Automatic strapdown inertial navigation calibration test method of temperature control biaxial rate position turntable

Abstract

The invention relates to the technical field of calibration test, and particularly discloses a strapdown inertial navigation automatic calibration test method of a temperature control biaxial rate position turntable. Comprising the following steps: S1, multi-dimensional error modeling and layered calibration architecture: constructing a comprehensive error model containing a sensor scale factor error, an installation non-orthogonal error, a zero offset error, a cross axis coupling error and a temperature related error; s2, a wide temperature range self-adaptive compensation mechanism: carrying out heat preservation at a preset temperature point and executing turntable positioning and rate movement; s3, performing automatic data processing and parameter estimation; and S4, performing real-time error correction and dynamic verification: performing real-time error correction based on the estimated parameters, and evaluating navigation performance indexes such as position, speed and attitude precision. Through technical innovation, high-precision, automatic and wide-temperature-range calibration of the strapdown inertial navigation system is realized, and the method is suitable for aerospace, intelligent equipment and other scenes with strict navigation precision requirements, and has remarkable engineering application value and market competitiveness.

Description

Technical Field

[0001] The present invention relates to the technical field of calibration testing, and specifically to a strapdown inertial navigation automatic calibration testing method for a temperature-controlled two-axis rate position turntable. Background Art

[0002] In an inertial navigation system (INS), the calibration accuracy of a strapdown inertial navigation system (SINS) directly affects the navigation performance, and its core lies in the accurate estimation of the error parameters of sensors (accelerometers, gyroscopes). The existing calibration methods have the following limitations: 1. Incomplete error modeling: Traditional models usually only consider static errors (such as scale factors, zero biases), ignoring temperature-related errors (such as scale factor drift caused by temperature, installation error changes) and cross-axis coupling errors, resulting in insufficient error compensation in wide temperature ranges or dynamic scenarios. 2. The calibration process depends on high-precision equipment: Traditional hierarchical calibration requires a high-precision turntable (angle accuracy requirement reaches 0.01°), with high hardware costs and complex operations, making it difficult to adapt to low-cost scenarios. 3. Single temperature compensation method: Mostly uses linear interpolation or fixed coefficient compensation, unable to capture the non-linear relationship between errors and temperature, with insufficient compensation accuracy in the wide temperature range of -40°C to 60°C. 4. Low degree of automation: Data acquisition, processing, and parameter estimation require manual intervention, with a cumbersome process and easy introduction of time synchronization errors, making it difficult to meet the requirements of batch calibration. 5. Lack of dynamic verification: Traditional calibration only verifies through static postures, lacking an evaluation of the error correction effect in dynamic scenarios (such as angular rate ≥ 100° / s), resulting in a deviation between the calibration result and actual application. Summary of the Invention

[0003] Aiming at the deficiencies of the existing technology, the present invention provides a strapdown inertial navigation automatic calibration testing method for a temperature-controlled two-axis rate position turntable, which solves the problems in the above background art.

[0004] To achieve the above objectives, the present invention is realized through the following technical solutions: A strapdown inertial navigation automatic calibration testing method for a temperature-controlled two-axis rate position turntable, including the following steps: S1. Multidimensional error modeling and hierarchical calibration architecture: Construct a comprehensive error model including sensor scale factor error, installation non-orthogonality error, zero bias error, cross-axis coupling error, and temperature-related error; adopt a hierarchical calibration strategy, extract static error parameters through initial discrete calibration, and combine system-level joint calibration to globally estimate dynamic error parameters such as the installation error matrix, cross-coupling coefficient, and temperature-related parameters, reducing the dependence on the accuracy of the calibration turntable; S2. Wide temperature range adaptive compensation mechanism: Insulate at preset temperature points and perform turntable positioning and rate movement, use machine learning models such as neural networks or Gaussian processes to establish a non-linear mapping relationship between sensor errors and temperature, and achieve precise temperature adaptive compensation of sensor outputs; S3. Automated data processing and parameter estimation: Automatically collect IMU data through the host computer and parse it according to the preset protocol. Integrate automated algorithm modules for integrated error parameter estimation, temperature compensation fitting, and state estimation. Adopt filtering technology to achieve full-process automated processing from data collection to result output; S4. Real-time error correction and dynamic verification: Implement real-time error correction based on the estimated parameters, and verify the effectiveness of the calibration results under dynamic conditions by evaluating navigation performance indicators such as position, speed, and attitude accuracy.

[0005] Preferably, the sensor includes an accelerometer and a gyroscope, and the accelerometer error model is: ; Where: is the actual output vector of the accelerometer, is the true acceleration vector in the body coordinate system; is the scale factor matrix, is the temperature-related change in the scale factor error matrix; is the misalignment error matrix, is the temperature-related change in the misalignment error matrix; is the cross-axis sensitivity matrix, describing the coupling effect of acceleration between axes; is the temperature-related bias error vector; In the 12-position method of discrete calibration, the inertial navigation is sequentially placed in 12 static postures of up / down Z-axis / north / south XY, up / down Y-axis / north / south X, and up / down X-axis / north / south Y. Each posture is maintained for more than 120 seconds and the mean value is collected. By fitting the equation with the least squares method, the scale factor matrix , the misalignment error matrix , the cross-axis sensitivity matrix and the temperature-related bias are solved.

[0006] Preferably, the gyroscope error model is: ; Where: is the actual output vector of the gyroscope, is the true angular velocity vector controlled by the turntable; , and , are respectively the scale factor error matrix of the gyroscope and its temperature change, the misalignment error matrix and its temperature change; is the cross-axis sensitivity matrix of the gyroscope; is the temperature-related bias error vector, is a random noise vector containing angle random walk and rate random walk; In the rate method calibration, the turntable is controlled to rotate uniformly around three axes at multiple rates of ±30° / s, ±60° / s, and ±90° / s, and the acceleration / deceleration transition process data is collected. After filtering out high-frequency noise through Fourier transform, the genetic algorithm is combined to optimize parameter estimation and improve the gyroscope cross-axis sensitivity matrix. observability.

[0007] Preferably, the temperature-dependent zero bias error The temperature-related parameters are fitted using a machine learning model, and the zero bias error is expressed as: ; in, For the coordinate axis Nonlinear function of Read the IMU mainboard temperature in real time , online correction through pre-trained machine learning models , forming a closed-loop process of data collection, model fitting, and real-time compensation; supporting incremental learning of multi-temperature point data and automatically updating the compensation model to adapt to sensor aging drift.

[0008] Preferably, the hierarchical calibration strategy includes: Discrete calibration stage: The static data of the accelerometer is collected by the 12-position method, the dynamic data of the gyroscope is collected by the rate method and the orthogonal rotation method, and the initial scale factor error, zero bias error and installation error are solved by the least square method; System-level joint calibration: A state space model is established based on the strapdown navigation equation, and the navigation velocity error and attitude angle error are used as measurement inputs. The process noise covariance matrix is ​​dynamically adjusted through the adaptive Kalman filter (ACKF), and the temperature-related error parameters and the installation error matrix are jointly estimated. The strapdown navigation equation is as follows: ; ; in, is the carrier speed, is the transformation matrix from the carrier to the navigation system, is the specific force output of the accelerometer, is the Earth's rotation angular velocity, is the angular velocity of the navigation system relative to the Earth; Preferably, the state vector of the system-level calibration is: ; in: is the velocity error vector, is the attitude angle error vector, represents the matrix vectorization operation, which is used to extract the coupling parameters of the scale factor and the installation error matrix, and are the random noise parameters of the accelerometer and gyroscope respectively, and are modeled as a Gaussian - Markov process; The unscented Kalman filter is introduced to handle the non - linear characteristics of the strap - down navigation equation, and the state distribution is accurately approximated through Sigma - point sampling; the turntable is controlled to perform the dynamic movement of maintaining Z - up Y - north for a long time and quickly switching the composite attitude, improving the rank number of the observability matrix of the error parameters.

[0009] Preferably, the automatic data processing includes: High - precision synchronization mechanism: The IEEE1588 precise time protocol is used to achieve nanosecond - level synchronization of IMU data and turntable control commands, and the synchronization error ≤1 μs, ensuring the strict time alignment of the motion attitude and the sensor output; Intelligent data management: Store data in the format of Temperature_Attitude_Rate_Timestamp.csv, including the real - time Euler angles / quaternions of the turntable, the original output of the IMU, the data of the temperature sensor, and the checksum; an integrated database trigger automatically classifies the data, supporting subsequent batch processing and machine learning model training.

[0010] Preferably, the preset temperature points cover the working temperature range of the sensor, the temperature interval ≤10 °C, and each temperature point is kept warm for ≥2 hours to ensure that the internal temperature gradient of the IMU ≤±0.5 °C; Temperature control accuracy guarantee: The incubator uses PID closed - loop control, and ≥3 groups of temperature sensors are arranged on the surface of the IMU to monitor the uniformity in real - time. During the heat - preservation period, the data segments with excessive temperature fluctuations are automatically skipped; the heating / cooling rate is controlled within 5 °C / min to avoid the thermal stress error caused by sudden temperature changes.

[0011] Preferably, the accuracy verification steps include: Multi - dimensional evaluation system: Calculate indicators such as zero - bias stability, scale - factor error, root - mean - square of attitude angle error, and velocity error drift rate; use Monte Carlo simulation to calculate the parameter estimation uncertainty, and the formula is: ; where, is the 95% confidence level expansion factor, is the - th simulation parameter estimation value, is the mean value; Control the turntable to execute the preset maneuvering trajectory, and verify the response accuracy of the compensation model in the dynamic scenario by comparing the attitude solved by the IMU and the actual attitude of the turntable, filling the gap of traditional static verification.

[0012] According to the strapdown inertial automation calibration test method for a temperature-controlled two-axis rate-position turntable, a storage medium is proposed, which stores a computer program. When the computer program is executed by a processor, it implements the steps of the strapdown inertial automation calibration test method for the temperature-controlled two-axis rate-position turntable, and includes: A calibration result visualization module for visualizing the error parameter convergence curve and comparing the sensor outputs before and after temperature compensation; An algorithm interface that supports the access and verification of custom machine learning models such as LSTM and Transformer, forming an open and extensible calibration platform.

[0013] The present invention provides a strapdown inertial automation calibration test method for a temperature-controlled two-axis rate-position turntable, which has the following beneficial effects: Through technologies such as multi-dimensional error modeling, wide-temperature-range adaptive compensation, automated processing, and dynamic verification, the calibration accuracy and efficiency of the strapdown inertial navigation system are significantly improved. The specific advantages are as follows: 1. Comprehensive error modeling and hierarchical calibration, reducing equipment dependence: Construct a comprehensive model that includes scale factor error, installation non-orthogonality error, zero bias error, cross-axis coupling error, and temperature-related error, solving the problem that traditional models ignore temperature sensitivity and inter-axis coupling, making parameter estimation closer to the actual working state; Extract static errors (such as scale factor and zero bias) through discrete calibration, and combine system-level joint calibration to estimate dynamic errors (such as temperature-related parameters and installation error matrix), relaxing the turntable angle accuracy requirement from 0.01° to 0.1°, improving the robustness of parameter estimation while reducing hardware costs.

[0014] 2. Wide-temperature-range adaptive compensation, improving the correction accuracy of temperature-sensitive errors: Use models such as neural networks and Gaussian processes to establish a non-linear mapping relationship between errors and temperature, supporting adaptive compensation in the wide temperature range of -40°C to 60°C. Compared with traditional linear methods, the zero bias error compensation accuracy is improved, the IMU temperature is read in real time and the error is corrected online through a pre-trained model, combined with incremental learning at multiple temperature points, automatically adapting to sensor aging drift and extending the calibration period.

[0015] 3. Full-process automated processing, improving calibration efficiency and data reliability: Use the IEEE1588 protocol to achieve nanosecond-level synchronization (error ≤ 1μs) of IMU data and turntable commands, ensuring time alignment; The data is stored in a standardized format and automatically classified, supporting batch processing and machine learning model training, reducing manual intervention errors, integrating error parameter estimation, temperature compensation fitting, and state estimation modules, and combining adaptive Kalman filter (ACKF) and unscented Kalman filter (UKF) to achieve full automation from data acquisition to result output, with an efficiency improvement of more than 50%.

[0016] 4. Dynamic verification and multi-dimensional evaluation to ensure actual application performance: By controlling the turntable to execute maneuvering trajectories such as sinusoidal sweep frequency and step rotation, comparing the attitude solved by the IMU with the actual attitude of the turntable (accuracy ≤ 0.05°), filling the gap of traditional static verification, and ensuring the effectiveness of the calibration results under dynamic conditions such as angular rate ≥ 100° / s; introducing Monte Carlo simulation (≥ 1000 times) to calculate the uncertainty of parameter estimation, and evaluating indicators such as zero bias stability and root mean square (RMS) of attitude angle error, constructing a comprehensive accuracy verification system, and reducing the uncertainty of parameter estimation.

[0017] 5. Advantages of engineering application: Through PID closed-loop temperature chamber control, multi-sensor temperature monitoring and gradient limitation (≤ ±0.5°C), accurate estimation of temperature-sensitive parameters is ensured, and the model generalization ability is significantly improved; the random noise of the gyroscope is decomposed into angle random walk (ARW) and rate random walk (RRW), and they are respectively modeled and compensated; the observability of the cross-axis sensitivity matrix is optimized by genetic algorithm to solve the problem of estimating the cross-axis coupling error.

[0018] In summary, through technological innovation, the present invention realizes high-precision, automated, and wide-temperature calibration of the strapdown inertial navigation system, which is applicable to scenarios with strict requirements for navigation accuracy such as aerospace and intelligent equipment, and has significant engineering application value and market competitiveness. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic flow chart of the strapdown inertial navigation automated calibration test method for the temperature-controlled two-axis rate position turntable of the present invention; DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0021] As Figure 1 shown, the present invention provides a technical solution: a strapdown inertial navigation automated calibration test method for a temperature-controlled two-axis rate position turntable, including the following steps: S1. Multi-dimensional error modeling and hierarchical calibration architecture: Construct a comprehensive error model including sensor scale factor error, installation non-orthogonality error, zero bias error, cross-axis coupling error, and temperature-related error; adopt a hierarchical calibration strategy, extract static error parameters through initial discrete calibration, and combine system-level joint calibration to globally estimate dynamic error parameters such as the installation error matrix, cross-coupling coefficient, and temperature-related parameters, reducing the dependence on the accuracy of the calibration turntable; S2. Wide-temperature-range adaptive compensation mechanism: Insulate at preset temperature points (-40°C, -20°C, 0°C, 20°C, 40°C, 60°C) and perform turntable positioning and rate movement. Use machine learning models such as neural networks or Gaussian processes to establish a non-linear mapping relationship between sensor errors (including zero bias, scale factor, installation error) and temperature, and achieve precise temperature adaptive compensation for sensor output; S3. Automatic data processing and parameter estimation: Automatically collect IMU data through the host computer and parse it according to the preset protocol. Integrate automatic algorithm modules for error parameter estimation, temperature compensation fitting, and state estimation, and use filtering technology to achieve full-process automatic processing from data collection to result output; S4. Real-time error correction and dynamic verification: Implement real-time error correction based on the estimated parameters, and verify the effectiveness of the calibration results under dynamic conditions such as angular rate ≥ 100° / s by evaluating navigation performance indicators such as position, speed, and attitude accuracy.

[0022] More specifically, the sensor includes an accelerometer and a gyroscope, and the accelerometer error model is: ; Where: is the actual output vector of the accelerometer, is the true acceleration vector in the body coordinate system; is the scale factor matrix, is the temperature-related change in the scale factor error matrix; is the installation non-orthogonal error matrix, is the temperature-related change in the installation error matrix; is the cross-axis sensitivity matrix, which describes the coupling effect of acceleration between axes; is the temperature-related zero bias error vector; In the 12-position method of discrete calibration, the inertial navigation is successively placed in 12 static postures of up / down Z-axis / north / south XY, up / down Y-axis / north / south X, and up / down X-axis / north / south Y. Each posture is maintained for more than 120 seconds and the mean value is collected. The scale factor matrix , the installation non-orthogonal error matrix , the cross-axis sensitivity matrix and the temperature-related zero bias are solved by fitting the equation with the least squares method.

[0023] The 12-position method is used for static calibration of the accelerometer, and the error parameters are solved through multi-posture data. The specific process is as follows: Step 1: Posture setting and data collection: Definition of 12 static postures: Z - axis direction: Z - axis upward, XY - plane points north; Z - axis upward, XY - plane points south; Z - axis downward, XY - plane points north; Z - axis downward, XY - plane points south; Y - axis direction: Y - axis upward, X - axis points north; Y - axis upward, X - axis points south; Y - axis downward, X - axis points north; Y - axis downward, X - axis points south; X - axis direction: X - axis upward, Y - axis points north; X - axis upward, Y - axis points south; X - axis downward, Y - axis points north; X - axis downward, Y - axis points south.

[0024] Data acquisition requirements: Each posture is maintained for ≥120 seconds to ensure stable sensor output; Collect the acceleration data output by the IMU and calculate the mean value, denoted as ( ).

[0025] Step 2: Error parameter solution Model linearization: Expand the error model and ignore the high - order small terms, and transform it into a linear equation system: ; Among them, is the design matrix containing the attitude matrix; is the vector of parameters to be estimated, is the observation noise.

[0026] Least - squares fitting: Solve the parameters by minimizing the following cost function:

[0027] Obtain the scale factor matrix , the misalignment error matrix , the cross - axis sensitivity matrix and the temperature - related bias .

[0028] Step 3: Temperature - sensitive error separation: Traditional calibration does not separate and , resulting in coupling of temperature and mechanical errors and a large estimation deviation; Repeat the 12 - position method calibration at multiple temperature points (such as - 40°C, 20°C, 60°C), and fit the at different temperatures as a function of temperature: ; Separate the static installation error and the temperature - related variation through polynomial fitting or machine learning models (such as linear regression) to achieve independent estimation of temperature - sensitive installation errors and improve the parameter accuracy in a high - temperature - drift environment.

[0029] Separation With After that, the installation error caused by temperature can be modeled separately, avoiding the aliasing of mechanical error and temperature error in the traditional model, and reducing the parameter estimation deviation by more than 30%. By standardizing the 12-position method and least squares fitting, there is no need to rely on a high-precision turntable (the angular accuracy requirement can be relaxed to 0.1°), reducing the calibration cost while improving the robustness.

[0030] More specifically, the gyroscope error model is: ; Where: is the actual output vector of the gyroscope, is the true angular velocity vector controlled by the turntable; , and , are respectively the scale factor error matrix of the gyroscope and its temperature change, the installation non-orthogonal error matrix and its temperature change; is the gyroscope cross-axis sensitivity matrix; is the temperature-related bias error vector, is the random noise vector including angle random walk (ARW) and rate random walk (RRW); In the rate method calibration, the turntable is controlled to rotate uniformly around the three axes at multiple rates of ±30° / s, ±60° / s, and ±90° / s. The data during the acceleration / deceleration transition process is collected. After filtering out the high-frequency noise through Fourier transform, the genetic algorithm is combined to optimize the parameter estimation to improve the observability of the gyroscope cross-axis sensitivity matrix .

[0031] Decompose the random noise into angle random walk (ARW) and rate random walk (RRW), and model them as discrete white noise and first-order Markov process respectively, supporting the independent identification and compensation of noise parameters.

[0032] The multi-rate dynamic calibration method is used to calibrate the gyroscope. The error parameters are calculated through the data during the acceleration / deceleration process. The specific process is as follows: Step 1: Turntable motion control and data collection: Rate setting: Control the turntable to rotate uniformly around the X, Y, and Z axes at a total of 6 rates of ±30° / s, ±60° / s, and ±90° / s. For each rate direction (such as +30° / s around the X axis), collect the complete acceleration-uniform-deceleration transition process data, and the duration is ≥300 seconds; Data acquisition: Synchronously acquire the raw gyroscope data (including μs-level timestamps) output by the IMU and the turntable angular velocity command to ensure time alignment (error ≤ 1 μs). Step 2: Signal preprocessing and feature extraction: Fourier transform noise reduction: Perform Fourier transform on the acquired angular velocity data to filter out high-frequency noise (cutoff frequency ≤ 10 Hz) and retain the low-frequency effective signal components. Transient process extraction: Intercept the data in the acceleration section (angular velocity rising from 0 to the target rate) and the deceleration section (from the target rate to 0), and extract the angular velocity ramp signal as the feature data section. Step 3: Parameter estimation and optimization: Linear model construction: Linearize the error model in the constant-speed section, ignore the temperature-related terms (static calibration scenario), and establish the observation equation: ; Initial value solution by least squares method: Use the data in the constant-speed section to estimate the initial values of , , and by the least squares method. Genetic algorithm optimization: Use the data in the acceleration / deceleration section as the input, and use the root mean square error (RMSE) between the predicted value and the measured value of the error model as the fitness function. Optimize the cross-axis sensitivity matrix and the noise parameters , by the genetic algorithm to improve the observability of the parameters. Step 4: Temperature-sensitive error separation: Repeat the rate method calibration at multiple temperature points (such as -40°C, 20°C, 60°C), and fit , , at different temperatures as functions of temperature (such as polynomial or Gaussian process model) to separate the static error and the temperature-related error: ; Realize independent modeling and compensation of temperature-sensitive errors.

[0033] Decompose the random noise into angular rate random walk (ARW) and rate random walk (RRW) and independently model them, reducing the estimation deviation of the noise parameters by more than 40% and improving the long-term stability of the navigation solution. Through multi-rate transient process data and genetic algorithm optimization, the cross-axis sensitivity matrix The rank of the observability matrix is increased by 50%, solving the problem of unobservability of dynamic error terms in traditional static calibration. After separating the static error and the temperature-related error, the bias stability of the gyroscope within the wide temperature range of -40°C to 60°C is improved to ≤0.1° / h (≤0.3° / h for the traditional method).

[0034] More specifically, the temperature-related bias error and the temperature-related parameters are fitted by a machine learning model, and the bias error is expressed as: ; where is a non-linear function for the coordinate axis ; Read the temperature of the IMU main board in real time , and correct it online through a pre-trained machine learning model , forming a closed-loop process of data acquisition, model fitting, and real-time compensation; supporting incremental learning of multi-temperature point data, and automatically updating the compensation model to adapt to sensor aging drift.

[0035] Use a machine learning model to capture the complex non-linear relationship between temperature and bias error, and improve the compensation accuracy in the wide temperature range (-40°C to 60°C).

[0036] The specific implementation is as follows: Model selection and definition: For each coordinate axis of the gyroscope, the temperature-related bias error is modeled as , where is a non-linear function, approximated by a neural network, support vector regression, or Gaussian process regression model; Data acquisition and model training: At preset temperature points (covering the working temperature range of the sensor, with an interval ≤10°C), collect the bias data of the gyroscope at different temperatures, construct a data set containing the temperature value and the corresponding bias error, and use this data set to train the machine learning model to determine the model parameters; Real-time error correction: Read the temperature of the main board through the IMU in real time , input it into the pre-trained machine learning model, and calculate and correct the bias error at this temperature online , forming a closed-loop process of data acquisition, model fitting, and real-time compensation; Incremental learning and model update: Support incremental learning of multi-temperature point data. When zero-bias data at a new temperature point is obtained, it is automatically added to the training data set to update the machine learning model to adapt to sensor aging drift and improve the long-term compensation accuracy of the model.

[0037] More specifically, the hierarchical calibration strategy includes: Discrete calibration stage: The static data of the accelerometer is collected by the 12-position method (each position is maintained for ≥120 seconds and the average value is taken), and the dynamic data of the gyroscope is collected by the rate method (multi-rate rotation of ±30° / s, ±60° / s, ±90° / s) and the orthogonal rotation method. The initial scale factor error, zero bias error, and installation error are solved by the least squares method; System-level joint calibration: Based on the strapdown navigation equation, a state space model is established. The navigation speed error and attitude angle error are used as measurement inputs, and the process noise covariance matrix is dynamically adjusted through adaptive Kalman filtering (ACKF) to jointly estimate the temperature-related error parameters and the installation error matrix; The strapdown navigation equation is as follows: ; ; Among them, is the vehicle speed, is the transformation matrix from the vehicle to the navigation system, is the specific force output of the accelerometer, is the angular rate of the Earth's rotation, is the angular rate of the navigation system relative to the Earth; The system-level calibration reuses the initial parameters of the discrete calibration as prior information, and realizes the hierarchical optimization of the error parameters by expanding the state vector, relaxing the turntable angle accuracy requirement from 0.01° of the traditional method to 0.1° The hierarchical calibration strategy realizes the high-precision estimation of the IMU error parameters through two stages of discrete calibration and system-level joint calibration, as follows: In the discrete calibration stage, the initial error parameter estimation values of the accelerometer and gyroscope are obtained: Accelerometer calibration method: The IMU is placed in 12 orthogonal positions in turn (such as the positive and negative directions of the X axis, the positive and negative directions of the Y axis, etc.), and each position is maintained for ≥120 seconds; The average value of the static data at each position is taken to eliminate random noise; A mathematical model including scale factor error, zero bias error, and installation error is constructed; The above error parameters are solved by the least squares method.

[0038] Gyroscope calibration method: Rate method: Rotate the IMU at different rates of ±30° / s, ±60° / s, ±90° / s, etc.; Orthogonal rotation method: Make the IMU rotate around three orthogonal axes; Data characteristics: Collect dynamic data, including angular rate information; Parameter solution: Similarly, the least squares method is used to estimate the scale factor, zero bias, and installation error.

[0039] System-level joint calibration further optimizes the error parameter estimation, especially temperature-related parameters, in the actual application environment. State space model construction: Based on the strapdown navigation equation, a mathematical model of the carrier motion is established. State vector expansion: includes velocity error, attitude error, various sensor error parameters (scale factor, zero bias, installation error), and temperature-related parameters. Measurement input: Select the navigation velocity error and attitude angle error as the observed values.

[0040] Adaptive Kalman filter (ACKF): According to the system operating state, the process noise covariance matrix is adjusted in real time. Compared with the traditional Kalman filter, it can better handle the system uncertainty and nonlinear characteristics. The temperature-related error parameters and installation error matrix are jointly estimated through ACKF.

[0041] Hierarchical optimization strategy to achieve hierarchical estimation of error parameters and reduce the dependence on high-precision turntables. Use the initial parameters obtained in the discrete calibration stage as the prior information for system-level calibration to improve the convergence speed and estimation accuracy of system-level calibration. Classify different types of error parameters according to importance and correlation, for example: velocity and attitude errors as the first layer, sensor zero bias as the second layer, scale factor as the third layer, and temperature-related parameters as the fourth layer. Relax the turntable accuracy: The traditional method requires the turntable angle accuracy to reach 0.01°. Through hierarchical optimization, the accuracy requirement is relaxed to 0.1°, and the redundant information of system-level joint calibration is used to compensate for the influence caused by insufficient turntable accuracy.

[0042] More specifically, the state vector of the system-level calibration is: ; Where: is the velocity error vector, is the attitude angle error vector, represents the matrix vectorization operation, which is used to extract the coupling parameters of the scale factor and the installation error matrix. and are the random noise parameters of the accelerometer and gyroscope respectively, modeled as a Gaussian-Markov process. Introduce the unscented Kalman filter (UKF) to handle the nonlinear characteristics of the strapdown navigation equation, and accurately approximate the state distribution through Sigma point sampling. Control the turntable to perform dynamic maneuvers of long-term holding in the Z-up Y-north direction and rapid switching of composite attitudes, and improve the rank of the observability matrix of error parameters.

[0043] The state vector includes random noise parameters. / , it supports the estimation and correction of zero-bias drift over time, and solves the problem of navigation solution drift caused by the lack of noise parameters in traditional calibration.

[0044] The state vector X is a column vector with a dimension of (3 + 3 + 3 + 3 + 9 + 9 + 3 + 3) = 36, and its specific form is: ; Velocity error vector : The velocity error in the navigation system (3D), which reflects the cumulative effect of accelerometer errors on the integration result; Attitude angle error vector : The attitude angle error in the navigation system (3D), which is the attitude solution deviation caused by gyroscope errors; Accelerometer zero-bias vector : It includes temperature-related zero-bias errors (3D) and is corrected in real time through a machine learning model; Gyroscope zero-bias vector : It includes temperature-related zero-bias errors (3D), and the temperature mapping relationship is fitted through a non-linear function; Scale factor and installation error coupling parameters and : Through matrix vectorization operation ( ), the product of the scale factor matrix ( ) and the installation non-orthogonal error matrix ( ) is expanded into a 9D vector to extract the coupling terms of static errors and temperature-related errors.

[0045] Random noise parameters and : They are the random noises of the accelerometer and gyroscope (3D) respectively, modeled as a Gaussian-Markov process to describe the characteristics of angle random walk (ARW) and rate random walk (RRW).

[0046] Implementation of unscented Kalman filter (UKF): Nonlinear model processing: For the nonlinear characteristics of the strapdown navigation equation (such as the attitude matrix differential equation), the UKF algorithm is used to accurately approximate the state distribution through Sigma point sampling, avoiding the linearization error of the traditional extended Kalman filter (EKF).

[0047] State prediction and update: Prediction stage: Predict the prior state value and covariance matrix , considering the dynamic changes of temperature-related error parameters (such as , ); Update stage: Using the navigation velocity error and attitude angle error as measurement inputs, and correct the state estimation through the measurement equation where is the measurement matrix, is the measurement noise.

[0048] Dynamic movement improves observability: Control the turntable to execute the following typical motion trajectories to enhance the rank of the observability matrix of the error parameters: Long-term static hold: Place the turntable in the "Z-axis up + Y-axis north" attitude and hold for ≥30 minutes to excite the accelerometer bias error and attitude error observability; Compound attitude rapid switching: Execute multi-axis compound attitude switching such as "X-axis 30° → Y-axis 60° → Z-axis 90°" at an angular rate of ≥100° / s, and each attitude is held for 5 - 10 seconds to excite the gyroscope cross-axis sensitivity matrix and scale factor error dynamic response; Sine sweep motion: Control the turntable to execute a sweep motion with an angular rate (frequency range 0.1 - 10 Hz) around a single axis, extract the response characteristics of the error parameters at different frequencies, and improve the identifiability of the random noise parameters ;

[0049] By modeling and as a Gaussian - Markov process, it supports the real-time estimation and correction of the bias error (such as sensor aging) that drifts with time, solves the navigation solution drift problem caused by ignoring the dynamic characteristics of noise in traditional calibration, and the bias stability is improved by ≥50%. Through the dynamic movement design, the rank of the observability matrix is increased from 20 - 25 in traditional static calibration to more than 30, ensuring that all error parameters (especially temperature-related terms and cross-axis coupling terms) can be effectively estimated. Compared with the EKF, the root mean square error (RMSE) of the UKF algorithm in dealing with the nonlinearity of the attitude matrix is reduced by 30%, and it has significant advantages especially in high-dynamic scenarios with an angular rate ≥150° / s.

[0050] More specifically, the automated data processing includes: High-precision synchronization mechanism: Use the IEEE1588 Precision Time Protocol (PTP) to achieve nanosecond-level synchronization of IMU data (including μs-level timestamps) and turntable control commands, with a synchronization error ≤1 μs, ensuring strict time alignment between the motion attitude and the sensor output; Intelligent Data Management: Store data in the format of Temperature_Attitude_Rate_Timestamp.csv, including the real-time Euler angles / quaternions of the turntable, the raw outputs of the IMU, the data of the temperature sensor, and the checksum; integrate database triggers to automatically classify data (static position data is stored in the "_pos" folder, and rate data is stored in the "_rate" folder), supporting subsequent batch processing and machine learning model training.

[0051] Ensure data integrity through a 3-byte frame header (0xAA, 0x55, 0xA5) and a 16-bit checksum, and use a real-time database to achieve efficient parsing and real-time calculation of large-scale data.

[0052] More specifically, the preset temperature points cover the working temperature range of the sensor, the temperature interval ≤ 10 °C, and each temperature point is thermally insulated for ≥ 2 hours to ensure that the internal temperature gradient of the IMU ≤ ±0.5 °C; Temperature Control Accuracy Guarantee: The incubator uses PID closed-loop control, and ≥ 3 groups of temperature sensors are arranged on the surface of the IMU to monitor the uniformity in real time. During the thermal insulation period, data segments with excessive temperature fluctuations are automatically skipped; the heating / cooling rate is controlled within 5 °C / min to avoid thermal stress errors caused by sudden temperature changes.

[0053] Provide stable temperature input conditions for the temperature-related error model to ensure the accurate estimation of temperature-sensitive parameters (such as , ) and improve the generalization ability of the model.

[0054] More specifically, the accuracy verification steps include: Multi-dimensional Evaluation System: Calculate indicators such as bias stability (Allan variance), scale factor error, root mean square (RMS) of attitude angle error, and speed error drift rate; use Monte Carlo simulation (≥ 1000 times) to calculate the parameter estimation uncertainty, and the formula is: ; Among them, is the 95% confidence level expansion factor, is the parameter estimation value of the -th simulation, is the mean value; Control the turntable to execute the preset maneuvering trajectory (such as sinusoidal sweep frequency, step rotation), and verify the response accuracy of the compensation model in the dynamic scenario by comparing the attitude solved by the IMU with the actual attitude of the turntable (accuracy ≤ 0.05 °), filling the gap in traditional static verification.

[0055] S5. Construction of a Multi-dimensional Evaluation System: S51. Calculation of Static and Dynamic Error Indicators: Zero-bias stability (Allan variance); Place the IMU at a static position on the turntable (such as horizontal north), collect continuous data for ≥ 2 hours, and calculate the mean difference of adjacent intervals by segmenting according to the time series; Formula: ; Where, is the segmented time interval, is the total number of data points. Extract the zero-bias instability parameter (unit: ° / h) through logarithmic fitting.

[0056] Scale factor error: Use the rate method to calibrate the data (uniform rotation in six directions of ±30° / s, ±60° / s, ±90° / s), and fit the linear relationship between the sensor output and the true angular rate; Calculate the deviation of the slope of the fitted straight line from the ideal value (such as 1), and the unit is ppm (parts per million).

[0057] Root mean square (RMS) of attitude angle error: Static scenario: When calibrating by the 12-position method, compare the attitude solved by the IMU with the reference attitude of the turntable (accuracy ≤ 0.01°), and calculate the RMS of each attitude angle error; Dynamic scenario: The turntable performs sinusoidal sweep frequency (frequency 0.1~10Hz, amplitude ±30°), synchronously collect the attitude solved by the IMU and the actual attitude of the turntable (accuracy ≤ 0.05°), and calculate the RMS error.

[0058] Velocity error drift rate: Obtain the velocity by integrating the accelerometer data through the strapdown navigation equation, and record the change of velocity error within ≥ 1 hour; Calculate the linear drift slope of the velocity error over time, and the unit is m / s / h.

[0059] S52. Monte Carlo simulation: Analysis of parameter estimation uncertainty; Number of simulations: ≥ 1000 times, and Gaussian noise (variance based on sensor specifications) is randomly injected into the original data for each simulation; Parameter range: Cover key parameters such as accelerometer / gyroscope zero-bias, scale factor, installation error matrix, etc.; Calculation formula: ; Where, (95% confidence level), is the parameter estimation value of the th simulation, is the mean value; Qualified standard: The uncertainty of key parameters needs to be ≤ 5% of the nominal value (such as the uncertainty of gyroscope zero-bias ≤ 0.005° / h).

[0060] S6. Verification of dynamic scenario response accuracy: S61. Preset Maneuvering Trajectory Execution: Sine Sweep Test: Trajectory Parameters: The frequency linearly increases from 0.1 Hz to 10 Hz, and each frequency point is maintained for 30 seconds, with a rotation amplitude of ±30° (around a single axis or multiple axes); Data Acquisition: Synchronously acquire IMU raw data (including μs-level timestamps) and turntable encoder data (accuracy ≤ 0.05°) through the IEEE1588 protocol.

[0061] Step Rotation Test: Trajectory Parameters: The turntable completes a step rotation from 0° to 90° within 50 ms (angular acceleration ≥ 1800° / s²), maintains this posture for 10 seconds and then returns; Indicators to Be Concerned About: Overshoot of the IMU-solved posture and settling time (time to reach an error ≤ 0.1°).

[0062] S62. Dynamic Error Comparison and Analysis: Reference Alignment: Use the output of the turntable encoder as the true value and unify the attitude expression coordinate system through quaternion conversion; Error Calculation: ; where is the number of sampling points. It is required that in a dynamic scenario (adjustable according to the application scenario).

[0063] Compensation Model Optimization: If the dynamic error exceeds the standard, the following operations are automatically triggered: Increase the dynamic excitation data in the system-level joint calibration (such as supplementing step trajectory data); Adjust the parameters of the machine learning compensation model (such as the number of hidden layer nodes of the neural network), and retrain the temperature-error mapping relationship.

[0064] Technical Association and Citation: Data Basis: Rely on the wide-temperature-range heat preservation data (temperature interval ≤ 10°C, heat preservation ≥ 2 hours) in step S2 and the automated data synchronization (synchronization error ≤ 1 μs) in step S3; Algorithm Support: Use the real-time error correction results (such as the zero bias value after temperature compensation) in step S4 for dynamic scenario solution; Hardware Requirements: The angle accuracy of the turntable ≤ 0.1° (meeting the requirements of hierarchical calibration), and the temperature control accuracy of the incubator ≤ ±0.5°C (see step S8).

[0065] Implementation Example Verification Process: Static Evaluation: Complete the calibration by the 12-position method at a constant temperature of 20°C, calculate the Allan variance, and obtain the gyro zero bias stability of 0.08° / h and the scale factor error ≤ 50 ppm; Monte Carlo simulation: Conduct 1000 simulations on the accelerometer zero bias to obtain the uncertainty ( ), meeting the design requirements; Dynamic test: The turntable performs a 1Hz sinusoidal sweep. The RMS error of the IMU attitude angle is 0.3°, which is better than the threshold of 0.5°, verifying the effectiveness of the compensation model.

[0066] According to the strapdown inertial navigation automatic calibration test method for the temperature-controlled two-axis rate position turntable, a storage medium is proposed, which stores a computer program. When the computer program is executed by a processor, it realizes the steps of the strapdown inertial navigation automatic calibration test method for the temperature-controlled two-axis rate position turntable, and includes: A calibration result visualization module for visualizing the error parameter convergence curve and comparing the sensor outputs before and after temperature compensation; An algorithm interface that supports the access and verification of custom machine learning models such as LSTM and Transformer, forming an open and extensible calibration platform.

[0067] Although the embodiments of the present invention have been shown and described, for those of ordinary skill in the art, it can be understood that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principles and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A strapdown inertial navigation automatic calibration test method for a temperature-controlled biaxial rate-position turntable, characterized in that, It includes the following steps: S1. Multi-dimensional error modeling and hierarchical calibration architecture: Construct a comprehensive error model including sensor scale factor error, misalignment error, zero bias error, cross-axis coupling error, and temperature-related error; Adopt a hierarchical calibration strategy, extract static error parameters through initial discrete calibration, and combine system-level joint calibration to globally estimate dynamic error parameters such as the installation error matrix, cross-coupling coefficient, and temperature-related parameters, reducing the dependence on the calibration turntable accuracy; S2. Wide-temperature-range adaptive compensation mechanism: Insulate at preset temperature points and perform turntable positioning and rate motion. Use machine learning models such as neural networks or Gaussian processes to establish a non-linear mapping relationship between sensor error and temperature, and achieve precise temperature adaptive compensation of sensor output; S3. Automated data processing and parameter estimation: Automatically collect IMU data through the host computer and parse it according to a preset protocol. Integrate automated algorithm modules for error parameter estimation, temperature compensation fitting, and state estimation. Use filtering techniques to achieve full-process automated processing from data collection to result output; S4. Real-time error correction and dynamic verification: Implement real-time error correction based on the estimated parameters, and verify the effectiveness of the calibration results under dynamic conditions by evaluating navigation performance indicators such as position, speed, and attitude accuracy.

2. The strapdown inertial automation calibration and testing method for the temperature-controlled biaxial rate-position turntable according to claim 1, wherein The sensor includes an accelerometer and a gyroscope, and the accelerometer error model is: ； Wherein: is the actual output vector of the accelerometer; is the true acceleration vector in the body coordinate system; is the scale factor matrix; is the change in the scale factor error matrix related to temperature; is the installation non-orthogonality error matrix; is the change in the installation error matrix related to temperature; is the cross-axis sensitivity matrix, which describes the coupling effect of acceleration between axes; is the temperature-related bias error vector; In the 12-position method of discrete calibration, the inertial navigation is successively placed in 12 static postures, namely, above and below the Z-axis / north and south in the XY plane, above and below the Y-axis / north and south in the X plane, and above and below the X-axis / north and south in the Y plane. Each posture is maintained for more than 120 seconds and the mean value is collected. The scale factor matrix is calculated by fitting the equation using the least squares method. and the installation non-orthogonal error matrix and the cross-axis sensitivity matrix and the temperature-related zero bias .

3. The strapdown inertial automation calibration and testing method for the temperature-controlled biaxial rate-position turntable according to claim 2, wherein The gyroscope error model is: ； Wherein: is the actual output vector of the gyroscope, is the true angular velocity vector controlled by the turntable; , and , are respectively the scale factor error matrix of the gyroscope and its temperature change, the installation non-orthogonal error matrix and its temperature change; is the cross-axis sensitivity matrix of the gyroscope; is the temperature-related zero bias error vector, is the random noise vector including angle random walk and rate random walk; In the rate method calibration, the turntable is controlled to rotate uniformly around three axes at multiple rates of ±30° / s, ±60° / s, and ±90° / s. The data during the acceleration / deceleration transition process is collected. After filtering out high-frequency noise through Fourier transform, the parameter estimation is optimized by combining the genetic algorithm to improve the observability of the cross-axis sensitivity matrix of the gyroscope. of.

4. The strapdown inertial automation calibration and testing method for the temperature-controlled biaxial rate-position turntable according to claim 3, wherein, The temperature-related zero-offset error and the temperature-related parameters are fitted using a machine learning model. The zero-offset error is expressed as: ； Among them, is a non-linear function for the coordinate axis ; Read the temperature of the IMU main board in real time , and correct it online through a pre-trained machine learning model , forming a closed-loop process of data acquisition, model fitting, and real-time compensation; supporting incremental learning of multi-temperature point data and automatically updating the compensation model to adapt to sensor aging drift.

5. The strapdown inertial automation calibration test method for the temperature-controlled biaxial rate-position turntable according to claim 4, characterized in that, The hierarchical calibration strategy includes: Discrete calibration stage: Use the 12-position method to collect static data of the accelerometer, and use the rate method and orthogonal rotation method to collect dynamic data of the gyroscope. Use the least squares method to solve the initial scale factor error, zero bias error, and installation error; System-level joint calibration: Based on the strapdown navigation equation, establish a state space model. Use the navigation speed error and attitude angle error as measurement inputs, and dynamically adjust the process noise covariance matrix through adaptive Kalman filtering (ACKF) to jointly estimate temperature-related error parameters and the installation error matrix; The strapdown navigation equation is as follows: ； ； wherein, is the carrier velocity, is the transformation matrix from the carrier to the navigation system, is the specific force output of the accelerometer, is the angular velocity of the Earth's rotation, is the angular velocity of the navigation system relative to the Earth.

6. The strapdown inertial automatic calibration and testing method for the temperature-controlled biaxial rate-position turntable according to claim 5, characterized in that The state vector of the system-level calibration is as follows: ; Wherein: is the velocity error vector, is the attitude angle error vector, represents the matrix vectorization operation, which is used to extract the coupling parameters of the scale factor and the installation error matrix, and are the random noise parameters of the accelerometer and the gyroscope respectively, and are modeled as a Gaussian - Markov process; Introduce unscented Kalman filtering to handle the non-linear characteristics of the strapdown navigation equation, and accurately approximate the state distribution through Sigma point sampling; Control the turntable to perform dynamic maneuvers of long-term holding in the Z-up Y-north direction and rapid switching of composite attitudes to improve the rank of the observability matrix of error parameters.

7. The strapdown inertial automation calibration and testing method for the temperature-controlled biaxial rate-position turntable according to claim 6, characterized in that The automated data processing includes: High-precision synchronization mechanism: Use the IEEE1588 precision time protocol to achieve nanosecond-level synchronization of IMU data and turntable control commands, with a synchronization error ≤1 μs, ensuring strict time alignment between the motion attitude and sensor output; Intelligent data management: Store data in the format of Temperature_Attitude_Rate_Timestamp.csv, including the turntable's real-time Euler angles / quaternions, IMU raw outputs, temperature sensor data, and checksum; Integrate database triggers to automatically classify data, supporting subsequent batch processing and machine learning model training.

8. The strapdown inertial automatic calibration test method for the temperature-controlled biaxial rate-position turntable according to claim 7, characterized in that The preset temperature points cover the operating temperature range of the sensor, the temperature interval ≤ 10 °C, and each temperature point is kept warm for ≥ 2 hours to ensure that the internal temperature gradient of the IMU ≤ ±0.5 °C; Temperature control accuracy guarantee: The temperature chamber adopts PID closed-loop control, and ≥ 3 groups of temperature sensors are arranged on the surface of the IMU to monitor the uniformity in real time. During the heat preservation period, the data segments with excessive temperature fluctuations are automatically skipped; the heating / cooling rate is controlled within 5 °C / min to avoid thermal stress errors caused by sudden temperature changes.

9. The strapdown inertial automation calibration test method for the temperature-controlled biaxial rate position turntable according to claim 8, characterized in that The accuracy verification steps include: Multi-dimensional evaluation system: Calculate indicators such as zero-bias stability, scale factor error, root mean square of attitude angle error, velocity error drift rate, etc.; use Monte Carlo simulation to calculate the parameter estimation uncertainty, and the formula is: ； Among them, is the 95% confidence level expansion factor, is the parameter estimation value of the th simulation, and is the mean value; Control the turntable to execute the preset maneuvering trajectory, and verify the response accuracy of the compensation model in the dynamic scenario by comparing the IMU-solved attitude with the actual attitude of the turntable, filling the deficiencies of traditional static verification.

10. A storage medium, characterized in that, It stores a computer program, and when the computer program is executed by a processor, it realizes the method steps described in any one of claims 1-9, and includes: A calibration result visualization module for visualizing the error parameter convergence curve and comparing the sensor outputs before and after temperature compensation; An algorithm interface that supports the access and verification of custom machine learning models such as LSTM and Transformer, forming an open and extensible calibration platform.

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