A method and apparatus for imputing missing data of an inertial measurement unit

Abstract

This invention belongs to the interdisciplinary field of inertial navigation and deep learning, and discloses a method for interpolating missing data in inertial measurement units (IMUs). The method involves constructing a baseline interpolation sequence based on the original IMU observation sequence with missing data, and using the difference between the two as the residual observation. Missing sensing information is constructed based on the original IMU observation sequence and concatenated with the residual observation to form an enhanced feature vector. Parallel bidirectional LNN and bidirectional LSTM branches are constructed to extract the enhanced feature vector, obtain dual-path residual prediction terms, and generate hidden states. The hidden states, uncertainty estimates, and the original IMU observation sequence are used as inputs. An adaptive fusion weight is calculated, and the dual-path residual prediction terms are fused to obtain a residual correction term, which is then superimposed onto the baseline interpolation sequence to output the interpolation result. This invention also discloses a device for interpolating missing data in inertial measurement units. This invention enhances the physical consistency of interpolation, improves sensing capabilities, and effectively improves interpolation accuracy when processing missing IMU data.

Description

Technical Field

[0001] This invention belongs to the field of interdisciplinary technology of inertial navigation and deep learning, and specifically relates to a method and apparatus for interpolating missing data of an inertial measurement unit. Background Technology

[0002] Inertial Measurement Units (IMUs) play a crucial role in autonomous driving, drones, and human motion recognition. However, due to factors such as limited sensor sampling frequency, signal interference, hardware failures, or communication packet loss, raw IMU sequences often suffer from data gaps. Existing interpolation methods (such as linear interpolation and polynomial interpolation) struggle to handle complex dynamic changes; while traditional recurrent neural networks (RNNs and LSTMs), although capable of processing sequences, often neglect the dynamic characteristics of IMU signals as a physically continuous system and are prone to accumulating errors when dealing with long periods of missing data.

[0003] For example, Chinese patent CN121541697A discloses a method for constructing a collaborative control system for multiple underwater robots. This method establishes a multi-parameter coupled data acquisition and preprocessing mechanism by utilizing a Doppler current profiler ADCP, an inertial measurement unit (IMU), and controller software. In particular, robust correction of the sampled data is achieved by using outlier point determination with three times the standard deviation and interpolation completion of two neighboring points. Chinese patent CN116399369A discloses a method for compensating the calibration coefficient error of an inertial navigation system for guided projectiles, comprising: acquiring the gyroscope and accelerator outputs of the inertial navigation system for guided projectiles; preprocessing the gyroscope and accelerator outputs to obtain the inertial navigation angular velocity error and acceleration error; extracting features based on the inertial navigation angular velocity error and acceleration error, and setting the model training input and model training output; training the model using an RNN model based on the model training input and output to obtain a calibration coefficient error training model; based on the calibration coefficient error training model, obtaining the real-time predicted output IMU calibration coefficient error based on the real-time measured gyroscope angular velocity and acceleration output of the inertial navigation system, and completing the calibration coefficient error compensation of the inertial navigation system for guided projectiles based on the real-time predicted output IMU calibration coefficient error.

[0004] Therefore, how to combine physical continuous dynamics with long-term temporal dependence to improve the interpolation accuracy of missing IMU data is a technical problem that urgently needs to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a method and apparatus for interpolating missing data of an inertial measurement unit (IMU), which can enhance the physical consistency of interpolation, improve sensing capabilities, and effectively improve interpolation accuracy when processing missing IMU data.

[0006] To achieve the above-mentioned objectives, the present invention provides the following technical solution:

[0007] A method for interpolating missing data in an inertial measurement unit includes the following steps:

[0008] S1. Construct a baseline interpolation sequence based on the original IMU observation sequence with missing data, and use the difference between the original IMU observation sequence and the baseline interpolation sequence as the residual observation.

[0009] S2. Construct missing sensing information based on the original IMU observation sequence, and concatenate the missing sensing information with the residual observation to form an enhanced feature vector;

[0010] S3. Construct parallel bidirectional LNN branches and bidirectional LSTM branches, which are used to extract enhanced feature vectors to obtain dual-path residual prediction terms and generate hidden states.

[0011] S4. The hidden states and uncertainty estimates of the bidirectional LNN branch and the bidirectional LSTM branch, as well as the original IMU observation sequence, are used as inputs. The adaptive fusion weights are calculated through the gated network G, and the dual-path residual prediction terms are fused to obtain the residual correction term. The correction term is then superimposed on the baseline interpolation sequence to output the interpolation result.

[0012] To address the shortcomings of existing methods in processing missing IMU data, such as insufficient perception of physical dynamic characteristics, weak long-range dependency capture capability, and difficulty in assessing the uncertainty of interpolation results, this invention provides a missing data interpolation method for inertial measurement units. The method provided by this invention can also be described as an IMU missing data interpolation method based on the fusion of a bidirectional-liquid neural network (LNN) and a bidirectional long-short-term memory (Bi-LSTM) network.

[0013] In S1, a baseline interpolation sequence is constructed from the original IMU observation sequence with missing data using a channel-by-channel linear interpolation method.

[0014] In S2, the constructed missing information includes:

[0015] Calculate the normalized distances of the current sample to the nearest valid observation point on the left and the nearest valid observation point on the right, providing the relative physical position of the current point with respect to the missing boundary;

[0016] Introduce the relative index of the current time within the window;

[0017] A binary missing mask is introduced to indicate whether there is a missing point at the current time, which is used to characterize the observation availability of each sensor channel at the current moment.

[0018] As a preferred embodiment of the present invention, the normalized distance refers to normalizing the distance to the interval [0,1]. For any sampling time t in the sequence, the nearest valid observation time is obtained by searching to the left. The nearest valid observation time is obtained by searching to the right. The normalized distance to the observation point on the left is calculated using the following formula. :

[0019] ;

[0020] in, This is the total length of the sliding window for the current processing sequence. The effect of introducing the normalized distance is that it provides explicit temporal information for bidirectional LNN and BiLSTM models, enabling the model to perceive the confidence distance between the current interpolation point and known reliable observations. When the calculated distance value is smaller, the model tends to utilize the local dynamics of neighboring observations; when the distance value is larger, the model relies more on long-range temporal features for inference.

[0021] In S3, two parallel branches are constructed to extract temporal features of different dimensions. Both branches adopt a bidirectional structure: the bidirectional LNN branch (BiLNN branch) uses a closed continuous-time neural network CfC to simulate continuous physical dynamics, capture the local smoothness characteristics of IMU signals under physical constraints, and output LNN residual prediction terms; the bidirectional LSTM branch uses BiLSTM to extract global temporal evolution laws and long-range context-dependent features, and outputs LSTM residual prediction terms.

[0022] Furthermore, the bidirectional LNN branch includes a forward branch and a backward branch, which are used to extract enhanced feature vectors and generate hidden states, respectively. The hidden states of the forward branch and the backward branch are concatenated and output as LNN residual prediction terms through a fully connected layer. In the bidirectional LSTM branch, the hidden state of the forward LSTM and the backward LSTM are concatenated and finally output as LSTM residual prediction terms.

[0023] Specifically, a bidirectional LNN branch is constructed, and CfC is used in the forward branch. Its hidden state evolution follows Processing reverse sequences in backward CfC Extract inverse features; concatenate bidirectional hidden states. Finally, the LNN residual prediction values ​​are output through a fully connected layer. In the bidirectional LSTM branch, the hidden layer states of the forward LSTM and the backward LSTM are concatenated. Finally, the LSTM residual prediction value is output. .

[0024] Furthermore, in S4, the uncertainty estimate is the difference magnitude of the two-way residual prediction terms.

[0025] Furthermore, in S4, the gating network G adopts a multilayer perceptron architecture. The input consists of the hidden states of the bidirectional LNN branch and the bidirectional LSTM branch, uncertainty estimates, and the original IMU observation sequences. It uses a two-layer fully connected network with the ReLU activation function in the middle and the Sigmoid activation function in the last layer to calculate the gating weights. .

[0026] The present invention also provides a missing data interpolation device for an inertial measurement unit, comprising:

[0027] The residual observation construction module constructs a baseline interpolation sequence based on the original IMU observation sequence with missing data, and uses the difference between the original IMU observation sequence and the baseline interpolation sequence as the residual observation.

[0028] The multi-dimensional feature construction module constructs missing sensing information based on the original IMU observation sequence and concatenates the missing sensing information with residual observations to form an enhanced feature vector.

[0029] The dual-path feature extraction module constructs parallel bidirectional LNN branches and bidirectional LSTM branches, which are used to extract enhanced feature vectors to obtain dual-path residual prediction terms and generate hidden states.

[0030] The adaptive gating fusion and output module takes the hidden state and uncertainty estimation of the bidirectional LNN branch and the bidirectional LSTM branch, as well as the original IMU observation sequence, as input. It calculates the adaptive fusion weights by time step and by channel through the gating network G, and obtains the residual correction term by fusing the dual residual prediction terms according to the adaptive fusion weights. The correction term is then superimposed on the baseline interpolation sequence to output the interpolation result.

[0031] The present invention also provides a computing device, including a memory and one or more processors, wherein the memory stores an executable program, and the one or more processors implement the above-described method for interpolating missing data of an inertial measurement unit when executing the program.

[0032] A computer-readable storage medium having a computer program stored thereon, which, when processed and executed, implements the missing data interpolation method for the aforementioned inertial measurement unit.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) Enhance interpolation physical consistency: By introducing the LNN branch and utilizing its approximate ordinary differential equation (ODE) characteristics, the fitting ability of the IMU continuous dynamic process is enhanced.

[0035] (2) Enhance perception capability: By encoding the distance between the left and right boundaries, the model can explicitly perceive the length of the missing segment and its own position, which solves the problem that traditional models are not sensitive to missing structures;

[0036] (3) Effectively improve interpolation accuracy: The residual learning architecture is adopted, and the model only needs to learn the correction of the linear baseline, which reduces the fitting difficulty; the dual-branch fusion mechanism balances local dynamics and long-range dependence;

[0037] (4) It has the ability to adapt to predict conflict: by calculating the difference magnitude of the predicted values ​​of BiLNN and BiLSTM branches and inputting it into the gating network, the model can perceive the confidence difference of different branches in a specific missing interval, thereby achieving smooth switching between scenarios where physical dynamics or long-range statistics are dominant. Attached Figure Description

[0038] Figure 1 This invention provides a flowchart for IMU missing data imputation using a hybrid bidirectional LNN and bidirectional LSTM model.

[0039] Figure 2 A schematic diagram of the structure of the bidirectional LNN model provided in the embodiment;

[0040] Figure 3 A schematic diagram of the adaptive gating fusion unit provided in the embodiment;

[0041] Figure 4 A schematic diagram of the hybrid model interpolation accelerometer results provided for an embodiment;

[0042] Figure 5 A schematic diagram of the hybrid model interpolation gyroscope results provided for the embodiment;

[0043] Figure 6 A graph showing the change in the loss function during the first 30 batches of training for the hybrid model provided in this example. Detailed Implementation

[0044] The following embodiments are intended to enable those skilled in the art to gain a more comprehensive understanding of the present invention, but do not limit the invention in any way.

[0045] In this invention, the inertial measurement unit used can be a six-axis or a nine-axis inertial measurement unit.

[0046] The invention will be further described in detail below with reference to the specific algorithm flow:

[0047] This invention provides a method for imputing missing IMU data based on the fusion of bidirectional LNN and bidirectional LSTM, and its overall execution flow is as follows: Figure 1As shown, the process begins by acquiring the original IMU sequence with missing values ​​and standardizing it. Then, a baseline is constructed using linear interpolation, and the residuals are calculated. Next, enhanced features containing missing perception information are constructed and input into parallel bidirectional LNN and bidirectional LSTM branches. Finally, the hidden states, residual features, and uncertainty estimates of each branch are extracted, and the fusion weights are calculated using a learnable gating network to obtain the final residual correction term, which is then superimposed on the baseline to output the interpolation result.

[0048] This embodiment uses the Oxford Inertial Navigation Dataset as the experimental benchmark. This dataset contains 100Hz inertial data (accelerometer and gyroscope, 6 channels in total) collected by a smartphone in various carrying modes (handheld, pocket, bag, on rails, etc.). The default IMU used is a six-axis IMU, including three-axis acceleration and three-axis angular velocity information. This type of IMU needs to meet a sampling frequency greater than 20Hz. In this embodiment, the optimizer used is the Adam optimizer, with an initial learning rate of 1e-3, a batch size of 64, and an initial training epoch of 100. Loss changes are monitored on the validation set; if the loss does not exceed 1e-3 for 10 consecutive iterations, early stopping is triggered.

[0049] Define the IMU currently being processed as The matrix is ​​3D, where T represents the time dimension and D represents the data acquisition dimension, typically D is 6 by default. However, the data dimension D is not limited to 6; this method is also applicable to sequences containing multimodal sensors such as magnetometers and pressure gauges.

[0050] S1. Windowed Segmentation and Standardization

[0051] First, a sliding window extraction is performed, with a window length of T=200 and a sliding step size of 100 (50% overlap), to extract sample segments from the original sequence. Then, the original acceleration and gyroscope six-channel data are Z-score standardized to a mean of 0 and a variance of 1, and inverse standardization is performed after interpolation. The Z-score standardization formula is as follows:

[0052] ,in Represents the mean of the sequence. This represents the variance of the sequence.

[0053] S2, Simulated Missing Generation

[0054] During the training phase, missing masks are generated under different missing ratio settings. This is used to simulate high-frequency missing data generated in real-world environments.

[0055] The mechanism for generating missing data in this invention adopts MCAR (Missing Completely At Random) and uses Bernoulli distribution to make each point either missing or not missing according to a specified probability, with the default proportion of missing data being 30%.

[0056] This invention employs a sequence-based partitioning method to avoid data from the same path appearing simultaneously in the training and test sets: 80% is used as the training set for updating model parameters; 10% is used as the validation set for adjusting hyperparameters and early stopping strategies; and 10% is used as the test set for evaluating the final interpolation accuracy.

[0057] S3. Baseline interpolation sequence construction and residual observation generation

[0058] Obtain the original IMU sequence with missing values Baseline interpolation sequences are constructed using a channel-by-channel linear interpolation method. Subtract the baseline interpolation sequence from the original observations to obtain the residual observations. In the missing locations, this value should be initialized to 0, transforming subsequent modeling tasks into predictions of residual correction terms. Calculate the difference between the observed values ​​and the baseline:

[0059] .

[0060] S4, Enhanced Missing Perception Features

[0061] Construct a multidimensional enhanced feature vector, denoted as Specifically, this includes:

[0062] (1) For time t, retrieve the index of the nearest observation point to its left. And the index of the nearest observation point on the right Then, the two are normalized to calculate the normalized distance from the current sample to the nearest valid observation point on the left. and the normalized distance from the nearest valid observation point on the right :

[0063] ;

[0064] ;

[0065] This feature provides the model with the relative physical location of the current point with respect to the missing boundary;

[0066] (2) Introduce the relative index within the window at the current time. ;

[0067] (3) Missing marker table and binary mask The value is 0 if there is a missing point and 1 if there is an observation. The binary mask is a D-dimensional vector defined by the channel and is used to characterize the observation availability of each sensing channel at the current moment.

[0068] (4) Combine the above features with Concatenate the vectors to form an enhanced feature vector: .

[0069] S5, Dual-path Parallel Feature Extraction 1

[0070] First, construct a bidirectional LNN model (bidirectional LNN branch), such as Figure 2 The diagram shown illustrates the internal structure of the bidirectional LNN model in this embodiment. The model consists of symmetrical forward and backward branches. Within each branch, the input feature sequence, along with a time vector, is input into the backbone network, and continuous-time dynamics are simulated through functions f, g, and h. In the forward sequence, the time vector is the forward sequence... In backward CfC, it is a reverse sequence. Inverse features are extracted. Specifically, this is achieved through the Sigmoid activation function. Time-varying gating weights are generated, and the outputs of f and g are subjected to Hadamard product and weighted mapping, which are then combined with the output of the h function to form the hidden state. The bidirectional hidden states are then concatenated. Finally, the LNN residual prediction values ​​are output through a fully connected layer. This branch can effectively capture the physical continuity of inertial signals.

[0071] In this embodiment, the BiLNN branch adopts the CfC (Closed-form Continuous-time Neural Networks) framework as its core dynamic implementation method, aiming to improve training efficiency on large-scale IMU datasets and ensure real-time performance when deployed online in embedded devices.

[0072] The BiLNN branch in this embodiment contains two layers of bidirectional CfC units with a hidden layer dimension of 64. It adopts a simplified form of linear transformation without a gate structure to reduce computational complexity and enhance the stability of dynamic simulation.

[0073] S6, Dual-path parallel feature extraction 2

[0074] Set up a bidirectional LSTM model with a hidden layer dimension of 128 and two layers (bidirectional LSTM branch), and concatenate the hidden layer states of the forward and backward LSTMs. Finally, the LSTM residual prediction value is output. This branch is responsible for capturing long-range statistical features such as gait cycles and movement trends.

[0075] The bidirectional LSTM branch in this embodiment contains two BiLSTM layers, with the hidden layer dimension set to 128 and Dropout set to 0.1.

[0076] S7, Adaptive Gating Fusion Mechanism

[0077] This embodiment designs a gating network G to allocate weights between the two branches. For example... Figure 3 The diagram shown is a schematic of the adaptive gating fusion unit in this embodiment. The gating network G adopts a multilayer perceptron architecture, and its input vector is composed of four parts: the hidden states of the two branches: , Original residual input And the magnitude of the difference between the two branch predictions as an estimate of uncertainty. A two-layer fully connected network is used, with ReLU activation function in the middle layer and Sigmoid activation function in the last layer to calculate the gating weights. This structure achieves dynamic weighted fusion of residual correction terms by learning semantic information from the hidden states. The fusion weights... The final output interpolation result is: .

[0078] The interpolation evaluation metric used in this embodiment is RMSE. The RMSE metric is calculated between the interpolated data and the original data. The RMSE metric is calculated as follows:

[0079] ;

[0080] Where N represents the number of missing points, Represents the original value. This represents the interpolated value.

[0081] The loss function used in this embodiment employs a mask-weighted mean square error calculation method, and its specific formula is shown below:

[0082]

[0083] in, The interpolated value, This is the original truth value.

[0084] To visually demonstrate the interpolation effect, Figure 4 and Figure 5Examples of interpolation for accelerometers (X, Y, Z axes) and gyroscopes (X, Y, Z axes) within a missing interval are given. In the figure, the solid line represents the ground truth, the blue scatter dots represent the observed values, and the red scatter dots represent the predicted values ​​of the model of this invention. It can be observed that in the interval where the observed values ​​are completely missing, the red predicted values ​​can highly fit the black ground truth curve, not only accurately restoring the amplitude of the signal, but also maintaining the motion trend and phase information of the signal, proving the effectiveness of the two-way dynamic modeling.

[0085] also, Figure 6 The graph shows the loss function changes over the first 30 training batches. The solid blue line represents the training loss, and the dashed red line represents the validation loss. As the number of training batches increases, both the training and validation losses decrease rapidly and smoothly and tend to stabilize, with no significant generalization gap between them, indicating that the model has good convergence and generalization capabilities.

[0086] The method of this invention may include an offline training phase and an online deployment phase. In the offline training phase, historical IMU sequence samples are used to jointly train a bidirectional liquid neural network branch, a bidirectional long short-term memory network branch, and a gated fusion network to obtain a trained data interpolation model. In the online deployment phase, the IMU sequence to be processed is input into the trained model. First, a linear interpolation baseline, residual representation, and missing boundary and location encoding features are generated based on the current observation sequence. These are then input into the bidirectional liquid neural network branch and the bidirectional long short-term memory network branch respectively to obtain residual correction terms relative to the baseline interpolation result. The gated fusion network then outputs adaptive fusion weights by time step and by channel to obtain the final interpolation result. The deployment can be implemented in a robot controller, edge computing device, embedded processor, host computer, server, or cloud platform. It can be used for offline batch repair of historical IMU data, as well as for near real-time data completion based on a sliding time window. Furthermore, the interpolated complete IMU sequence can be further provided to downstream task modules such as attitude calculation, trajectory reconstruction, motion recognition, navigation and positioning, or morphological perception. In some embodiments, only forward inference is performed during the online deployment phase without updating model parameters, in order to reduce computational overhead and improve system stability.

[0087] Implementation effect

[0088] Experiments were conducted on various scenarios using the Oxford dataset. The proposed fusion method reduced the root mean square error (RMSE) of the interpolation residuals by an average of 12.5% ​​and 13.6% compared to a single BiLSTM model and a single bidirectional LNN model, respectively. Furthermore, under the same experimental conditions, our hybrid model was compared with common time series interpolation methods (including Transformer models, GRU models, and average interpolation). Experimental results show that the proposed BiLNN-BiLSTM fusion model achieved the lowest RMSE in all test scenarios, validating the superiority of our approach. The results are shown in the table below.

[0089] Table 1. Comparison of interpolation results of different models in three scenarios.

[0090]

[0091] It should be noted that the applicability of this invention to missing data is not limited to the completely random missing data (MCAR) scenario. The missing IMU data can manifest as random point-like missing data, continuous time-period missing data, channel-level local missing data, simultaneous missing data across multiple channels, or a combination of these missing data forms. During model training, validation, or testing, missing samples can be constructed based on completely random missing data, missing data dependent on observed information, and continuous packet loss caused by actual operating conditions such as communication interruptions, buffer overflows, short-term sensor failures, and electromagnetic interference. However, those skilled in the art should understand that the baseline imputation, residual modeling, missing boundary and location encoding, dual-branch temporal feature extraction, and adaptive gating fusion mechanisms proposed in this invention are also applicable to IMU data imputation under other types of missing data modes, and are not limited to MCAR as the sole limiting condition.

[0092] Based on the same inventive concept, the embodiment also provides a missing data interpolation device for an inertial measurement unit, comprising:

[0093] The residual observation construction module constructs a baseline interpolation sequence based on the original IMU observation sequence with missing data, and uses the difference between the original IMU observation sequence and the baseline interpolation sequence as the residual observation.

[0094] The multi-dimensional feature construction module constructs missing sensing information based on the original IMU observation sequence and concatenates the missing sensing information with residual observations to form an enhanced feature vector.

[0095] The dual-path feature extraction module constructs parallel bidirectional LNN branches and bidirectional LSTM branches, which are used to extract enhanced feature vectors to obtain dual-path residual prediction terms and generate hidden states.

[0096] The adaptive gating fusion and output module takes the hidden state and uncertainty estimation of the bidirectional LNN branch and the bidirectional LSTM branch, as well as the original IMU observation sequence, as input. It calculates the adaptive fusion weights by time step and by channel through the gating network G, and obtains the residual correction term by fusing the dual residual prediction terms according to the adaptive fusion weights. The correction term is then superimposed on the baseline interpolation sequence to output the interpolation result.

[0097] Based on the same inventive concept, the embodiment also provides a computing device, including a memory and one or more processors, wherein the memory stores an executable program, and the one or more processors implement the above-described inertial measurement unit missing data interpolation method when executing the program.

[0098] Based on the same inventive concept, the embodiment also provides a computer-readable storage medium storing a computer program thereon, which, when processed and executed, implements the above-described method for interpolating missing data of the inertial measurement unit.

[0099] It should be noted that the missing data interpolation device, electronic device, and computer-readable storage medium of the inertial measurement unit provided in the above embodiments all belong to the same inventive concept as a missing data interpolation method for an inertial measurement unit. For details of its specific implementation process, please refer to an embodiment of a missing data interpolation method for an inertial measurement unit, which will not be repeated here.

[0100] The specific embodiments described above illustrate the technical solution and beneficial effects of the present invention in detail. It should be understood that the above description is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, additions, and equivalent substitutions made within the scope of the principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for interpolating missing data in an inertial measurement unit, characterized in that, Includes the following steps: S1. Construct a baseline interpolation sequence based on the original IMU observation sequence with missing data, and use the difference between the original IMU observation sequence and the baseline interpolation sequence as the residual observation. S2. Construct missing sensing information based on the original IMU observation sequence, and concatenate the missing sensing information with the residual observation to form an enhanced feature vector; S3. Construct parallel bidirectional LNN branches and bidirectional LSTM branches, which are used to extract enhanced feature vectors to obtain dual-path residual prediction terms and generate hidden states. S4. The hidden states and uncertainty estimates of the bidirectional LNN branch and the bidirectional LSTM branch, as well as the original IMU observation sequence, are used as inputs. The adaptive fusion weights are calculated through the gated network G, and the dual-path residual prediction terms are fused to obtain the residual correction terms. The correction terms are then superimposed on the baseline interpolation sequence to output the interpolation results. In S2, the constructed missing information includes: Calculate the normalized distances of the current sample to the nearest valid observation point on the left and the nearest valid observation point on the right, providing the relative physical position of the current point with respect to the missing boundary; Introduce the relative index of the current time within the window; A binary missing mask is introduced to indicate whether there is a missing point at the current time, which is used to characterize the observation availability of each sensor channel at the current moment; In S4, the uncertainty estimate is the difference magnitude of the two-way residual prediction terms.

2. The method for interpolating missing data in an inertial measurement unit according to claim 1, characterized in that, In S1, a baseline interpolation sequence is constructed from the original IMU observation sequence with missing data using a channel-by-channel linear interpolation method.

3. The method for interpolating missing data in an inertial measurement unit according to claim 1, characterized in that, In S3, the bidirectional LNN branch uses a closed continuous-time neural network CfC to simulate continuous physical dynamics, capture the local smoothing characteristics of IMU signals under physical constraints, and output LNN residual prediction terms; the bidirectional LSTM branch uses BiLSTM to extract global temporal evolution laws and long-range context-dependent features, and outputs LSTM residual prediction terms.

4. The method for interpolating missing data in an inertial measurement unit according to claim 3, characterized in that, The bidirectional LNN branch includes a forward branch and a backward branch, which are used to extract enhanced feature vectors and generate hidden states, respectively. The hidden states of the forward branch and the backward branch are concatenated and output as LNN residual prediction terms through a fully connected layer. In the bidirectional LSTM branch, the hidden layer states of the forward LSTM and the backward LSTM are concatenated, and finally the LSTM residual prediction term is output.

5. The method for interpolating missing data in an inertial measurement unit according to claim 1, characterized in that, In S4, the gating network G employs a multilayer perceptron architecture. The inputs are the hidden states of the bidirectional LNN and bidirectional LSTM branches, uncertainty estimates, and the original IMU observation sequences. It uses a two-layer fully connected network with ReLU activation in the middle and a Sigmoid activation function in the last layer to compute the gating weights. .

6. A missing data interpolation device for an inertial measurement unit employing the method described in any one of claims 1-5, characterized in that, include: The residual observation construction module constructs a baseline interpolation sequence based on the original IMU observation sequence with missing data, and uses the difference between the original IMU observation sequence and the baseline interpolation sequence as the residual observation. The multi-dimensional feature construction module constructs missing sensing information based on the original IMU observation sequence and concatenates the missing sensing information with residual observations to form an enhanced feature vector. The dual-path feature extraction module constructs parallel bidirectional LNN branches and bidirectional LSTM branches, which are used to extract enhanced feature vectors to obtain dual-path residual prediction terms and generate hidden states. The adaptive gating fusion and output module takes the hidden state and uncertainty estimation of the bidirectional LNN branch and the bidirectional LSTM branch, as well as the original IMU observation sequence, as input. It calculates the adaptive fusion weights by time step and by channel through the gating network G, and obtains the residual correction term by fusing the dual residual prediction terms according to the adaptive fusion weights. The correction term is then superimposed on the baseline interpolation sequence to output the interpolation result.

7. An electronic device, characterized in that, It includes a memory and one or more processors, wherein the memory stores an executable program, and the one or more processors, when executing the program, implement the missing data interpolation method for the inertial measurement unit according to any one of claims 1-5.

8. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is processed and executed, it implements the missing data interpolation method for the inertial measurement unit according to any one of claims 1-5.

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