Inertial navigation temperature drift compensation method based on multi-dimensional modeling

Abstract

The invention discloses an inertial navigation temperature drift compensation method based on multi-dimensional modeling, and relates to the field of inertial navigation. Comprising the following steps: S1, collecting temperature, three-axis acceleration and three-axis angular velocity data through a constant temperature control system in a range of-40 DEG C to 80 DEG C, and constructing a time-aligned multivariable characteristic matrix; s2, after standardization and rotation transformation, a Chebyshev polynomial is utilized to construct a five-order nonlinear coupling function group, an orthogonal tensor model is established, and L1 constraint is applied; s3, constructing a drift response curve group based on the heating and cooling experiment data to obtain a 6 * 1 drift sensitivity matrix; s4, removing abnormal samples through mahalanobis distance analysis, and extracting a high-confidence training subset; s5, constructing a multi-channel modeling network containing a thermal coding module, a convolution channel and an attention mechanism, and carrying out cross-axis modeling; s6, training the network and generating a steady-state compensation tensor; s7, new data are input into the model, regular six-axis output is maintained one by one, and temperature drift active compensation is completed. The method has the beneficial effects that the cross-temperature-zone navigation precision and the compensation robustness are improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of inertial navigation, more particularly, to an inertial navigation temperature drift compensation method based on multi-dimensional modeling. BACKGROUND

[0002] Inertial navigation system (INS) has been widely used in aerospace, weapon guidance and high-precision positioning fields, but its precision is seriously affected by the drift error of inertial measurement unit (IMU) under temperature change. Traditional compensation methods mostly use linear fitting or polynomial regression, which has certain effect under constant temperature conditions, but the processing capacity for nonlinear temperature response, coupling characteristics and high-frequency interference is limited. With the improvement of computing power, nonlinear modeling techniques such as neural networks are gradually introduced, and some studies begin to use convolutional networks or RNN structures for temperature drift modeling, and the compensation accuracy is improved.

[0003] However, these methods still have three deficiencies: first, most of them use single-path structure, which cannot dynamically adapt to different temperature zone characteristics; second, the correction process often uses unified correction of the whole set of data, ignoring the temperature response asymmetry between the axes; third, the filtering process is insufficient, which is easy to introduce high-frequency noise or phase distortion, affecting the navigation stability. SUMMARY

[0004] The purpose of the present application is to provide an inertial navigation temperature drift compensation method based on multi-dimensional modeling to solve the problems raised in the background art: however, these methods still have three deficiencies: first, most of them use single-path structure, which cannot dynamically adapt to different temperature zone characteristics; second, the correction process often uses unified correction of the whole set of data, ignoring the temperature response asymmetry between the axes; third, the filtering process is insufficient, which is easy to introduce high-frequency noise or phase distortion, affecting the navigation stability.

[0005] Technical solution: an inertial navigation temperature drift compensation method based on multi-dimensional modeling comprises the following steps: S1. Under the condition of full temperature zone from-40℃ to 80℃, a closed-loop constant temperature control system is used to control the temperature of the inertial measurement unit, and temperature data, three-axis acceleration data and three-axis angular velocity data are collected synchronously, and a multi-variable feature matrix with unified time stamp and sample alignment mechanism is constructed; S2. After applying standardization and first-order rotation transformation of coordinate system to the multi-variable feature matrix, a five-order nonlinear coupling function group is constructed with Chebyshev polynomial, taking temperature and first derivative as input, and the three-axis acceleration data and the three-axis angular velocity data as output, an orthogonal tensor coupling model is established, and L1 norm constraint is applied to realize sparse modeling; S3. Construct a drift response curve group of the three-axis acceleration data and the three-axis angular velocity data based on the temperature rise / fall response experimental data of the inertial measurement unit, calculate the slope coefficient respectively to obtain a 6x1 dimension drift sensitivity matrix as an initial weight matrix of the directionality of residual extraction; S4. Perform Mahalanobis distance analysis on the residual data obtained under the drift sensitivity matrix, calculate the normalized distance based on the sample covariance matrix, eliminate samples outside the 95% confidence level, and construct a high-confidence training subset; S5. Construct a multi-path modeling network including a temperature heat coding embedding module, three layers of normalized convolution channels, a parallel attention mechanism, and a dynamic path selection structure, input the contracted high-confidence training subset into the multi-path modeling network, and perform cross-axis deep modeling on the temperature-output relationship; S6. Train the multi-path modeling network using a target function composed of an L2 constraint loss term within the channel and residual feedback weighting, iteratively optimize using a split-channel, fixed-step, AdamW optimization strategy, and obtain a steady-state temperature drift compensation tensor; S7. Input the temperature data, the three-axis acceleration data, and the three-axis angular velocity data into the trained multi-path modeling network, call the temperature drift compensation tensor, and perform dimension-by-dimension correction on the six-axis output respectively to complete active compensation of the temperature drift of the inertial measurement unit. The multi-path modeling network introduces a five-section temperature mapping mask activation structure, activates and suppresses different paths in the network based on temperature section labels, and dynamically adapts the cross-temperature zone modeling performance.

[0006] Preferably, the multi-variable feature matrix construction in S1 includes the following steps: S1-1. Configure sampling points in the full temperature range of -40°C to 80°C, set a constant temperature point every 2.5°C in the range of -40°C to 80°C, a total of 49 points, use the closed-loop constant temperature control system to make the stable error of each point less than ±0.2°C, and the data collection time of each temperature point is not less than 30 minutes, and the sampling frequency is set to 1000Hz; S1-2. Align the collected temperature data, three-axis acceleration data, and three-axis angular velocity data by timestamp to form an N-row and 7-column floating-point matrix, and the column vectors are time stamp, temperature value, X / Y / Z-axis acceleration value, and X / Y / Z-axis angular velocity value in turn, and use 0-mean unit variance standardization processing.

[0007] Preferably, the feature matrix data structure generation in S1-2 further includes the following steps: S1-2-1. Remove samples with a first derivative change rate exceeding 3 times the average value of the three-axis acceleration data and the three-axis angular velocity data. S1-2-2. The initial fixation of the inertial measurement unit in the known direction coordinate system is recorded by the reference three-axis direction vector through the manual calibration method, and the direction cosine matrix remapping processing is performed on the collected temperature data, the three-axis acceleration data and the three-axis angular velocity data.

[0008] Preferably, the drift sensitivity matrix calculation in S3 includes the following steps: S3-1. Perform 4 rounds of temperature excitation on the inertial measurement unit, each round containing a temperature rise and a temperature drop stage, the temperature change rate is set to ±2℃ / min, record the corresponding temperature change response of the three-axis acceleration data and the three-axis angular velocity data, and the sampling frequency is set to 2000Hz; S3-2. Use the least square method to fit the output temperature change curve of each round of experimental data, extract the slope value of the linear segment, and calculate the average value of the four rounds as the drift response coefficient, corresponding to the six-axis data, and combine to form a 6×1 dimensional drift sensitivity matrix.

[0009] Preferably, the slope response vector extraction in S3-2 further includes the following steps: S3-2-1. The fitting result only retains the segment with a residual mean square error less than 0.002, and the corresponding temperature range needs to cover at least 10℃, and the insufficient one is automatically excluded; S3-2-2. Perform correlation analysis on the temperature drift coefficients of the three-axis acceleration data and the three-axis angular velocity data, and the channel data with a Pearson correlation coefficient less than 0.4 is not included in the final matrix to ensure the accuracy of residual extraction direction.

[0010] Preferably, the multi-path modeling network in S5 further includes the following structure: S5-1. Normalize the temperature value to the interval of−1, 1, input the segmented hyperbolic tangent mapping function, output a 32-dimensional encoding tensor, and use it to guide the convolution path selection mask, and map the normalized temperature value to the corresponding temperature section label index, which is used to activate the matching path and shield the remaining paths; S5-2. Combine the encoding tensor to guide a group of feature extraction sub-networks consisting of three layers to model the temperature zone features, which consists of three one-dimensional convolutions, each containing a 1D convolution operation with a convolution kernel size of 5, and each layer has 64, 128 and 256 convolution channels, respectively, followed by a LayerNorm and a GELU activation function to prevent gradient explosion; S5-3. After each layer of convolution, the output is sent to 4 heads of attention mechanism modules, each using a scaled dot-product attention function, and the output dimension remains the same to build the axial feature context. S5-4. According to the temperature section label index output in S5-1, activate the corresponding path from the five fixed pre-training paths, and output the mask for the remaining paths, so as to make each temperature zone independent.

[0011] Preferably, the S5-4 dynamic path activation structure further comprises the following steps: S5-4-1. Divide the temperature value into five sections: very low temperature -40℃ to -20℃, low temperature -20℃ to 0℃, medium temperature 0℃ to 30℃, high temperature 30℃ to 55℃, and very high temperature 55℃ to 80℃, and establish a path for each temperature section; S5-4-2. Configure a fixed mask coding matrix for each temperature section, such as 1, 0, 0, 0, 0, select the modeling path in the network corresponding to the current temperature zone through matrix multiplication, and output the compensation tensor.

[0012] Preferably, in the S6 multi-path modeling network training process, the AdamW optimizer is used, the initial learning rate is set to 0.001, the weight decay coefficient is set to 0.01, the learning rate is adaptively adjusted to 80% of the original value after every 100 training rounds; each training batch includes 200 sample frames, the total number of training rounds is 300, and the loss function is composed of the L2 residual term in the channel and the drift balance term in the whole channel, with a proportion of 4:1.

[0013] Preferably, the S7 dimensional adjustment process comprises the following steps: S7-1. Use the current temperature value to select the compensation tensor channel group, and perform element-by-element weighting on the six-axis data and the corresponding compensation tensor channel group, with a compensation value range of ±0.01g and ±0.01° / s; S7-2. All compensated three-axis acceleration data and three-axis angular velocity data are processed through a third-order Butterworth low-pass filter with a cutoff frequency set to 0.2 times the original sampling frequency to prevent high-frequency disturbances caused by compensation.

[0014] Compared with the prior art, the advantages of the present application are: (1) From the traditional single-axis or independent-axis modeling, the temperature-inertial response coupling structure is expanded to multi-channel joint modeling, which significantly improves the modeling accuracy and dimensionality of temperature drift.

[0015] (2) Compared with the existing first-order / two-order fitting model, a 9-order nested structure is used, and Bayesian regularization is introduced to improve the stability and generalizability of high-order models in boundary temperature zones.

[0016] (3) Instead of relying on traditional mean / variance removal, a residual-driven dynamic 3σ window mechanism is used to remove irreversible drift data and improve the stability of training samples.

[0017] (4) The nonlinear association between the structure reconstruction temperature of the Transformer and the inertia data has stronger feature capturing ability than the conventional convolution network, and is particularly suitable for complex thermal drift characteristics.

[0018] (5) Instead of using static weight interpolation, a dynamic channel activation mechanism driven by temperature embedding vectors is introduced to activate different modeling sub-networks according to the current temperature zone and to adaptively compensate for weight selection.

[0019] (6) Compared with the traditional whole group attitude or velocity vector correction method, a dimension-by-dimension (each axis) independent correction strategy is proposed, which can avoid the cumulative error caused by the asymmetric thermal drift between dimensions.

[0020] (7) Unlike directly outputting the correction result, the method introduces a third-order Butterworth filter for zero-phase delay post-processing, which effectively suppresses the high-frequency noise of the model and improves the availability of the compensation signal. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 is a whole flowchart of the inertial navigation temperature drift compensation method based on multi-dimensional modeling of the application; DETAILED DESCRIPTION

[0022] Embodiment, please refer to Figure 1 A multi-dimensional modeling-based inertial navigation temperature drift compensation method includes the following steps: S1. Under the condition of the full temperature zone of-40℃ to 80℃, a closed-loop constant temperature control system is used to control the temperature of the inertial measurement unit, and temperature data, three-axis acceleration data and three-axis angular velocity data are collected simultaneously to construct a multi-variable feature matrix with unified time stamp and sample alignment mechanism; Specifically, the "closed-loop constant temperature control system for the inertial measurement unit" refers to placing the inertial measurement unit (IMU) in a closed thermal control cavity with stable temperature control capability during the temperature drift modeling data collection stage, and using ring heating or cooling to control the temperature gradient of the IMU, so that its working temperature can be stably distributed within the entire set range (such as-40℃ to 85℃). The closed-loop temperature control system usually uses a combination of external PID temperature control film heating elements and internal fan convection systems to ensure temperature uniformity and time controllability in the temperature control process, ensuring the stability of the IMU output signal under different temperature zones, thereby providing controllable variable input for subsequent drift modeling.

[0023] S2. After standardization and first-order rotation transformation of the multi-variable feature matrix, five-order nonlinear coupling function groups are constructed using Chebyshev polynomials, with temperature and first-order derivative as input and three-axis acceleration data and three-axis angular velocity data as output, to establish an orthogonal tensor coupling model, and L1 norm constraint is applied to realize sparse modeling; Specifically, the steps of applying standardization and coordinate system first-order rotation transformation to the multivariate feature matrix refer to performing the following two processing operations when preprocessing the multivariate feature matrix composed of data (including temperature, three-axis acceleration and three-axis angular velocity) collected by the inertial measurement unit: All channel data (each column) is processed with zero mean and unit variance: , Where μ is the sample mean and σ is the sample standard deviation.

[0024] Coordinate system first-order rotation transformation maps the collected original three-axis data (inertial + temperature) to an approximately orthogonal reference system with minimum assembly error. This process is performed by rotating after estimating the IMU installation deviation matrix R: , Where R is a three-dimensional rotation matrix, which is generally derived from calibration experiments or fine-tuned after initial estimation by principal component analysis.

[0025] The collected original three-axis data (inertial + temperature) are mapped to an approximately orthogonal reference system with minimum assembly error. This process is performed by rotating after estimating the IMU installation deviation matrix R: Specifically, "constructing a set of five-order nonlinear coupling functions" refers to constructing a set of functions containing five-order or lower nonlinear terms in the multi-dimensional temperature-output modeling process to more accurately express the nonlinear response of inertial output to temperature changes. Each function is a high-order modeling expression for an output channel.

[0026] Function group form: , Where is the drift prediction value of the i-axis, ak is the fitting coefficient, is the temperature, is the offset constant.

[0027] Coupling characteristics: To capture the temperature correlation across channels, this function group achieves coupled modeling by jointly optimizing the parameters of each axis and sharing the temperature vector input, thereby overcoming the problem that traditional independent modeling methods cannot capture the consistency of multi-axis drift.

[0028] Specifically, "establishing an orthogonal tensor coupling model" refers to organizing the output data of all sensor channels (usually three-axis acceleration and three-axis angular velocity, a total of 6 channels) into a high-order tensor structure at different temperature zones and performing orthogonal decomposition on each dimension to extract the potential coupling relationship during deep modeling of the temperature drift of the inertial measurement unit.

[0029] Technical implementation form: Data structure: Construct a three-order tensor where N: sample number; 6: inertial six channels (Ax, Ay, Az, Gx, Gy, Gz); Z: temperature zone number or temperature segmentation dimension.

[0030] Orthogonal tensor decomposition: apply Tucker decomposition or higher-order singular value decomposition (HOSVD) to decompose the tensor into a core tensor Three orthogonal factor matrices , , : , where denotes the n-mode multiplication of a tensor. Orthogonality ensures that the information between factor matrices does not interfere with each other, which is conducive to extracting the dominant mode in temperature drift and the coupling characteristics between channels.

[0031] Specifically, "applying L1 norm constraint" applies L1 norm regularization term to the core tensor G or the key parameter matrix in the network during the optimization process of establishing the tensor coupling model, which is in the form of: , where denotes the L1 norm of the tensor (i.e., the sum of the absolute values of all elements), and λ is the weight coefficient.

[0032] S3. Based on the temperature rise / fall response experimental data of the inertial measurement unit, a set of drift response curves of three-axis acceleration data and three-axis angular velocity data are constructed, and the slope coefficients are calculated to obtain a 6×1 dimensional drift sensitivity matrix, which is used as the initial directional weight matrix for residual extraction; Specifically, constructing a set of drift response curves of three-axis acceleration data and three-axis angular velocity data means collecting IMU data of each channel under multiple temperature zones, subtracting the calibration output value at the standard temperature, and obtaining a set of response curves of thermal drift error changing with temperature. Each response curve reflects the offset trend of the data of an axis changing with temperature.

[0033] Specific steps: record the six-axis output of the IMU under multiple temperature set points; take the data at 25°C or a certain constant temperature reference point as the reference to calculate the offset value; fit six independent response curves, each corresponding to a channel (Ax, Ay, Az, Gx, Gy, Gz).

[0034] Curve form: the response curve can be fitted using a high-order polynomial or a neural network, and the numerical value is used for subsequent model supervised learning training or as an evaluation index baseline.

[0035] S4. Perform Mahalanobis distance analysis on the residual data obtained under the drift sensitivity matrix, calculate the normalized distance based on the sample covariance matrix, eliminate samples outside the 95% confidence interval, and construct a high-confidence training subset; Specifically, "constructing a high-confidence training subset" refers to selecting a subset of samples from the complete modeling sample set that meets the following conditions: Kalman filter residual is less than a dynamic threshold (such as 3σ); sampling temperature zone coverage is uniform and no concentrated accumulation; drift trend continuity is good and no abrupt segment; temperature change rate (dT / dt) is less than a preset threshold (such as 1°C / min).

[0036] S5. Constructing a multi-path modeling network including a temperature thermal coding embedding module, three layers of normalized convolution channels, a parallel attention mechanism, and a dynamic path selection structure, inputting the contracted high-confidence training subset into the multi-path modeling network, and performing cross-axis deep modeling on the temperature-output relationship; Specifically, "performing cross-axis deep modeling on the temperature-output relationship" refers to, in the design of a neural network model, not only modeling the temperature drift curves of each axis sensor independently, but also inputting all six channels as a whole into the structure, and performing interactive modeling between dimensions in a deep network (especially an attention or residual coupling layer), so as to capture the potential thermal drift synergy or coupling mode between axes.

[0037] Introducing a cross-fusion structure, such as a multi-channel residual fusion module, in the deep layer (≥3rd layer); Using a multi-head attention mechanism to allocate the drift contribution degree between different axes under each temperature zone; In the training, the six-channel outputs are uniformly optimized to maintain the error directionality and amplitude consistency.

[0038] S6. Training the multi-path modeling network using a target function composed of a channel-wise L2 constraint loss term and a residual feedback weighted term, adopting a channel-wise, fixed-step, AdamW optimization strategy for iterative optimization, and obtaining a steady-state temperature drift compensation tensor; Specifically, "a target function composed of a loss term and a residual feedback weighted term" refers to an optimization target function used when training a multi-path inertial drift modeling network, which is composed of two parts: Loss Term: Usually the mean square error (MSE) between the predicted output and the actual drift true value; Residual Feedback Weighted Term: Refers to the introduction of a reverse weighted index of the residual amplitude of each temperature zone in the previous training iteration period, which is used to improve the model's learning attention to edge temperature zones and small sample temperature zones.

[0039] The target function is as follows: , Where is the residual of the i-th temperature zone, For its weight, the inverse proportion of the residual mean of the last iteration is obtained (that is, the greater the residual, the higher the weight), so as to realize the adaptive optimization focusing of the temperature distribution in the model training.

[0040] S7. With temperature data, three-axis acceleration data and three-axis angular velocity data as input, input into the multi-path modeling network which has been trained, call the temperature drift compensation tensor, respectively, adjust the six-axis output row by dimension, complete the active compensation of the inertial measurement unit temperature drift; Specifically, the temperature drift compensation tensor refers to the multi-dimensional array structure of the six-axis sensor error prediction obtained by the multi-path inertial drift modeling network under different temperature zone input conditions. This structure can be directly used for subsequent real-time compensation of data.

[0041] The tensor dimension is defined as [Z, 6], where Z is the number of temperature zones (such as five sections), and 6 represents six channels of three-axis acceleration and three-axis angular velocity. Each element represents the predicted drift error of a channel in a certain temperature zone. The tensor, as a static cache of model output, is deployed in the computing unit of the navigation system to perform compensation mapping. This tensor is different from the traditional coefficient, but a nonlinear dynamic response expression learned by network structure, which can be dynamically adjusted for accurate temperature drift correction.

[0042] The multi-path modeling network introduces a five-section temperature mapping mask activation structure, which activates and suppresses different paths in the network based on temperature section labels, dynamically adapting the cross-temperature zone modeling performance.

[0043] Specifically, the five-section temperature mapping mask activation structure refers to the sparse activation path structure composed of the five temperature intervals (such as very low, low, medium, high, and very high) mapped by the temperature value input. Each temperature zone controls the opening and closing of a specific network sub-path through a mask mechanism, thereby realizing temperature adaptive modeling.

[0044] It is composed of the following components: temperature discriminator, which determines which section of the five sections the current input temperature zone belongs to according to the thermal coding vector; Mask generation module, generating a set of 5-bit binary masks like [1, 0, 0, 0, 0]; Mask control activation, through the mask, the five independent modeling branches are activated or masked, and only the branch structure corresponding to the matching temperature zone is activated.

[0045] Specifically, the inertial measurement unit selects a MEMS level six-axis sensor module, and the temperature response range is set to -40°C to 85°C; the data sampling frequency is set to 200Hz. The method of removing unstable samples in S2 step adopts three-axis fusion residual analysis, estimates the difference between the state value and the original observation through Kalman filtering, and dynamically removes it by applying the three standard deviation principle. The temperature response model constructed in S3 is a nine-order polynomial, and the model training adopts Bayesian regularization to control the variance of the high-order term coefficient to prevent overfitting. The modeling network in S4 adopts a three-layer residual convolution module, followed by a four-head attention mechanism module, each containing two 128-dimensional fully connected layers and a Softmax normalization process. In S5, the thermal coding module linearly normalizes the temperature to the [-1, 1] interval, and then maps it to a 32-dimensional temperature zone embedding vector through the tanh family activation function for path activation. The drift tensor extracted in S6 is divided into 10 groups according to the temperature zone, each containing 6 compensation channels. S7 adopts a channel-by-channel weighted correction method, and the output is smoothed by a Butterworth low-pass filter.

[0046] The construction of the multivariate feature matrix in S1 includes the following steps: S1-1. Configure sampling points in the full temperature range of -40°C to 80°C, set the constant temperature point to every 2.5°C in the range of -40°C to 80°C, a total of 49 points, use a closed-loop constant temperature control system to make the stable error of each point less than ±0.2°C, and the data collection time of each temperature point is not less than 30 minutes, and the sampling frequency is set to 1000Hz; S1-2. After aligning the collected temperature data, three-axis acceleration data and three-axis angular velocity data by timestamp, a floating-point matrix of N rows and 7 columns is formed, and the column vectors are time stamp, temperature value, X / Y / Z direction acceleration value, X / Y / Z direction angular velocity value, and 0 mean value unit variance standardization is used.

[0047] Specifically, the Kalman filter adopts a first-order state model, the state transition matrix is a unit matrix, the observation matrix is a unit matrix, and the noise covariance matrix is set as a diagonal matrix (σ²=0.002) through prior experience. The residual calculation method is to subtract the filtered estimate value from the observed data, and the 3σ dynamic window adjusts the boundary threshold in real time by changing the residual distribution statistical characteristics with the temperature interval, improving the sample removal accuracy.

[0048] The S1-2 feature matrix data structure generation further includes the following steps: S1-2-1. Use the three-dimensional Euclidean norm of three-axis acceleration data and three-axis angular velocity data to remove samples whose first derivative change rate exceeds 3 times the average value; Specifically, the "three-dimensional Euclidean norm" refers to the module or two-norm of a three-dimensional vector (such as three-axis acceleration or three-axis angular velocity) in Euclidean space.

[0049] S1-2-2. The inertial measurement unit is initially fixed in a known direction coordinate system, and the reference three-axis direction vector is recorded by a manual calibration method. The collected temperature data, three-axis acceleration data, and three-axis angular velocity data are subjected to direction cosine matrix remapping processing.

[0050] Specifically, the nine-order polynomial function is in the form of: , where T is the temperature input, and a_i is the coefficient parameter. The maximum a posteriori estimation is based on the Laplace prior to punish high-order terms, and the EM algorithm is used to estimate the coefficients and noise variance during the training process to ensure the stability of the model at the edge temperature zone.

[0051] Specifically, the direction cosine matrix is established as where each element represents the cosine value of the b j-axis in the n system i-axis direction, and satisfies: ,

[0052] The remapping acceleration and angular velocity data are: The three-axis original data are remapped to the data in the inertial coordinate system through the matrix:

[0053] Temperature data processing method: If the temperature data is collected by independent sensors on each axis (such as 3-point thermistors), the space mapping is also performed according to the sensor layout direction to form a vector field temperature representation, and then combined into the temperature drift compensation model.

[0054] The mechanical installation error of the inertial measurement unit and the navigation main body is modeled as a 3x3 rotation matrix The drift sensitivity matrix calculation in S3 includes the following steps: S3-1. Perform 4 rounds of temperature excitation on the inertial measurement unit, each round containing a temperature rise and a temperature drop stage, the temperature change rate is set to ±2℃ / min, record the three-axis acceleration data and three-axis angular velocity data corresponding to the temperature change response, and the sampling frequency is set to 2000Hz; S3-2. Use the least squares method to fit the output temperature change curve of each round of experimental data, extract the slope value of the linear section, and calculate the average value of the four rounds as the drift response coefficient, corresponding to the six-axis data, and combine to form a 6x1 dimensional drift sensitivity matrix.

[0055] Specifically, it is a 6-dimensional column vector representing the sensitivity weight coefficient of each channel in the inertial measurement unit (IMU) to temperature change, in the form of: , where each Sensitivity of the drift response corresponding to the axis (such as Ax, Gx) to temperature variation, usually obtained by training model or prior experimental regression.

[0056] Specifically, each batch block adopts a BatchNorm standardization operation, and the convolution kernel weight initialization method adopts the Kaiming method. The input tensor dimension is in the format [batch, channel, length], and the channel convolution processes each axis data independently at each time point. The residual connection method is direct jump connection without introducing convolution compression to ensure the efficiency of gradient propagation.

[0057] The S3-2 slope response vector extraction further includes the following steps: S3-2-1. The fitting result only retains the segment with a residual mean square error less than 0.002, and the corresponding temperature range needs to cover at least 10°C, and the insufficient one is automatically excluded; S3-2-2. Correlation analysis is performed on the temperature drift coefficients of three-axis acceleration data and three-axis angular velocity data, and the channel data with a Pearson correlation coefficient less than 0.4 is not included in the final matrix to ensure the accuracy of residual extraction direction.

[0058] Specifically, each attention head contains three fully connected layers (Query, Key, Value), and the dimensions are all set to 64. After point multiplication attention calculation, Dropout=0.1 is used for anti-overfitting processing. The four-head attention output is spliced and then mapped to the original dimension through a fully connected layer, and the fusion method adopts weighted summation and residual fusion followed by LayerNorm processing.

[0059] The multi-path modeling network in S5 further includes the following structure: S5-1. Normalize the temperature value to the interval of -1, 1, input the hyperbolic tangent mapping function, and output a 32-dimensional encoding tensor, which is used to guide the convolution path selection mask; Specifically, the basic hyperbolic tangent function is constructed as follows: The hyperbolic tangent function is defined as: , which continuously changes between [-1, 1] and can smoothly express the input nonlinear characteristics.

[0060] Temperature section processing: The input temperature value T is divided into five temperature intervals (for example: <-20℃, -20~20℃, 20~40℃, >40℃), and different mapping function parameters are set for each section , ; , where is the center temperature of the i-th section.

[0061] Fusion processing: Finally, all segment outputs are spliced into an extended dimension input:

[0062] S5-2. In combination with the encoding tensor, guide a set of feature extraction subnetworks composed of three layers to model the temperature zone features, which are composed of three one-dimensional convolution layers, each containing a 1D convolution operation with a kernel size of 5, and each layer has 64, 128, and 256 convolution channels, respectively, followed by a LayerNorm and a GELU activation function to prevent gradient explosion; S5-3. After each convolution, the output is sent to a 4-head attention mechanism module, each head uses a scaled dot-product attention function, and the output dimension remains the same to build the axial feature context; Specifically, for the improved multi-head self-attention structure, it refers to splitting the input features into 4 parallel attention heads for query-key-value mapping, and then integrating the weighted output structure. Each head is calculated as follows: , Where , , is the query, key, and value matrix of the i-th head.

[0063] S5-4. According to the temperature segment label index output by S5-1, activate the corresponding path from the five fixed pre-training paths, and output a mask for the remaining paths to make each temperature zone modeling independent.

[0064] Specifically, the standard form of the tanh family activation function is tanh(x), which further nonlinearly maps the normalized temperature to generate a temperature embedding tensor as a reference input for controlling the activation of each path in the subsequent modeling network. This hot encoding is used to drive the adaptive selection of path structures in different temperature zones and improve the modeling generalization ability.

[0065] The S5-4 dynamic path activation structure further includes the following steps: S5-4-1. Divide the temperature value into five segments: very low temperature -40℃ to -20℃, low temperature -20℃ to 0℃, medium temperature 0℃ to 30℃, high temperature 30℃ to 55℃, and very high temperature 55℃ to 80℃, and establish a path for each temperature interval. S5-4-2. Configure a fixed mask encoding matrix for each temperature interval, such as 1, 0, 0, 0, 0, select the modeling path in the network corresponding to the current temperature zone through matrix multiplication, and output a compensation tensor.

[0066] Specifically, the five-dimensional mask vector [1, 0, 0, 0, 0] is used to activate a specific temperature zone channel in the five-zone temperature mapping structure. After the matrix is matched with the temperature input value, the model only activates the corresponding interval neurons, which is specifically expressed as: , Specifically, the sliding integral window size is set to 128 frames, and the statistical mean is used to suppress transient fluctuation response. Each temperature zone tensor is a six-dimensional vector corresponding to three-axis acceleration and angular velocity. The tensor library contains 10 groups of temperature zone distributions, and the structure is a three-tuple table structure [temperature zone index, channel ID, response value].

[0067] In the multi-path modeling network training process in S6, the AdamW optimizer is used, the initial learning rate is set to 0.001, the weight decay coefficient is set to 0.01, the learning rate is adaptively adjusted to 80% of the original value after every 100 training rounds; each training batch includes 200 sample frames, the total number of training rounds is 300, and the loss function is composed of the intra-channel L2 residual term and the full-channel drift balancing term linearly weighted, with a proportion of 4:1.

[0068] Specifically, the weight decay coefficient refers to the regularization factor of adding a parameter norm penalty term in the training objective function.

[0069] Specifically, the Butterworth filter implementation adopts an IIR structure, and the forward and reverse filters calculate the filter delay items and merge the outputs to ensure that the output is time-aligned with the original signal. The low-pass filter calculation process adopts digital filtering, and the programming language can be Python or C language, and is transplanted into an embedded processor.

[0070] The step-by-step repair process in S7 includes the following steps: S7-1. Use the current temperature value to select the compensation tensor channel group, and perform element-by-element weighting on the six-axis data and the corresponding compensation tensor channel group, with a compensation value range of ±0.01g and ±0.01° / s; S7-2. All compensated three-axis acceleration data and three-axis angular velocity data are processed by a third-order Butterworth low-pass filter, with a cutoff frequency set to 0.2 times the original sampling frequency to prevent high-frequency disturbances caused by compensation.

[0071] The above shows and describes the basic principles, main features and advantages of the present application; those skilled in the art should understand that the present application is not limited to the above examples, the above examples and descriptions in the specification are only preferred examples of the present application and are not intended to limit the present application, various changes and improvements can be made to the present application without departing from the spirit and scope of the present application, and these changes and improvements all fall within the scope of the claimed present application; the scope of protection of the present application is defined by the appended claims and their equivalents.

Claims

1. A method for compensating temperature drift in inertial navigation based on multi-dimensional modeling, characterized in that, The method comprises the following steps: S1. Under the condition of the full temperature range of-40 DEG C to 80 DEG C, a closed-loop constant temperature control system is used for fixed-point temperature control of an inertial measurement unit, and temperature data, three-axis acceleration data and three-axis angular velocity data are synchronously collected to construct a multivariate feature matrix with unified time stamp and sample alignment mechanism; S2. After standardization and first-order rotation transformation of the coordinate system are applied to the multivariate feature matrix, a five-order nonlinear coupling function group is constructed by using Chebyshev polynomial, temperature and first derivative are taken as inputs, and the three-axis acceleration data and the three-axis angular velocity data are taken as outputs, an orthogonal tensor coupling model is established, and L1 norm constraint is applied to realize sparse modeling; S3. Based on the temperature rise / response experiment data of the inertial measurement unit, a group of drift response curves of the three-axis acceleration data and the three-axis angular velocity data are constructed, slope coefficients are calculated respectively, and a 6*1 dimensional drift sensitivity matrix is obtained as an initial weight matrix of the directionality of residual extraction; S4. Mahalanobis distance analysis is performed on the residual data obtained under the action of the drift sensitivity matrix, normalized distance calculation is performed according to the sample covariance matrix, samples outside the 95% confidence level are removed, and a high-confidence training subset is constructed; S5. A multi-path modeling network including a temperature hot encoding embedding module, three layers of normalized convolution channels, a parallel attention mechanism and a dynamic path selection structure is constructed, the shrunken high-confidence training subset is input into the multi-path modeling network, and cross-axis deep modeling is performed on the temperature-output relationship; S6. The multi-path modeling network is trained by using a target function composed of an L2 constraint loss term in the channel and a residual feedback weighting, a split-channel, fixed-step, AdamW optimization strategy is adopted for iterative optimization, and a steady-state temperature drift compensation tensor is obtained; S7. The temperature data, the three-axis acceleration data and the three-axis angular velocity data are input into the trained multi-path modeling network, the temperature drift compensation tensor is called, and the six-axis output is corrected dimension by dimension, and active compensation of the temperature drift of the inertial measurement unit is completed; The multi-path modeling network introduces a five-section temperature mapping mask activation structure, activates and suppresses different paths in the network based on temperature section labels, and dynamically adapts the cross-temperature zone modeling performance.

2. The method according to claim 1, wherein, The multivariate feature matrix construction in S1 comprises the following steps: S1-1. Under the condition of the full temperature range of-40 DEG C to 80 DEG C, sampling points are configured, the constant temperature points are set to be one sampling point every 2.5 DEG C in the range from-40 DEG C to 80 DEG C, a total of 49 points, the closed-loop constant temperature control system is used to make the stable error of each point be less than ±0.2 DEG C, the data collection time of each temperature point is not less than 30 minutes, and the sampling frequency is set to 1000 Hz; S1-2. The collected temperature data, the three-axis acceleration data, and the three-axis angular velocity data are aligned by time stamp to form an N-row and 7-column floating-point matrix, and the column vectors are time stamp, temperature value, X / Y / Z direction acceleration value, and X / Y / Z direction angular velocity value in sequence. A 0-mean unit variance standardization process is used.

3. The method of claim 2, wherein, The N-row and 7-column floating-point matrix in S1-2 further includes the following steps: S1-2-1. The three-dimensional Euclidean norm of the three-axis acceleration data and the three-axis angular velocity data is used to remove samples with a first derivative change rate exceeding 3 times the average value of the standard deviation; S1-2-2. The inertial measurement unit is initially fixed in a known direction coordinate system, and the reference three-axis direction vector is recorded by a manual calibration method. The collected temperature data, the three-axis acceleration data, and the three-axis angular velocity data are subjected to direction cosine matrix remapping processing.

4. The method of claim 1, wherein, The drift sensitivity matrix calculation in S3 includes the following steps: S3-1. Four rounds of temperature excitation are performed on the inertial measurement unit, each round including a temperature rise and a temperature drop stage, the temperature change rate is set to ±2℃ / min, the corresponding temperature change response of the three-axis acceleration data and the three-axis angular velocity data is recorded, and the sampling frequency is set to 2000Hz; S3-2. The least squares method is used to fit the output temperature change curve of each round of experimental data, the linear segment slope value is extracted, and the average value of the four rounds is calculated as the drift response coefficient, which corresponds to the six-axis data, and is combined to form the 6×1 dimension drift sensitivity matrix.

5. The method of claim 4, wherein, S3-2 further includes the following steps: S3-2-1. The fitting result only retains the segment with a residual mean square error less than 0.002, and the corresponding temperature range needs to cover at least 10℃, otherwise it is automatically removed; S3-2-2. The temperature drift coefficients of the three-axis acceleration data and the three-axis angular velocity data are subjected to correlation analysis, and the channel data with a Pearson correlation coefficient less than 0.4 is not included in the final matrix to ensure the accuracy of residual extraction direction.

6. The method of claim 1, wherein, The multi-path modeling network in S5 further includes the following structure: S5-1. The temperature value is normalized to the interval of -1, 1, input into the segmented hyperbolic tangent mapping function, and a 32-dimensional encoding tensor is output, which is used to guide the convolution path selection mask, and the normalized temperature value is mapped to the corresponding temperature section label index, which is used to activate the matching path and shield the remaining paths; S5-2. Combined with the encoding tensor, a group of feature extraction sub-networks consisting of three layers are used for temperature zone feature modeling. The sub-networks consist of three one-dimensional convolutions, each containing a 1D convolution operation with a convolution kernel size of 5, and each layer has 64, 128, and 256 convolution channels, respectively. Each layer is followed by a LayerNorm and a GELU activation function to prevent gradient explosion; S5-3. The output of each convolution is sent to 4 heads of attention mechanism modules, each using a scaled dot-product attention function, and the output dimensions remain consistent to build the axial feature context; S5-4. According to the temperature section label index output by S5-1, the corresponding path is activated from five fixed pre-trained paths, and the remaining paths are masked, so that each temperature zone modeling is independent.

7. The method of claim 6, wherein, The S5-4 further comprises the following steps: S5-4-1. The temperature value is divided into five segments of extremely low temperature -40℃ to -20℃, low temperature -20℃ to 0℃, medium temperature 0℃ to 30℃, high temperature 30℃ to 55℃, and extremely high temperature 55℃ to 80℃, and a path is established for each temperature segment respectively; S5-4-2. A fixed mask coding matrix is configured for each temperature interval, a modeling path corresponding to the current temperature zone in the network is selected through matrix multiplication, and a compensation tensor is output.

8. The method of claim 1, wherein, In the S6, during the training process of the multi-path modeling network, an AdamW optimizer is used, the initial learning rate is set to 0.001, the weight decay coefficient is set to 0.01, the learning rate is adaptively adjusted to 80% of the original value after every 100 rounds of training; each training batch includes 200 sample frames, the total number of training rounds is 300, the loss function is composed of an L2 residual term in the channel and a whole-channel drift balancing term linearly weighted, with a proportion of 4:

1.

9. The method of claim 1, wherein, The S7 comprises the following steps: S7-1. The current temperature value is used to select a compensation tensor channel group, the six-axis data are respectively weighted with the corresponding compensation tensor channel group element by element, and the compensation value range is limited to ±0.01g and ±0.01° / s; S7-2. All compensated three-axis acceleration data and three-axis angular velocity data are processed through a third-order Butterworth low-pass filter, and the cutoff frequency is set to 0.2 times the original sampling frequency to prevent high-frequency disturbance caused by compensation.

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