and poor versatility. Data enhancement is performed by adding noise to the inertial navigation data, and a consistency loss term is added to the loss function so that the network can obtain the same results as much as possible when performing on the same slice data, regardless of whether there is data enhancement or not. Such a design can make the training network more robust to noise and sensor degradation, and less susceptible to these conditions. The introduction of the attention mechanism in the training network can save training resources, speed up training, and effectively improve the accuracy of training. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 The figure is a flow chart of the method of the present invention.

[0041] Figure 2 It is a design block diagram of the inertial positioning network model in the implementation scheme of the present invention.

[0042] Figure 3 It is a design block diagram of the adversarial neural network in the implementation scheme of the present invention.

[0043] Figure 4 It is a design diagram of the complete training process in the implementation scheme of the present invention. DETAILED DESCRIPTION

[0044] The specific implementation modes of the present invention are described below so that those skilled in the art can understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation modes. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations utilizing the concept of the present invention are protected.

[0045] like Figure 1 As shown, in one embodiment of the present invention, an inertial positioning method based on data enhancement includes the following steps:

[0046] Acquire data collected by an inertial sensor IMU, and perform alignment based on data measured by a magnetometer, wherein the collected data is initial inertial data;

[0047] Normalizing the initial inertial data, and performing time series segmentation processing on the normalized initial inertial data to obtain inertial training data;

[0048] Perform strong enhancement and weak enhancement on the inertial training data respectively to obtain strong enhancement training data and weak enhancement training data;

[0049] Introduce the attention mechanism into the LSTM network and build an inertial positioning network model for inertial positioning;

[0050] The inertial positioning network model is trained using the inertial training data, the strong enhancement training data and the weak enhancement training data to obtain a trained inertial positioning network model;

[0051] The inertial data of the inertial sensor IMU is acquired in real time and input into the trained inertial positioning network model to obtain the inertial positioning result.

[0052] In this embodiment, the data measured by the inertial sensor IMU in the data set is normalized, and the y-axis of the measuring device is aligned with the direction of negative gravity through the data measured by the magnetometer.

[0053] The expression of the inertia training data is:

[0054] X i =D[iN,(i+1)N-1]

[0055] Among them, X i is the i-th inertial training data; D[] is the initial inertial data frame function; i is the data number, which is a non-negative integer; N is the data frame length.

[0056] The inertial training data is strongly enhanced and weakly enhanced respectively to obtain strongly enhanced training data and weakly enhanced training data. Specifically:

[0057] Noise is added to the acceleration and angular velocity data of the inertial training data to obtain weakly enhanced training data; for the inertial training data, a portion of data is randomly selected, deleted and scrambled to obtain strongly enhanced training data; the expression of the weakly enhanced training data is:

[0058] X i,aug =D aug [iN,(i+1)N-1]

[0059] D aug (t)=D(t)+ò(t)

[0060]

[0061] Among them, X i,aug is the weakly enhanced training data obtained based on the i-th inertial training data; D aug [] is the frame function of the weakly enhanced data sequence; i is the data number, which is a non-negative integer; N is the data frame length; D aug (t) is the time series of weakly enhanced data; D(t) is the time series of inertial training data; ò(t) is the Gaussian noise introduced at time t; is the variance of Gaussian noise; N(·) is the distribution function.

[0062] In this embodiment, data preprocessing is performed to segment the data collected by the inertial sensor IMU into time windows to form an input sequence. Assuming that the entire sequence of data collected by each pedestrian is D, every N frames are selected as a sequence until all data are segmented.

[0063] Generate synthetic data and perform data enhancement. Data enhancement can balance samples when the data set is unbalanced, improve training accuracy, and increase training robustness when the number of samples is small. Here, noise is added to the acceleration and angular velocity data of the original data set to perform weak enhancement. At the same time, a portion of the data in each time window is randomly selected, deleted, and scrambled to simulate sensor degradation or inaccuracy. These data are called strongly enhanced data.

[0064] like Figure 2 As shown, the inertial positioning network model includes several groups of inertial positioning prediction units and output units based on time series parallelism; the inertial positioning prediction unit includes a first LSTM network layer, a second LSTM network layer, an attention mechanism and an FC fully connected layer connected in sequence; the first LSTM network layer is connected to the attention mechanism; the first LSTM network layer of the inertial positioning prediction unit for inputting the i-th time series data is connected to the first LSTM network layer of the inertial positioning prediction unit for inputting the i+1-th time series data; the second LSTM network layer of the inertial positioning prediction unit for inputting the i-th time series data is connected to the second LSTM network layer of the inertial positioning prediction unit for inputting the i+1-th time series data; the FC fully connected layer of each inertial positioning prediction unit is connected to the output unit; the time series data includes inertial training data, weak enhancement data and strong enhancement data.

[0065] In this embodiment, a neural network is constructed and a long short-term memory network (LSTM) is selected to extract the features of the IMU inertial navigation data, which can make better use of the time series information of the time window. Introducing the attention layer in the LSTM network and adding the attention mechanism can enable the network to capture the long-term dependencies of the sequence, thereby increasing the accuracy of the network model.

[0066] like Figure 3 and Figure 4 As shown, the inertial positioning network model is trained using inertial training data, strong enhancement training data and weak enhancement training data to obtain a trained inertial positioning network model, which is specifically:

[0067] Inputting the inertial training data into the first inertial positioning network model to obtain the inertial prediction result;

[0068] Input the weakly enhanced training data into the second inertial positioning network model to obtain the weakly enhanced inertial prediction result;

[0069] Inputting the strongly enhanced training data into the third inertial positioning network model to obtain the strongly enhanced inertial prediction results;

[0070] The inertial prediction results are compared with the weakly enhanced inertial prediction results and the strongly enhanced inertial prediction results to obtain the weakly enhanced consistency loss and the strongly enhanced consistency loss;

[0071] The weak enhancement consistency loss, the strong enhancement consistency loss, the loss function of the first inertial positioning network model, the loss function of the second inertial positioning network model and the loss function of the third inertial positioning network model are summed to obtain the supervised loss; the inertial positioning network model is trained based on the supervised loss to obtain a trained inertial positioning network model; the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model have the same network structure as the inertial positioning network model; the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model have the same network parameters.

[0072] The loss functions of the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model are all the mean square error between the predicted results and the actual results.

[0073] The supervision loss is expressed as:

[0074] L loss =L sup +L aug_weak +L aug_strong +λL consistency,weak +βL consistency,strong

[0075]

[0076] Among them, L loss To monitor the loss; L sup is the loss function of the first inertial positioning network model; L aug_weak is the loss function of the second inertial positioning network model; L aug_strong is the loss function of the third inertial positioning network model; λ is the weight of the weakly enhanced consistency loss; L consistency,weak is the weakly enhanced consistency loss; β is the weight of the strongly enhanced consistency loss; L consistency,strong is the strong enhanced consistency loss; i is the data number, which is a non-negative integer; n is the upper limit of the data number; is the weakly enhanced inertial prediction result of the weakly enhanced training data obtained based on the i-th inertial training data; is the inertia prediction result of the i-th inertia training data; is the strong enhancement inertia prediction result of the i'th strong enhancement training data; m is the upper limit of the strong enhancement training data number; i' is the data number, which is a non-negative integer; is the inertia prediction result of the inertia training data corresponding to the i'th strongly enhanced training data.

[0077] In this embodiment, the original data set and the data set after data enhancement are trained in different paths. Such a network design does not require pre-training for any specific task. When the data set is small, different types of data augmentation are performed to increase the samples available for data training. During the training process, for the time series of the same segment, the data set itself, weakly enhanced data, and strongly enhanced data refer to each other, which can improve the stability and robustness of the model in dealing with interference noise and other situations.

[0078] At the same time, although the network structure is similar to the teacher-student model, there is no need to pre-train a better model to distill the data, nor is there any need to annotate the data a second time, which saves training resources. The model only needs to enhance the data and introduce regular consistency loss to help the network model improve robustness and accuracy through semi-supervised learning. There are three paths in the model, among which the mixed use of strong enhancement and weak enhancement can also increase robustness. At the same time, the weights of the two enhancement paths can also be adjusted to make the weak enhancement path with less distortion have a larger weight, so that the performance of the model can be improved.

[0079] In this process, the loss function in supervision is constructed by calculating the mean square error between the predicted position and the true position of each time series.

[0080] At the same time, the consistency regularization loss is constructed to ensure that the training of both the normal data and the enhanced data paths is effective. For the same sequence, the difference between the prediction results of the normal data and the prediction results of the enhanced data is compared to represent the consistency loss function.

[0081] In this embodiment, a data set for testing is input into the model to obtain a result, a predicted trajectory can be drawn according to the prediction result, and the positioning accuracy of the model can be evaluated by comparing the predicted trajectory with the actual trajectory.

[0082] Processing existing data sets can simulate situations where the inertial sensor noise is large or the inertial sensor data accuracy is reduced. Predicting the data in these situations can verify the robustness of the model.

Claims

1. An inertial positioning method based on data enhancement, characterized in that: The following steps are involved: Acquire data collected by an inertial sensor IMU, and perform alignment based on data measured by a magnetometer, wherein the collected data is initial inertial data; Normalizing the initial inertial data, and performing time series segmentation processing on the normalized initial inertial data to obtain inertial training data; Perform strong enhancement and weak enhancement on the inertial training data respectively to obtain strong enhancement training data and weak enhancement training data; Introduce the attention mechanism into the LSTM network and build an inertial positioning network model for inertial positioning; The inertial positioning network model is trained using the inertial training data, the strong enhancement training data and the weak enhancement training data to obtain a trained inertial positioning network model; The inertial data of the inertial sensor IMU is acquired in real time and input into the trained inertial positioning network model to obtain the inertial positioning result.

2. The inertial positioning method based on data enhancement according to claim 1, characterized in that: The expression of the inertia training data is: X i =D[iN,(i+1)N-1] Among them, X i is the i-th inertial training data; D[] is the initial inertial data frame function; i is the data number, which is a non-negative integer; N is the data frame length.

3. The inertial positioning method based on data enhancement according to claim 1, characterized in that: The inertial training data is strongly enhanced and weakly enhanced respectively to obtain strongly enhanced training data and weakly enhanced training data. Specifically: Add noise to the acceleration and angular velocity data of the inertial training data to obtain weakly enhanced training data; For the inertial training data, a part of the data is randomly selected, deleted and scrambled to obtain strongly enhanced training data; The expression of the weakly enhanced training data is: X i,aug =D aug [iN,(i+1)N-1] D aug (t)=D(t)+ò(t) Among them, X i,aug is the weakly enhanced training data obtained based on the i-th inertial training data; D aug [] is the frame function of the weakly enhanced data sequence; i is the data number, which is a non-negative integer; N is the data frame length; D aug (t) is the time series of weakly enhanced data; D(t) is the time series of inertial training data; ò(t) is the Gaussian noise introduced at time t; is the variance of Gaussian noise; N(·) is the distribution function.

4. The inertial positioning method based on data enhancement according to claim 1, characterized in that: The inertial positioning network model includes a plurality of groups of inertial positioning prediction units and output units based on time series parallelism; the inertial positioning prediction unit includes a first LSTM network layer, a second LSTM network layer, an attention mechanism and an FC fully connected layer connected in sequence; the first LSTM network layer is connected to the attention mechanism; The first LSTM network layer of the inertial positioning prediction unit for inputting the i-th time series data is connected to the first LSTM network layer of the inertial positioning prediction unit for inputting the i+1-th time series data; the second LSTM network layer of the inertial positioning prediction unit for inputting the i-th time series data is connected to the second LSTM network layer of the inertial positioning prediction unit for inputting the i+1-th time series data; the FC fully connected layer of each inertial positioning prediction unit is connected to the output unit; the time series data includes inertial training data, weak enhancement data and strong enhancement data.

5. The inertial positioning method based on data enhancement according to claim 1, characterized in that: The inertial positioning network model is trained using the inertial training data, the strong enhancement training data and the weak enhancement training data to obtain a trained inertial positioning network model, specifically: Inputting the inertial training data into the first inertial positioning network model to obtain the inertial prediction result; Input the weakly enhanced training data into the second inertial positioning network model to obtain the weakly enhanced inertial prediction result; Inputting the strongly enhanced training data into the third inertial positioning network model to obtain the strongly enhanced inertial prediction results; The inertial prediction results are compared with the weakly enhanced inertial prediction results and the strongly enhanced inertial prediction results to obtain the weakly enhanced consistency loss and the strongly enhanced consistency loss; The weak enhancement consistency loss, the strong enhancement consistency loss, the loss function of the first inertial positioning network model, the loss function of the second inertial positioning network model and the loss function of the third inertial positioning network model are summed to obtain the supervised loss; the inertial positioning network model is trained based on the supervised loss to obtain a trained inertial positioning network model; the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model have the same network structure as the inertial positioning network model; the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model have the same network parameters.

6. The inertial positioning method based on data enhancement according to claim 5, characterized in that: The loss functions of the first inertial positioning network model, the second inertial positioning network model and the third inertial positioning network model are all the mean square error between the predicted results and the actual results.

7. The inertial positioning method based on data enhancement according to claim 5, characterized in that: The supervision loss is expressed as: L loss =L sup +L aug_weak +L aug_strong +λL consistency,weak +βL consistency,strong Among them, L loss To monitor the loss; L sup is the loss function of the first inertial positioning network model; L aug_weak is the loss function of the second inertial positioning network model; L aug_strong is the loss function of the third inertial positioning network model; λ is the weight of the weakly enhanced consistency loss; L consistency,weak is the weakly enhanced consistency loss; β is the weight of the strongly enhanced consistency loss; L consistency,strong is the strong enhanced consistency loss; i is the data number, which is a non-negative integer; n is the upper limit of the data number; is the weakly enhanced inertial prediction result of the weakly enhanced training data obtained based on the i-th inertial training data; is the inertia prediction result of the i-th inertia training data; is the strong enhancement inertia prediction result of the i'th strong enhancement training data; m is the upper limit of the strong enhancement training data number; i' is the data number, which is a non-negative integer; is the inertia prediction result of the inertia training data corresponding to the i'th strongly enhanced training data.

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