Automatic calibration method and system of inertial measurement unit, and electronic equipment

Abstract

The invention provides an automatic calibration method and system for an inertial measurement unit, and electronic equipment, and relates to the technical field of sensors, the method comprises the following steps: building an IMU multi-modal calibration environment, and deploying multiple groups of reference sensors; designing a working environment test parameter table, performing simulation test on the to-be-calibrated IMU, and synchronously recording IMU multi-modal test data and multi-modal reference data; establishing an error parameter model; and constructing a calibration multi-objective function, performing minimization solution on the error parameter model, and performing closed-loop optimization correction on the to-be-calibrated IMU. According to the method and the device, the technical problems that in the prior art, as IMU error calibration is usually carried out in an ideal environment state, complex coupling errors caused by a multi-factor coupling effect are neglected, the compensation precision of calibration parameters under complex actual working conditions is seriously reduced, and IMU output drift is remarkably increased are solved; and the output precision of the IMU in a full working condition environment and the robustness of calibration parameters are improved.

Description

Technical Field

[0001] This application relates to the field of sensor technology, specifically to an automated calibration method and system for inertial measurement units, and electronic equipment. Background Technology

[0002] As the core sensor for measuring the acceleration and angular velocity of an object, the accuracy of the inertial measurement unit (IMU) directly determines the reliability of the system's attitude perception and navigation positioning. Therefore, it is widely used in the core stability control of humanoid robots, motion attitude measurement and control and dynamic balance adjustment, autonomous navigation and positioning of AGVs / AMRs, low-speed unmanned logistics vehicles, and high-precision measurement and control of unmanned systems in various complex environments. To ensure accuracy, the IMU must be calibrated before deployment to identify and compensate for its inherent sensor errors. However, most existing calibration methods are performed under ideal laboratory conditions, neglecting the combined impact of multiple factors such as temperature and humidity changes, random vibrations, electromagnetic interference, and air pressure fluctuations on IMU errors in actual working environments. Existing calibration methods have significant limitations in dealing with such multi-physics dynamic coupling effects, leading to a significant decrease in the error compensation effect of calibration parameters obtained based on ideal environments under actual complex working conditions. This results in significant drift in the IMU output, severely weakening the control accuracy and long-term stability of the entire inertial measurement unit.

[0003] In summary, the existing technology has the technical problem that, since IMU error calibration is usually performed under ideal environmental conditions, the complex coupling error caused by the multi-factor coupling effect is ignored, resulting in a serious decrease in the compensation accuracy of the calibration parameters under complex actual working conditions and a significant increase in IMU output drift. Summary of the Invention

[0004] The purpose of this application is to provide an automated calibration method, system, and electronic device for inertial measurement units (IMUs) to solve the technical problem in the prior art where IMU error calibration is usually performed under ideal environmental conditions, neglecting the complex coupling error caused by multi-factor coupling effects, resulting in a serious decrease in the compensation accuracy of calibration parameters under complex actual working conditions and a significant increase in IMU output drift.

[0005] To achieve the above objectives, this application provides an automated calibration method, system, and electronic device for inertial measurement units.

[0006] Firstly, this application provides an automated calibration method for an inertial measurement unit (IMU). This automated calibration method is implemented through an automated calibration system for the IMU. The method includes: establishing an IMU multimodal calibration environment, which integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module; and deploying multiple sets of reference sensors within the IMU multimodal calibration environment; designing an IMU operating environment test parameter table; and configuring the IMU operating environment test parameter table according to the IMU operating environment test parameter table. The environmental test parameter table drives the IMU multimodal calibration environment to simulate and test the IMU to be calibrated, and simultaneously records the IMU multimodal test data and the multimodal reference data of the multiple sets of reference sensors; combined with the multimodal reference data, the error sources of the IMU multimodal test data are decomposed and quantified to establish an IMU error parameter model; a calibration multi-objective function is constructed, and the IMU error parameter model is minimized based on the calibration multi-objective function to determine the target IMU calibration parameters, and the target IMU calibration parameters are used to perform closed-loop optimization and correction on the IMU to be calibrated.

[0007] Optionally, IMU operating environment factor information is defined, including temperature, humidity, vibration, electromagnetic interference, and air pressure; the operating application scenario of the IMU to be calibrated is analyzed according to the IMU operating environment factor information to obtain the IMU operating environment factor boundary; a multimodal parameter combination strategy is constructed, including operating scenario coverage and test parameter gradient; test parameters are designed based on the multimodal parameter combination strategy for the IMU operating environment factor boundary to generate an IMU operating environment test parameter table.

[0008] Optionally, based on the multimodal parameter combination strategy, single-modal and multimodal scene coverage analysis is performed on the boundary of the IMU working environment factors to obtain the environmental factor scene coverage parameter combination; according to the IMU calibration accuracy requirements, the selection density of environmental test parameters is determined; test gradient partitioning is performed on the environmental factor scene coverage parameter combination according to the environmental test parameter selection density to obtain the environmental factor scene parameter step size set; test parameters are designed for the environmental factor scene coverage parameter combination based on the environmental factor scene parameter step size set to generate the IMU working environment test parameter table.

[0009] Optionally, the multimodal reference data and the IMU multimodal test data are correlated and matched according to timestamps to obtain multimodal reference sequence data and IMU multimodal test sequence data; IMU error types are defined, including deterministic error, random error, and environmental coupling error; error source decomposition is performed on the IMU multimodal test sequence data according to the IMU error types to obtain IMU test error source signals; and the IMU test error source signals are quantized and modeled using the multimodal reference sequence data to establish an IMU error parameter model.

[0010] Optionally, a signal wavelet basis function is selected based on the characteristic information of the IMU error type; the signal wavelet basis function is used to perform multi-scale decomposition on the IMU multimodal test sequence data to obtain IMU signal approximation coefficients and IMU signal detail coefficients; error source correlation extraction is performed on the IMU signal approximation coefficients and IMU signal detail coefficients to obtain IMU error source correlation signal coefficients; and error signal reconstruction is performed sequentially based on the IMU error source correlation signal coefficients to obtain the IMU test error source signal.

[0011] Optionally, based on the IMU test error source signal, a deterministic error signal, a random error signal, and an environmental coupling error signal are obtained; the deterministic error signal, the random error signal, and the environmental coupling error signal are respectively fitted with the multimodal reference sequence data to generate a deterministic error parameter model, a random error parameter model, and an environmental coupling error parameter model; the deterministic error parameter model, the random error parameter model, and the environmental coupling error parameter model are fused and optimized to establish an IMU error parameter model.

[0012] Optionally, the IMU error parameter model is calibrated and analyzed to initialize the calibration parameter particle space; the fitness of the calibration parameter particle space is calculated based on the calibration multi-objective function to obtain the IMU parameter particle fitness set; a neighborhood topology update mechanism is introduced to iteratively update and evaluate the IMU parameter particle fitness set in the calibration parameter particle space, and minimize the solution until the preset convergence condition is met to determine the target IMU calibration parameters.

[0013] Optionally, the IMU to be calibrated is tested, verified, and compared using the target IMU calibration parameters to obtain IMU error distribution parameters; a PID controller is then used to perform closed-loop optimization and correction of the target IMU calibration parameters based on the IMU error distribution parameters.

[0014] Secondly, this application also provides an automated calibration system for an inertial measurement unit (IMU), used to execute an automated calibration method for an IMU as described in the first aspect. The automated calibration system includes: a calibration environment setup module for setting up an IMU multimodal calibration environment, which integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module, and deploys multiple sets of reference sensors within the IMU multimodal calibration environment; and a simulation testing module for designing an IMU operating environment test parameter table and performing tests according to the IMU operating environment parameters. The test parameter table drives the IMU multimodal calibration environment to simulate and test the IMU to be calibrated, simultaneously recording the IMU multimodal test data and the multimodal reference data of the multiple sets of reference sensors; the error decomposition module is used to decompose and quantify the error sources of the IMU multimodal test data by combining the multimodal reference data, and establish an IMU error parameter model; the closed-loop correction module is used to construct a calibration multi-objective function, minimize the IMU error parameter model based on the calibration multi-objective function, determine the target IMU calibration parameters, and perform closed-loop optimization correction on the IMU to be calibrated using the target IMU calibration parameters.

[0015] Thirdly, this application also provides an electronic device, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the automated calibration method for an inertial measurement unit as described in any one of the first aspects above.

[0016] One or more technical solutions provided in this application have at least the following technical effects or advantages: By constructing an IMU multimodal calibration environment, which integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module, and deploying multiple sets of reference sensors within the environment, a test parameter table for the IMU operating environment is designed. The IMU multimodal calibration environment is then driven to simulate and test the IMU to be calibrated according to this table, simultaneously recording the IMU multimodal test data and the multimodal reference data from the multiple sets of reference sensors. The error sources of the IMU multimodal test data are decomposed and quantified using the multimodal reference data, establishing an IMU error parameter model. A calibration multi-objective function is constructed, and the IMU error parameter model is minimized based on this function to determine the target IMU calibration parameters. Finally, the target IMU calibration parameters are used to perform closed-loop optimization and correction on the IMU to be calibrated. In other words, by building a multimodal calibration environment integrating temperature, humidity, vibration, electromagnetic, and air pressure control and reference sensors, a test parameter table covering single-mode and multimodal combinations is designed. Wavelet transform is used to decompose and quantize the IMU test data into multi-scale error sources, and a calibration multi-objective function is constructed to solve the parameters by combining particle swarm optimization and PID closed-loop correction. This accurately separates and compensates for IMU errors, improving the output accuracy of the IMU and the robustness of the calibration parameters under all operating conditions.

[0017] The above description is merely an overview of the technical solution of this application. To better understand the technical means of this application and to facilitate its implementation according to the description, and to make the above and other objects, features, and advantages of this application more apparent, specific embodiments of this application are described below. It should be understood that the content described in this section is not intended to identify key or important features of the embodiments of this application, nor is it intended to limit the scope of this application. Other features of this application will become readily apparent through the following description. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely exemplary. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0019] Figure 1 This is a flowchart illustrating an automated calibration method for an inertial measurement unit according to this application.

[0020] Figure 2 This is a schematic diagram of the structure of an automated calibration system for an inertial measurement unit according to this application.

[0021] Figure 3 This is a schematic diagram of the structure of an exemplary electronic device of this application.

[0022] Explanation of reference numerals in the attached diagram: Calibration environment setup module 11, Simulation test module 12, Error decomposition module 13, Closed-loop correction module 14, Bus 300, Receiver 301, Processor 302, Transmitter 303, Memory 304, Bus interface 305. Detailed Implementation

[0023] This application provides an automated calibration method, system, and electronic equipment for inertial measurement units (IMUs). It addresses the technical problem in existing technologies where IMU error calibration is typically performed under ideal environmental conditions, neglecting complex coupling errors caused by multi-factor coupling effects. This leads to a significant decrease in the compensation accuracy of calibration parameters under complex real-world operating conditions and a substantial increase in IMU output drift. By constructing a multi-modal calibration environment integrating temperature, humidity, vibration, electromagnetic, and barometric pressure control and reference sensors, and designing a test parameter table covering single-modal and multi-modal combinations, the application utilizes wavelet transform to decompose and quantize the IMU test data into multi-scale error sources. Furthermore, it constructs a multi-objective calibration function combined with particle swarm optimization and PID closed-loop correction for parameter solving, accurately separating and compensating for IMU errors, thereby improving the IMU's output accuracy and the robustness of calibration parameters under all operating conditions.

[0024] The technical solutions of this application will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. It should be understood that this application is not limited to the exemplary embodiments described herein. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application. It should also be noted that, for ease of description, only the parts related to this application are shown in the accompanying drawings, not all of them.

[0025] Example 1, please refer to the appendix. Figure 1 This application provides an automated calibration method for an inertial measurement unit (IMU), wherein the automated calibration method is applied to an automated calibration system for an IMU, and the automated calibration method specifically includes the following steps: An IMU multimodal calibration environment is established, which integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module. At the same time, multiple sets of reference sensors are deployed in the IMU multimodal calibration environment.

[0026] Specifically, a mounting base with good rigidity, flatness, and electromagnetic shielding is selected as the foundation. A vibration simulation device, i.e., a multi-axis vibration table, is securely installed at the center of this base; the table surface will serve as the mounting base for the upper equipment. The enclosure of the high-precision temperature and humidity control module is fixed to the vibration table surface using a rigid transition bracket, ensuring that vibration is effectively transmitted to the interior of the enclosure. Inside the environmental chamber, an electromagnetic interference device needs to be designed and installed. This typically involves symmetrically arranging multiple sets of Helmholtz coils or antennas of a specific shape on the inner wall of the enclosure, and leading them out of the enclosure via shielded cables to a programmable signal source and power amplifier to generate a controllable electromagnetic field. The air inlet, exhaust port, and pressure sensor interface of the air pressure control module are connected to the interior of the environmental chamber through sealed pipelines, ensuring that the enclosure maintains good airtightness even when subjected to temperature and humidity changes and vibration.

[0027] Inside the environmental chamber, a high-rigidity, non-magnetic sensor mounting fixture is installed in the central region. The IMU to be calibrated is securely mounted in the center of this fixture. Then, adjacent to the IMU to be calibrated, multiple sets of reference sensors are mechanically rigidly connected; these reference IMUs should have an accuracy level at least one order of magnitude higher than the IMU to be calibrated. A triaxial accelerometer reflection target is determined on the sensor mounting fixture or on the surface of the IMU housing. High-precision, metrologically calibrated temperature, humidity, and absolute pressure sensors are evenly distributed around the IMU to be calibrated and at several representative spatial locations within the environmental chamber. A triaxial magnetometer is installed near the IMU to monitor the ambient magnetic field. Feedback signals from all reference sensors and environmental control modules, as well as output signals from the IMU to be calibrated, are all connected to a data acquisition system with multi-channel synchronous sampling capabilities. This system is managed by a central control unit, which is responsible for sending preset command sequences to the temperature and humidity controller, vibration controller, electromagnetic signal source, and air pressure controller. It also synchronously triggers all data channels to start and stop recording, ensuring that each data sample has a unified, high-precision timestamp. This completes the hardware integration and signal tuning of the entire multimodal calibration environment.

[0028] Design an IMU operating environment test parameter table, drive the IMU multimodal calibration environment according to the IMU operating environment test parameter table to simulate the test of the IMU to be calibrated, and synchronously record the IMU multimodal test data and the multimodal reference data of the multiple sets of reference sensors.

[0029] Furthermore, this application also includes the following steps: defining IMU operating environment factor information, which includes temperature and humidity, vibration, electromagnetic interference, and air pressure; performing test boundary analysis on the working application scenario of the IMU to be calibrated according to the IMU operating environment factor information to obtain the IMU operating environment factor boundary; constructing a multimodal parameter combination strategy, which includes working scenario coverage and test parameter gradient; and designing test parameters for the IMU operating environment factor boundary based on the multimodal parameter combination strategy to generate an IMU operating environment test parameter table.

[0030] Furthermore, this application also includes the following steps: performing single-modal and multi-modal scene coverage analysis on the IMU operating environment factor boundary based on the multi-modal parameter combination strategy to obtain the environmental factor scene coverage parameter combination; determining the selection density of environmental test parameters according to the IMU calibration accuracy requirements; performing test gradient partitioning on the environmental factor scene coverage parameter combination according to the environmental test parameter selection density to obtain the environmental factor scene parameter step size set; designing test parameters for the environmental factor scene coverage parameter combination based on the environmental factor scene parameter step size set to generate an IMU operating environment test parameter table.

[0031] Specifically, the operating environment factors of the IMU are defined, and the set of environmental variables to be considered is clearly defined as temperature, humidity, vibration, electromagnetic interference, and air pressure. Among them, temperature and humidity can be considered together, but they need to be set separately in actual control; vibration requires defining the frequency range and vibration magnitude; electromagnetic interference requires defining the frequency range and electric / magnetic field strength; and air pressure requires defining the absolute pressure range.

[0032] Collect the technical specifications and measured environmental data of typical equipment for the IMU's intended operation to determine the lower and upper limits of each environmental factor that may occur in actual use. For example, for an IMU used in a logistics autonomous vehicle, the operating temperature boundary is taken from the vehicle's operation in cold and hot regions; the humidity boundary is 5% to 98% relative humidity; the vibration boundary needs to be determined based on the road surface and engine spectrum, specifying its frequency range and the maximum value of the acceleration power spectral density within a specific frequency band; the electromagnetic interference boundary needs to be determined based on automotive-grade standards, specifying the intensity and frequency range of radio frequency field strength and pulse interference; and the air pressure boundary is 70% to 103% of standard atmospheric pressure. From this, the minimum and maximum values ​​of each factor are obtained, which constitute the IMU's operating environmental factor boundaries.

[0033] The strategy for constructing multimodal parameter combinations includes operational scenario coverage and test parameter gradient. Operational scenario coverage requires that the test parameter combination must cover all typical operating conditions that the IMU may encounter in actual use. Test parameter gradient requires that when a single environmental factor changes, the density of test points should be sufficient to capture the nonlinear relationship between that factor and the IMU error.

[0034] Based on a multimodal parameter combination strategy, single-modal and multimodal scenario coverage analysis was performed on the boundary of the IMU operating environment factors to obtain the environmental factor scenario coverage parameter combination. All single-modal test scenarios were enumerated, meaning only one environmental factor was changed each time, while other factors remained at their nominal values. Several typical values ​​were selected within the boundary range of this factor for testing. The goal of single-modal analysis was to select key operating points that could characterize the variation law of this factor throughout the entire boundary range. First, boundary endpoints and intermediate typical values ​​were selected, and then additional densification points were added based on empirically identified nonlinear sensitive areas. After the single-modal analysis was completed, a list containing all single-factor test points was obtained.

[0035] Enumerating multimodal test scenarios involves simultaneously changing two or more environmental factors. Since the number of multimodal combinations grows exponentially with the number of factors, selection based on actual importance is necessary. Orthogonal design is used to select a representative subset from all factor combinations. Due to the sheer number of all factor combinations, reasonable selection is crucial. Selection criteria include combinations with high probability of occurrence in actual working conditions, combinations known to have strong coupling effects, and representative combinations in the orthogonal experimental design. Taking orthogonal design as an example, the number of factors and their levels participating in the multimodal test are determined. Then, an orthogonal table of appropriate specifications is selected, and the factor levels are filled into the table. Each row of the orthogonal table represents a multimodal test combination. For example, selecting four factors—temperature (4 levels), vibration frequency (3 levels), vibration amplitude (3 levels), and air pressure (3 levels)—using an L18 orthogonal table can yield 18 or more representative multimodal combinations. The result of multimodal analysis is a list of multimodal parameter combinations, where each row contains the explicitly set values ​​for all factors. The single-factor test point list obtained from unimodal analysis is merged with the multi-factor combination list obtained from multimodal analysis to form a complete set of environmental factor scenario coverage parameters. This includes test points where only one factor is changed, as well as test points where multiple factors are changed simultaneously. It is important to note that in unimodal testing, all other factors for each factor retain their nominal values, while in multimodal testing, all factors are set according to the combination table, without the concept of nominal values.

[0036] The density of environmental test parameters is determined based on the IMU calibration accuracy requirements. The IMU calibration accuracy requirements are quantitative requirements based on the tolerance of attitude, velocity, and position measurement errors in the final application scenario of the IMU. The density of environmental test parameters refers to the concentration of test points within the range of variation of each environmental factor. The calibration accuracy requirements are translated into the maximum allowable step size for each environmental factor. For example, if preliminary experiments or consulting the device datasheet reveal that the IMU's zero bias sensitivity to temperature changes is 0.02° / h / ℃, then to control temperature-induced errors within the order of 0.1° / h, the temperature step size should not exceed 5℃. Similarly, if the nonlinear relationship between vibration-induced errors and vibration frequency is expressed as a change of 0.05° / h per octave on logarithmic coordinates, then at least two points per octave are required to control the interpolation error within 0.05° / h. Without prior information, a conservative default density is adopted: temperature is taken every 5°C, humidity every 20%, vibration frequency at 3 to 5 points per octave on logarithmic coordinates, vibration amplitude at 6 points (0.1g, 0.3g, 0.5g, 1g, 2g, 5g), electromagnetic interference frequency at 100MHz in the main sensitive frequency band, field strength at 1, 3, 10, and 30V / m, and air pressure at 10kPa. For high-precision requirements, the density needs to be further increased; for consumer-grade requirements, the density can be appropriately relaxed, such as on the order of 100°C / h.

[0037] Based on the determined environmental test parameter selection density, test gradient partitioning is performed on each environmental factor scenario coverage parameter combination to obtain the environmental factor scenario parameter step size set. The specific method for gradient partitioning is as follows: for each environmental factor, a specific sequence of test point values ​​is calculated based on its boundary range and the environmental test parameter selection density. For example, if the temperature boundary is -40℃ to 85℃, and the selection density is one point every 5℃, then the temperature step size set is -40, -35, -30, -25, -20, -15, -10, -5, 0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, a total of 26 points. The environmental factor scenario parameter step size set is the collection of test point sequences for each factor obtained after gradient partitioning of all environmental factors.

[0038] Based on the environmental factor scenario parameter step set, test parameters are designed for combinations of environmental factor scenario coverage parameters to generate an IMU operating environment test parameter table. The core task of test parameter design is to allocate the specific values ​​in the step set to each test condition and add necessary test control information. All single-mode test conditions are listed. For each environmental factor, each value in its step set is treated as an independent test condition, while all other factors are set to nominal values. For example, temperature single-mode testing has 26 conditions, humidity single-mode testing has several conditions, vibration single-mode testing needs to consider all combinations of frequency and amplitude, electromagnetic interference single-mode testing has combinations of frequency and field strength, and air pressure single-mode testing has 6 conditions. In practical applications, the number of single-mode tests for vibration and electromagnetic interference may be too large, requiring trimming based on importance, such as taking only a portion of the frequency step set to represent the frequency. All multi-mode test conditions are listed. Based on the combination scheme selected by multi-mode coverage analysis, corresponding specific values ​​are selected from the step sets of each factor to form a multi-mode condition. Convert all orthogonal array rows into a specific list of operating conditions. Merge the single-modal and multi-modal operating condition lists and sort them in a specific order. First, perform all nominal operating conditions, then conduct single-modal tests for each factor separately, and finally perform multi-modal tests. Write the detailed parameters of each operating condition into a structured file to form the final IMU operating environment test parameter table. Each row of the table includes the test number, temperature setpoint, relative humidity setpoint, vibration frequency, vibration acceleration amplitude, electromagnetic interference frequency, electromagnetic field strength, air pressure setpoint, test duration, data sampling rate, and operating condition type. The IMU operating environment test parameter table is the final output structured table. Each row represents an independent test condition, including setpoints for factors such as temperature, humidity, vibration, electromagnetic interference, and air pressure, as well as control information such as the test number, duration, and sampling parameters.

[0039] The IMU operating environment test parameter table is loaded into the host computer control software of the IMU multimodal calibration environment, which has functions such as parameter parsing, device driving, data acquisition, and status monitoring. The host computer control software reads each row of the IMU operating environment test parameter table and extracts all parameters of the current operating condition according to the fields in the table. Temperature and humidity setpoints are sent to the temperature and humidity control module via the communication interface, and air pressure setpoints are sent to the air pressure control module simultaneously. The temperature, humidity, and air pressure modules begin to adjust the environment inside the chamber. The control software reads the values ​​from the feedback sensors in real time and uses a proportional-integral-derivative algorithm for closed-loop adjustment until the temperature, humidity, and air pressure stabilize within the error tolerance of the setpoints. After the temperature, humidity, and air pressure stabilize, if the current operating condition includes vibration excitation, the control software sends waveform parameters to the power amplifier of the vibration simulation device. For sinusoidal fixed-frequency vibration, the frequency and acceleration amplitude need to be set; for swept-frequency vibration, the start frequency, end frequency, sweep rate, and amplitude need to be set; for random vibration, the power spectral density curve needs to be set. After the vibration device is started, the control software monitors the actual vibration level in real time through a reference accelerometer installed on the vibration table or fixture, and adjusts the drive signal to make the actual vibration reach the set value. Similarly, if the current working condition includes electromagnetic interference, the control software sends the frequency and field strength set values ​​to the signal generator. The signal generator drives the antenna or coil to generate an electromagnetic field, and at the same time, it adjusts the output power through a closed loop through a reference electric field probe or magnetic field probe inside the cavity to make the actual field strength reach the set value.

[0040] Once all environmental parameters have stabilized at their target values, the host computer control software initiates the data acquisition system. It simultaneously reads all output channels of the IMU to be calibrated and all output channels of all reference sensors at a preset sampling rate, and adds a high-precision timestamp to each sampling point. The data acquisition system continues to run until the set test duration for this condition is reached. During the acquisition process, the host computer control software also monitors in real time whether environmental parameters drift beyond tolerance. If deviations occur, it automatically fine-tunes the corresponding modules to ensure constant environmental conditions throughout the entire test.

[0041] After data acquisition for one operating condition is completed, data acquisition is stopped, and the acquired data is saved as separate files according to the operating condition number and test time. It is then determined whether there is a next test operating condition. If so, the above process is repeated: first, the environmental parameters are adjusted to the setpoints for the next operating condition; after stabilization, data is acquired and saved, until all operating conditions are completed. Throughout the entire test sequence, the control software should also record the start and end times of each operating condition, real-time curves of environmental parameters, and log information such as any abnormal events, for subsequent troubleshooting. After all operating conditions are tested, the control software automatically restores the temperature, humidity, vibration, electromagnetic, and air pressure modules to a safe state and generates a test report summarizing the execution status of each operating condition, the actual average and standard deviation of environmental parameters, data file paths, and other information. The raw data acquisition phase is complete, yielding multimodal test data for the IMU to be calibrated and multimodal reference data for the reference sensor. Both are strictly aligned in time and cover all preset operating conditions. IMU multimodal test data consists of the raw measurements output by the IMU under calibration during simulation testing, including the outputs of the triaxial accelerometer, triaxial gyroscope, and possibly the internally integrated temperature sensor. Multimodal reference data from multiple reference sensors is data synchronously acquired by high-precision reference sensors deployed in the calibration environment. This data is typically used as a benchmark for comparison with the output of the IMU under calibration, thereby identifying IMU errors. By strictly controlling the experimental environment conditions, IMU output data is obtained under various combined operating conditions. Real-time adjustments to the outputs of each environmental module are made using reference sensor feedback, ensuring a high degree of consistency between the actual environmental conditions under each operating condition and the set values ​​in the test parameter table, thus improving test repeatability and data quality.

[0042] The error sources of the IMU multimodal test data are decomposed and quantified by combining the multimodal reference data, and an IMU error parameter model is established.

[0043] Furthermore, this application also includes the following steps: associating and matching the multimodal reference data and the IMU multimodal test data according to timestamps to obtain multimodal reference sequence data and IMU multimodal test sequence data; defining IMU error types, including deterministic error, random error, and environmental coupling error; performing error source decomposition on the IMU multimodal test sequence data according to the IMU error types to obtain IMU test error source signals; and quantizing and modeling the IMU test error source signals in conjunction with the multimodal reference sequence data to establish an IMU error parameter model.

[0044] Furthermore, this application also includes the following steps: selecting a signal wavelet basis function based on the characteristic information of the IMU error type; using the signal wavelet basis function to perform multi-scale decomposition on the IMU multimodal test sequence data to obtain IMU signal approximation coefficients and IMU signal detail coefficients; extracting error source correlation from the IMU signal approximation coefficients and IMU signal detail coefficients to obtain IMU error source correlation signal coefficients; and reconstructing the error signal sequentially based on the IMU error source correlation signal coefficients to obtain the IMU test error source signal.

[0045] Furthermore, this application also includes the following steps: obtaining deterministic error signals, random error signals, and environmental coupling error signals based on the IMU test error source signals; performing error fitting on the deterministic error signals, random error signals, and environmental coupling error signals respectively using the multimodal reference sequence data to generate deterministic error parameter models, random error parameter models, and environmental coupling error parameter models; and fusing and optimizing the deterministic error parameter models, random error parameter models, and environmental coupling error parameter models to establish an IMU error parameter model.

[0046] Specifically, during the testing process, all sensor data is recorded by the same central data acquisition system, and each data sample is assigned a timestamp from the same high-precision clock within the system at the time of acquisition. Since the sampling rates of different sensors may differ, and the sampling times may not be perfectly synchronized, time alignment is required. A unified target time series is used as the main time axis. For each reference sensor channel, linear interpolation is used to calculate its corresponding value at each equally spaced time point on the main time axis, based on the timestamp inherent in its original data points, resulting in multimodal reference sequence data and IMU multimodal test sequence data. Each row in these two sets of sequence data strictly corresponds to the same physical moment.

[0047] IMU error types are defined, including deterministic errors, random errors, and environmental coupling errors. Deterministic errors are constant under static conditions and are typically caused by physical defects. Deterministic errors mainly include zero bias, scaling factor error, and installation error. Zero bias refers to the sensor's non-zero output under zero input conditions; scaling factor error refers to the proportional deviation between the sensor's output change and its input change; and installation error refers to the cross-axis sensitivity caused by the inability to achieve perfect orthogonality of the sensor's sensitive axes during packaging. Random errors are usually driven by random noise processes within the sensor, manifesting as random fluctuations in the output signal. Their statistical characteristics are stable, but their instantaneous values ​​are unpredictable, making them a key factor limiting the lower limit of IMU accuracy. Environmental coupling errors are the IMU's output response to the dynamics of the external environment; they are not an independent error source but rather changes in deterministic or random deviations modulated or caused by changes in the external environment.

[0048] Select appropriate wavelet basis functions based on the characteristics of IMU error types. Consider the frequency domain distribution characteristics and time domain waveform features of various errors. Take a representative segment of IMU test data and perform power spectral density analysis to observe the spectral distribution range of various errors. Typically, deterministic errors are mainly distributed in the ultra-low frequency band from DC to a few hertz; temperature-related errors in environmental coupling errors are also concentrated in the low frequency band, while vibration coupling errors are concentrated at the fundamental frequency and its harmonics; random errors are distributed over a wider frequency band and usually exhibit white noise characteristics. Based on these frequency band distributions, select wavelet basis functions with high vanishing moments and good frequency domain localization capabilities, such as the Daubechies 4th order wavelet. A high vanishing moment means that the wavelet can effectively approximate low-order polynomial trends, which is beneficial for separating low-frequency deterministic errors; good frequency domain localization helps separate vibration coupling components at specific frequencies. If there is no prior information, experiment with several commonly used wavelet basis functions, compare their reconstruction accuracy for known error signals, and select the one with the best performance. Different wavelet basis functions have different properties such as regularity, vanishing moments, and symmetry, making them suitable for different types of signals. For example, wavelets with high vanishing moments are better suited for approximating polynomial trends, while wavelets with good regularity are better suited for processing smooth signals.

[0049] The selected wavelet basis functions are used to perform multi-scale decomposition on the IMU multimodal test sequence data. Taking the db4 wavelet as an example, the decomposition level is set to five to eight levels. The original signal is used as input, and the approximation coefficients cA1 and detail coefficients cD1 are obtained by passing the signal through a low-pass filter and a high-pass filter, respectively. Then, cA1 is downsampled to obtain the first level decomposition result. Next, cA1 is used as input, and the above process is repeated to obtain the second level approximation coefficients cA2 and detail coefficients cD2. This process is repeated until the Lth level. The detail coefficients cD1, cD2, ..., cD... of each level are... L Corresponding to signal components in different frequency bands, the first layer of detail coefficients corresponds to the highest frequency band, approximately one-quarter to one-half of the sampling rate; the second layer of detail coefficients corresponds to the second highest frequency band; and so on; the Lth layer of approximation coefficients cA LThe lowest frequency band corresponds to DC to the sampling rate divided by two to the power of L+1. For IMU data with a sampling rate of 2000Hz, if eight decomposition layers are selected, the frequency band corresponding to cA8 is approximately 0Hz to 3.9Hz, the frequency band corresponding to cD8 is approximately 3.9Hz to 7.8Hz, and the frequency band corresponding to cD1 is approximately 500Hz to 1000Hz. In this way, different error components are distributed across different coefficient layers. IMU signal approximation coefficients are wavelet coefficients corresponding to the low-frequency components obtained at each decomposition layer during wavelet multi-scale decomposition. They represent the signal's profile or trend at a coarser scale, typically corresponding to the low-frequency components in the signal. For IMU data, the approximation coefficients mainly include deterministic errors and slow changes caused by environmental factors. IMU signal detail coefficients are wavelet coefficients corresponding to the high-frequency components obtained at each decomposition layer during wavelet multi-scale decomposition. Detail coefficients represent the signal's local changes or transient components at a finer scale, typically corresponding to the high-frequency components in the signal. For IMU data, the detail coefficients mainly include random noise, high-frequency components of vibration interference, and peak components of electromagnetic interference.

[0050] Error source correlation extraction is performed on the IMU signal approximation coefficients and IMU signal detail coefficients. For each level of decomposition, the correlation between the coefficients and the reference sensor data in the corresponding frequency band is calculated. For example, cA8, the lowest frequency approximation coefficient, is correlated with the reference temperature data. Since temperature changes slowly, its spectrum is concentrated in the ultra-low frequency band. If the correlation coefficient is high, the coefficient of this level is marked as a temperature coupling error coefficient. The detail coefficients cD5 or cD6 are cross-correlated with the envelope or fundamental frequency component of the reference vibration signal. If a significant synchronous modulation relationship is found, it is marked as a vibration coupling error coefficient. For random noise, it usually manifests as the residual part of all detail coefficients that cannot be significantly correlated with any reference signal, and its statistical characteristics conform to the white noise or colored noise model. Deterministic errors are directly derived from cA8. L The mean value is extracted. Spectral analysis is used to aid judgment; a Fast Fourier Transform is performed on each layer of coefficients to observe whether the frequency corresponding to the peak value matches the known interference source frequency, such as the low-frequency component of the 900MHz electromagnetic interference falling into the IMU passband after nonlinear demodulation. Each layer of coefficients is assigned to one or more error source categories, forming a set of IMU error source associated signal coefficients. The IMU error source associated signal coefficients are wavelet coefficient subsets that, after error source association extraction, are labeled as belonging to a certain type of error source. For example, coefficients in the first layer of detail coefficients whose frequency components match the known electromagnetic interference frequency are classified as electromagnetic coupling error coefficients; the highest layer approximation coefficients are classified as zero-bias coefficients; and other coefficients related to the harmonics of the vibration frequency are classified as vibration coupling error coefficients.

[0051] For each error source category, all wavelet coefficients corresponding to that category are retained, while all other coefficients are set to zero. An inverse wavelet transform is performed on the modified coefficient sequence to reconstruct the time-domain signal, which serves as the error waveform contributed individually by the error source. This process is repeated to obtain deterministic error signals, random error signals, and environmental coupling error signals, respectively. The relationship between these reconstructed error signals and the original IMU signal satisfies: Original IMU signal = Ideal signal + Deterministic error signal + Random error signal + Environmental coupling error signal. Since the ideal signal is unknown, in practical applications, reference sensor data is usually scaled and used as an estimate of the ideal signal; therefore, the error signal = IMU signal - Reference signal. The error source signals obtained through wavelet decomposition reconstruction are a decomposition of this total error.

[0052] For example, taking the X-axis data of a vibration-single-mode IMU accelerometer as an example, the data includes a temperature of 25°C, humidity of 50%, vibration of 20Hz / 0.5g, no electromagnetic interference, air pressure of 101kPa, and a duration of 120 seconds. The sampling rate is 2000Hz, and the data length is 240,000 points. Power spectrum analysis of this data segment revealed the presence of a DC component, 20Hz and its harmonic components, and broadband white noise background. Therefore, the Daubechies wavelet (db4) with a vanishing moment of 4 was selected, as this wavelet can effectively separate the polynomial trend and harmonic components. The db4 wavelet was used to decompose the 240,000 data points, yielding approximation coefficients cA1 to cA8 and detail coefficients cD1 to cD8. The frequency bands corresponding to each layer are as follows: cA8 is 0Hz to 3.9Hz, including DC and ultra-low frequencies; cD8 is 3.9Hz to 7.8Hz; cD7 is 7.8Hz to 15.6Hz; cD6 is 15.6Hz to 31.2Hz, including the 20Hz fundamental frequency; cD5 is 31.2Hz to 62.5Hz, including the 40Hz second harmonic; cD4 is 62.5Hz to 125Hz, including the 60Hz third harmonic; cD3 is 125Hz to 250Hz; cD2 is 250Hz to 500Hz; and cD1 is 500Hz to 1000Hz. The mean value of cA8 is calculated to be -0.05m / s. 2The mean value of cA8 represents the zero bias of the accelerometer, i.e., the deterministic error. The mean value of cA8 is marked as the zero bias coefficient. The cross-correlation coefficient between the cD6 coefficient and the reference vibration signal is calculated to be 0.92, indicating a strong correlation. Therefore, cD6 is marked as the vibration coupling error coefficient. Similarly, cD5 is correlated with the 40Hz component, and cD4 is correlated with the 60Hz component; these are also marked as vibration coupling error coefficients (nonlinear harmonics). For the unmarked coefficients in cD1 to cD3, and cD7 and cD8, their power spectra exhibit flat white noise characteristics; these are marked as random error coefficients. Since there are no temperature changes or electromagnetic interference in this operating condition, there are no temperature coupling or electromagnetic coupling markings. The mean value of cA8 is retained, while other fluctuations in cA8 and all detail coefficients are set to zero. The reconstructed deterministic error signal is obtained, which actually only contains the zero bias constant value of -0.05 m / s. 2 By retaining the coefficients cD6, cD5, and cD4, and setting the remaining coefficients to zero, the vibration coupling error signal is reconstructed. This signal exhibits a sinusoidal waveform of 20Hz and its harmonics, with an amplitude of approximately 0.02m / s². 2 Unlabeled coefficients from cD1, cD2, cD3, cD7, and cD8 are retained, while the rest are set to zero. The reconstructed random error signal exhibits a mean of zero and a standard deviation of approximately 0.005 m / s. 2 Gaussian white noise. The three reconstructed signals are added together and then compared with the total error of the original IMU signal minus the reference acceleration to verify the reconstruction accuracy. The reconstruction error is less than 1% of the amplitude of the original signal, proving that the decomposition and reconstruction are effective.

[0053] The deterministic error signal, random error signal, and environmental coupling error signal are acquired for each test condition. For each condition, the original IMU output signal, after wavelet multi-scale decomposition and error source correlation reconstruction, yields three independent time-domain waveforms: the deterministic error signal, the random error signal, and the environmental coupling error signal. These three waveforms are added together on the same time axis, and then the ideal value after the reference sensor's direct scaling transformation is added to obtain the original IMU output. In practice, due to the boundary effects of wavelet decomposition and reconstruction, stable data from the middle segment of each condition is typically selected for subsequent fitting to avoid edge distortion.

[0054] By combining multimodal reference sequence data, a deterministic error signal is fitted to generate a deterministic error parameter model. The deterministic error model typically takes the following form: for an accelerometer, the measured output = true acceleration × scale factor + zero bias + cross-coupling caused by installation error. Reference motion data for each operating condition is extracted, i.e., the outputs of the reference accelerometer and reference gyroscope, and after unit conversion, are used as the true acceleration and true angular velocity, along with the corresponding deterministic error signal e. detAll operating condition data, especially those with different directional and magnitude motion excitations, such as the six-position method in turntable calibration, are merged into a large dataset. Then, a linear regression equation is established: [Equation omitted for brevity]. det =K * actual input + b, where K is the combination of the scaling factor error matrix and the installation error matrix, and b is the zero bias vector. K and b are solved using the least squares method. For nonlinear deterministic errors, such as scaling factor nonlinearity over a large input range, higher-order terms, such as quadratic terms, are added. The final deterministic error parameter model is obtained in the form: Accelerometer X-axis error = zero bias X + scaling error X × a x +Installation error XY×a y +Installation error XZ×a z , where a x a y a z It is real acceleration.

[0055] A random error parameter model is generated by fitting the random error signal. The random error signal typically exhibits a stationary random process with zero mean. A sufficiently long random error signal sequence is extracted from the static or uniform motion segment of each operating condition. The Allen variance of this sequence is calculated. For different correlation times, from the minimum sampling interval to one-tenth of the total data length, the Allen variance is calculated. The relationship between the Allen variance and different correlation times is plotted on a log-log plot. A typical Allen variance curve can be decomposed into components such as quantization noise, angle random walk, zero-bias instability, rate random walk, and rate ramp. The coefficients of each noise source are obtained through least-squares fitting. For example, the angle random walk coefficient is given by the intercept of the negative half-power segment of different correlation times. The final generated random error parameter model is usually expressed in the form of power spectral density or Allen variance coefficients. For example, gyroscope random error = angle random walk coefficient × white noise + rate random walk coefficient × integral of white noise.

[0056] An environmental coupling error parameter model is generated by fitting the environmental coupling error signal. The environmental coupling error signal, separated from wavelet decomposition, is related to reference environmental variables and their interaction terms. The environmental coupling error signal under each operating condition is aligned with the corresponding reference environmental variable sequence in time. Since some environmental variables change slowly while others change rapidly, they need to be processed separately. Data from all operating conditions are merged, and regularized least squares is used to screen out significant influencing terms and estimate the coefficients. The final environmental coupling error parameter model is a multivariate function with temperature, humidity, vibration parameters, electromagnetic parameters, and air pressure as independent variables. For example, for temperature coupling error, temperature sensor data is used as the independent variable, and the error signal as the dependent variable. A multinomial regression is used to fit the relationship between error and temperature, and the coefficients are the model parameters, such as: Environmental coupling error signal = -0.001*ΔT + 0.00002*ΔT 2 ΔT is the temperature difference relative to the reference temperature. For vibration coupling error, a transfer function model of the error and vibration acceleration needs to be established. The coefficients of the transfer function are obtained through frequency domain least squares. The environmental coupling error signal = 0.008 * vibration amplitude. 2 +0.0005 * vibration frequency * vibration amplitude.

[0057] The deterministic error parameter model, the random error parameter model, and the environmental coupling error parameter model are fused and optimized. Since the actual input used when fitting the deterministic error model individually may already include the influence of environmental coupling, and the environmental coupling model assumes that the deterministic error has been completely subtracted during fitting, but in reality, coupling may exist between the two, thus requiring fusion optimization. Using the parameters of the three sub-models as initial values, a total error model is constructed: Total Prediction Error = Deterministic Model + Random Model + Environmental Coupling Model. The random model only provides statistical characteristics and is usually replaced by zero-mean noise during prediction; therefore, fusion optimization mainly targets the adjustable parameters in the deterministic and environmental coupling models. A loss function is defined by substituting the complete dataset of all operating conditions, such as the sum of the squares of the differences between the predicted error and the actual error under all operating conditions. A nonlinear optimization algorithm is used to jointly adjust the parameters in the deterministic and environmental coupling models to minimize the loss function. Cross-validation is used during optimization to prevent overfitting. After optimization, a set of globally optimal parameters is obtained. Substituting this set of parameters into the model forms the final IMU error parameter model, which can be expressed as IMU measurement value = true value + f. det (actual value) + f coup (Environmental variables) + random noise, where f det and f coupIt is a deterministic mapping in the form of a known function. The IMU error parameter model takes true acceleration, true angular velocity, temperature, humidity, vibration parameters, electromagnetic field strength, and air pressure as inputs and outputs the IMU's measurement error. IMU errors are clearly divided into three categories: deterministic, stochastic, and environmentally coupled, allowing for targeted modeling. Through wavelet multi-scale decomposition, aliasing errors were successfully quantified and separated, independently extracting errors from different physical sources from the original signal. Three sub-models—deterministic, stochastic, and environmentally coupled—were established, and a globally optimal IMU error parameter model was obtained through fusion and optimization. This enables online prediction and compensation of additional IMU errors in practical applications, simply by monitoring environmental variables in real time, thereby significantly improving navigation accuracy under complex conditions.

[0058] A calibration multi-objective function is constructed, and the error parameter model of the IMU is minimized based on the calibration multi-objective function to determine the target IMU calibration parameters. The target IMU calibration parameters are then used to perform closed-loop optimization and correction on the IMU to be calibrated.

[0059] Furthermore, this application also includes the following steps: performing calibration analysis on the IMU error parameter model and initializing the calibration parameter particle space; calculating the fitness of the calibration parameter particle space based on the calibration multi-objective function to obtain the IMU parameter particle fitness set; introducing a neighborhood topology update mechanism to iteratively update and evaluate the IMU parameter particle fitness set within the calibration parameter particle space, minimizing the solution until a preset convergence condition is met, and determining the target IMU calibration parameters.

[0060] Specifically, the IMU error parameter model is calibrated and analyzed to clarify the number, range, and optimization objectives of the parameters to be calibrated. The IMU error parameter model is expanded to list all unknown parameters. For example, for an IMU with a three-axis accelerometer and a three-axis gyroscope, this includes the zero bias, scaling factor error, and installation error of each axis of the accelerometer; similar parameters for the gyroscope; and environmental coupling parameters such as temperature drift coefficient, vibration rectification coefficient, electromagnetic coupling coefficient, air pressure influence coefficient, and cross-coupling terms. Reasonable search boundaries are set for each parameter; for example, the zero bias boundary for the accelerometer is -0.1 times full scale to 0.1 times full scale; the scaling factor error boundary is -5% to 5%. The composition of the multi-objective function is defined, typically by weighting the sum of the squares of the predicted error and the measured error under various operating conditions, plus a penalty term for parameter variations.

[0061] The size of the particle swarm is determined, typically set to 50 to 200 particles. The position vector dimension of each particle is equal to the number of parameters to be calibrated. For each particle, an initial position is assigned using a uniform random number generator within the search boundary of each parameter. Simultaneously, an initial velocity is randomly assigned to each dimension of each particle, typically ranging from 10% to 20% of the parameter boundary span. Hyperparameters for particle swarm optimization are set: the inertia weight is typically initialized to 0.9 and linearly decays to 0.4 with iterations; the individual learning factor is typically set to 1.5; the social learning factor is the corresponding neighborhood learning factor in the neighborhood topology, typically set to 1.5. After initialization, an initial particle swarm is obtained, where the position of each particle represents a set of candidate calibration parameters.

[0062] The design of a multi-objective function requires comprehensive consideration of calibration accuracy and generalization ability. Specifically, it takes the form: Total Cost = Sum of (Root Mean Square of Compensated Residual Errors under Each Condition) + Regularization Term × L2 Norm of the Parameter Vector. The method for calculating the compensated residual error involves substituting the calibration parameters corresponding to the particle into the IMU error parameter model, compensating the raw IMU data for each test condition, comparing it with reference sensor data to obtain an error sequence, and then calculating the root mean square of this sequence. The root mean squares of all conditions are then summed. The regularization term is used to prevent the parameters from becoming too large; it is usually a very small coefficient, such as 1e. -6 The smaller the value of the multi-objective function, the better the performance of the set of calibration parameters on the test dataset.

[0063] Fitness calculations are performed on the calibration parameter particle space based on the calibration multi-objective function to obtain the IMU parameter particle fitness set. Specifically, for each particle in the particle swarm, its position vector is parsed into specific calibration parameter values, such as zero bias. All test conditions are traversed, and for the raw IMU data under each condition, error compensation is performed using these parameters, i.e., the prediction error is subtracted from the raw output. The difference between the compensated data and the reference sensor data is calculated to obtain the residual error. The root mean square of the residual error under all conditions is calculated, and a regularization term is added to obtain the multi-objective function value of the particle, which is its fitness; a smaller fitness is better. The particle's number, position, velocity, and calculated fitness are recorded as a data item, and these data for all particles constitute the fitness set. The particle with the smallest fitness in the current iteration is recorded as the global best candidate.

[0064] A neighborhood topology update mechanism is introduced, iteratively updating and minimizing the fitness set of IMU parameter particles within the calibration parameter particle space until a preset convergence condition is met. All particles are arranged in a ring according to their numbers, and each particle communicates only with its two neighboring particles on either side, not with the entire swarm. For each particle, its optimal neighborhood position is the position of the particle with the lowest fitness among itself and its neighbors. For each particle, its current fitness is compared with its historical best fitness; if the current fitness is better, the particle's individual historical best position is updated. For each particle, the particle with the lowest fitness in its neighborhood (itself + neighbors) is found, and its position is taken as its optimal neighborhood position. According to the particle swarm velocity update formula, the new velocity of each particle in each dimension is calculated. New velocity = inertia weight × current velocity + individual learning factor × random number × (individual historical best position - current position) + neighborhood learning factor × random number × (optimal neighborhood position - current position), where the random number is a uniformly distributed random number between 0 and 1. The inertia weight decreases linearly with the number of iterations, e.g., from 0.9 to 0.4, to balance global exploration and local exploitation. The position of each particle is updated: new position = current position + new velocity. If the new position exceeds a preset parameter boundary, it is pulled back to the boundary, e.g., set as the boundary value, and the corresponding velocity component is reversed and multiplied by a bounce coefficient, e.g., 0.5, to prevent the particle from flying off the boundary. The fitness of each particle at the new position is calculated, and the fitness set is updated. Preset convergence conditions are checked, such as the improvement in the global best fitness being less than a preset threshold in ten consecutive iterations, or reaching the maximum number of iterations. If either condition is met, iteration stops; otherwise, the next iteration continues. After iteration, the particle with the lowest fitness is selected from the final particle swarm, and its position vector is the target IMU calibration parameter. The target IMU calibration parameter is the parameter vector corresponding to the optimal fitness in the particle swarm after iteration convergence, i.e., the minimum multi-objective function value.

[0065] Particle swarm optimization (PSO), as a heuristic global optimization algorithm, does not rely on gradient information and can effectively search complex parameter spaces, avoiding getting trapped in local optima. In standard PSO, all particles share global optimum information, which can easily lead to the swarm rapidly clustering to a local optimum. By limiting the communication range of each particle, different regions within the swarm can maintain their own search directions, slowing down information propagation and thus providing more opportunities to discover better solutions. Furthermore, by incorporating regularization terms, overfitting caused by excessively large parameter values ​​is avoided, ensuring that the calibrated parameters maintain good compensation performance even under conditions outside of training.

[0066] Furthermore, this application also includes the following steps: testing, verifying, and comparing the IMU to be calibrated using the target IMU calibration parameters to obtain IMU error distribution parameters; and using a PID controller to perform closed-loop optimization and correction of the target IMU calibration parameters based on the IMU error distribution parameters.

[0067] Specifically, for each frame of IMU raw output and synchronously acquired environmental variables, the error value to be deducted is calculated according to a fixed formula. This error value is then subtracted from the raw value to obtain the compensated output. For example, the compensation value = raw value - [zero bias + scale factor error × raw value + temperature coefficient × (current temperature - 25℃) + vibration coefficient × vibration amplitude]. 2 +Electromagnetic coefficient × Field strength 2 The compensated measurement value is calculated using the formula: +pressure coefficient × (101.3 - current pressure) + cross term.

[0068] Select a set of independent validation test cases, which must not be exactly the same as the training test cases used for particle swarm optimization. Typically, 20% of the total dataset is allocated as the validation set. The validation test cases should cover typical temperature points, vibration conditions, electromagnetic interference levels, and air pressure ranges. During validation testing, simultaneously record the raw output of the IMU to be calibrated, the compensated data from the compensation calculation program, and the measurement data from the reference sensor. All data should have the same sampling rate and strictly aligned timestamps.

[0069] The residual error sequence is obtained by subtracting the compensated data from the reference true value point by point. For example, for the accelerometer X-axis, the length of the residual error sequence is equal to the total number of sampling points in the verification condition. Statistical analysis is performed on this sequence to extract the IMU error distribution parameters. The arithmetic mean of the residual error is calculated and denoted as the residual zero bias; the standard deviation of the residual error is calculated and denoted as the residual random noise; the residual errors are grouped according to temperature values, and the average residual error is calculated within each temperature interval. Then, these average values ​​are linearly regressed with the temperature, and the resulting slope is the residual temperature drift coefficient; for the vibration condition, the residual error is linearly regressed with the square of the vibration amplitude, and the resulting slope is the residual vibration rectification coefficient; the maximum absolute value and root mean square value of the residual error are recorded. The IMU error distribution parameters are statistical characteristics of the residual error obtained through test verification comparison. They mainly include the mean of the residual error, the standard deviation of the residual error, the linear slope of the residual error with temperature, the proportional coefficient of the residual error with the square of the vibration amplitude, and the maximum value and root mean square value of the residual error, expressing the gap between the current calibration parameters and the ideal compensation.

[0070] Based on the IMU error distribution parameters, a PID controller is used to perform closed-loop optimization and correction of the target calibration parameters. An independent PID controller is designed for each calibration parameter requiring correction. The input deviation of each PID controller is the error distribution parameter corresponding to that parameter, and the output is the correction amount for that parameter. The calculation formula for the PID controller is: Correction amount = Proportional coefficient × Current deviation + Integral coefficient × Cumulative deviation + Derivative coefficient × (Current deviation - Previous deviation). The proportional, integral, and derivative coefficients need to be pre-tuned based on the actual system's response characteristics, typically using the Ziegler-Nichols method or empirical trial-and-error. Generally, the proportional coefficient can be taken as 0.5~0.8, the integral coefficient as 0.05~0.1, and the derivative coefficient as 0.01~0.05. For example, suppose that after testing and verification, the residual zero bias of the accelerometer's X-axis is found to be +0.0023 m / s². 2 (That is, the compensated output is on average 0.0023 larger than the true value). This value is fed into the zero-bias PID controller. The controller first calculates the proportional term: 0.7 × 0.0023 = 0.00161; the integral term is initially 0; the derivative term is 0, so the correction is +0.00161. This correction is added to the current zero-bias parameter, and the new zero-bias = original zero-bias + correction - 0.02989 m / s 2 Meanwhile, the integral term is updated to a cumulative deviation of 0.0023.

[0071] After each correction, the updated calibration parameters are used to re-perform the test and verification comparison, repeating the aforementioned test and verification comparison process to obtain the new error distribution parameters. Then, PID correction is performed again, and this process is iterated repeatedly. After each iteration, it is checked whether all error distribution parameters meet the preset convergence conditions. For example, the convergence condition is set to the absolute value of the residual zero bias being less than 0.0001 m / s. 2 The absolute value of the residual temperature drift coefficient is less than 0.00005 m / s. 2 / ℃, the absolute value of the residual vibration rectification coefficient is less than 0.0005m / s 2 / g 2 The standard deviation of residual random noise is less than 0.001 m / s. 2 Furthermore, the change in these parameters is less than 10% in two consecutive iterations. When all conditions are met, the iteration stops, and the current calibration parameters are taken as the final result.

[0072] If convergence is not achieved after exceeding the preset limit of iterations, the PID controller parameters are checked for rationality, or the operating conditions are verified to include overly extreme conditions that prevent convergence. In this case, particle swarm optimization is performed again. The converged calibration parameters are stored in the non-volatile memory of the IMU, and a calibration report is generated, recording the error distribution parameter change curves and final accuracy indicators for each iteration. The integral term of the PID controller automatically eliminates steady-state errors, ensuring that the calibration parameters eventually converge to the ideal value that makes the residual mean zero. The proportional term accelerates the convergence speed, and the derivative term suppresses overshoot and oscillations; the combination of these three elements achieves fast and stable parameter optimization.

[0073] In summary, the automated calibration method for inertial measurement units provided in this application has the following technical effects: A multimodal IMU calibration environment is established, integrating a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module. Multiple sets of reference sensors are deployed within this environment. An IMU operating environment test parameter table is designed, and the multimodal calibration environment is driven to simulate and test the IMU to be calibrated according to this table, simultaneously recording the IMU multimodal test data and the multimodal reference data from the multiple sets of reference sensors. The multimodal reference data is combined to decompose and quantify the error sources of the IMU multimodal test data, establishing an IMU error parameter model. A calibration multi-objective function is constructed, and the IMU error parameter model is minimized based on this function to determine the target IMU calibration parameters. The target IMU calibration parameters are then used to perform closed-loop optimization and correction on the IMU to be calibrated. In other words, by building a multimodal calibration environment integrating temperature, humidity, vibration, electromagnetic, and air pressure control and reference sensors, a test parameter table covering single-mode and multimodal combinations is designed. Wavelet transform is used to decompose and quantize the IMU test data into multi-scale error sources, and a calibration multi-objective function is constructed to solve the parameters by combining particle swarm optimization and PID closed-loop correction. This accurately separates and compensates for IMU errors, improving the output accuracy of the IMU and the robustness of the calibration parameters under all operating conditions.

[0074] Example 2: Based on the same inventive concept as the automated calibration method for an inertial measurement unit in Example 1, this application also provides an automated calibration system for an inertial measurement unit. Please refer to the appendix. Figure 2The automated calibration system for an inertial measurement unit (IMU) includes: a calibration environment setup module 11, used to set up an IMU multimodal calibration environment, which integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module, and deploys multiple sets of reference sensors in the IMU multimodal calibration environment; a simulation test module 12, used to design an IMU operating environment test parameter table, drive the IMU multimodal calibration environment to perform simulation tests on the IMU to be calibrated according to the IMU operating environment test parameter table, and synchronously record the IMU multimodal test data and the multimodal reference data of the multiple sets of reference sensors; an error decomposition module 13, used to decompose and quantify the error sources of the IMU multimodal test data by combining the multimodal reference data, and establish an IMU error parameter model; and a closed-loop correction module 14, used to construct a calibration multi-objective function, minimize the IMU error parameter model based on the calibration multi-objective function, determine the target IMU calibration parameters, and perform closed-loop optimization correction on the IMU to be calibrated using the target IMU calibration parameters.

[0075] Furthermore, the simulation test module 12 in the automated calibration system of the inertial measurement unit is also used for: defining IMU operating environment factor information, including temperature, humidity, vibration, electromagnetic interference, and air pressure; performing test boundary analysis on the working application scenario of the IMU to be calibrated according to the IMU operating environment factor information to obtain the IMU operating environment factor boundary; constructing a multimodal parameter combination strategy, including working scenario coverage and test parameter gradient; and designing test parameters for the IMU operating environment factor boundary based on the multimodal parameter combination strategy to generate an IMU operating environment test parameter table.

[0076] Furthermore, the simulation test module 12 in the automated calibration system of the inertial measurement unit is also used for: performing single-modal and multi-modal scene coverage analysis on the boundary of the IMU working environment factors based on the multi-modal parameter combination strategy to obtain the environmental factor scene coverage parameter combination; determining the selection density of environmental test parameters according to the IMU calibration accuracy requirements; performing test gradient partitioning on the environmental factor scene coverage parameter combination according to the environmental test parameter selection density to obtain the environmental factor scene parameter step size set; and designing test parameters for the environmental factor scene coverage parameter combination based on the environmental factor scene parameter step size set to generate an IMU working environment test parameter table.

[0077] Furthermore, the error decomposition module 13 in the automated calibration system of the inertial measurement unit is also used for: associating and matching the multimodal reference data and the IMU multimodal test data according to timestamps to obtain multimodal reference sequence data and IMU multimodal test sequence data; defining IMU error types, including deterministic error, random error and environmental coupling error; performing error source decomposition on the IMU multimodal test sequence data according to the IMU error types to obtain IMU test error source signals; and quantizing and modeling the IMU test error source signals in combination with the multimodal reference sequence data to establish an IMU error parameter model.

[0078] Furthermore, the error decomposition module 13 in the automated calibration system of the inertial measurement unit is also used to: select a signal wavelet basis function according to the characteristic information of the IMU error type; use the signal wavelet basis function to perform multi-scale decomposition on the IMU multimodal test sequence data to obtain IMU signal approximation coefficients and IMU signal detail coefficients; perform error source correlation extraction on the IMU signal approximation coefficients and IMU signal detail coefficients to obtain IMU error source correlation signal coefficients; and reconstruct the error signal sequentially based on the IMU error source correlation signal coefficients to obtain the IMU test error source signal.

[0079] Furthermore, the error decomposition module 13 in the automated calibration system of the inertial measurement unit is also used to: obtain deterministic error signals, random error signals, and environmental coupling error signals based on the IMU test error source signals; perform error fitting on the deterministic error signals, random error signals, and environmental coupling error signals respectively in combination with the multimodal reference sequence data to generate deterministic error parameter models, random error parameter models, and environmental coupling error parameter models; and perform fusion and optimization on the deterministic error parameter models, random error parameter models, and environmental coupling error parameter models to establish an IMU error parameter model.

[0080] Furthermore, the closed-loop correction module 14 in the automated calibration system of the inertial measurement unit is also used for: performing calibration analysis on the IMU error parameter model and initializing the calibration parameter particle space; calculating the fitness of the calibration parameter particle space based on the calibration multi-objective function to obtain the IMU parameter particle fitness set; introducing a neighborhood topology update mechanism to iteratively update and evaluate the IMU parameter particle fitness set in the calibration parameter particle space, minimizing the solution until a preset convergence condition is met, and determining the target IMU calibration parameters.

[0081] Furthermore, the closed-loop correction module 14 in the automated calibration system of the inertial measurement unit is also used to: test, verify and compare the IMU to be calibrated using the target IMU calibration parameters to obtain the IMU error distribution parameters; and use a PID controller to perform closed-loop optimization correction of the target IMU calibration parameters based on the IMU error distribution parameters.

[0082] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on the differences from other embodiments. The automated calibration method and specific examples of an inertial measurement unit in the foregoing embodiment one are also applicable to the automated calibration system of an inertial measurement unit in this embodiment. Through the foregoing detailed description of the automated calibration method of an inertial measurement unit, those skilled in the art can clearly understand the automated calibration system of an inertial measurement unit in this embodiment. Therefore, for the sake of brevity, it will not be described in detail here.

[0083] Example 3: Based on the same inventive concept as the automated calibration method for an inertial measurement unit in Example 1 above, this application also provides an electronic device, including: at least one processor; a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, the instructions being executed by the at least one processor to enable the at least one processor to perform the steps of the automated calibration method for an inertial measurement unit described in any one of Examples 1 above.

[0084] Appendix Figure 3 This is a schematic diagram of the structure of an exemplary electronic device of this application. Figure 3 In this document, the bus architecture is represented by bus 300. Bus 300 may include any number of interconnected buses and bridges, and bus 300 connects various circuits including one or more processors represented by processor 302 and memory represented by memory 304. Bus 300 may also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits, which are well known in the art and therefore will not be described further herein. Bus interface 305 provides an interface between bus 300 and receiver 301 and transmitter 303. Receiver 301 and transmitter 303 may be the same element, i.e., a transceiver, providing a unit for communicating with various other devices over a transmission medium. Processor 302 is responsible for managing bus 300 and general processing, while memory 304 can be used to store data used by processor 302 during operation.

[0085] The above description of the disclosed embodiments enables those skilled in the art to make or use this application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of this application. Therefore, this application is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[0086] Obviously, those skilled in the art can make various modifications and variations to this application without departing from the spirit and scope of this application. Therefore, if such modifications and variations fall within the scope of this application and its equivalents, this application also intends to include such modifications and variations.

Claims

1. An automated calibration method for an inertial measurement unit, characterized in that, include: An IMU multimodal calibration environment is established, which integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module. At the same time, multiple sets of reference sensors are deployed in the IMU multimodal calibration environment. Design an IMU operating environment test parameter table, drive the IMU multimodal calibration environment to simulate the IMU to be calibrated according to the IMU operating environment test parameter table, and synchronously record the IMU multimodal test data and the multimodal reference data of the multiple sets of reference sensors; The error sources of the IMU multimodal test data are decomposed and quantified by combining the multimodal reference data, and an IMU error parameter model is established. A calibration multi-objective function is constructed, and the error parameter model of the IMU is minimized based on the calibration multi-objective function to determine the target IMU calibration parameters. The target IMU calibration parameters are then used to perform closed-loop optimization and correction on the IMU to be calibrated.

2. The automated calibration method for an inertial measurement unit as described in claim 1, characterized in that, Design an IMU operating environment test parameter table, including: Define IMU operating environment factor information, which includes temperature and humidity, vibration, electromagnetic interference, and air pressure; Based on the IMU operating environment factor information, the working application scenario of the IMU to be calibrated is analyzed to obtain the IMU operating environment factor boundary. A multimodal parameter combination strategy is constructed, which includes working scenario coverage and test parameter gradient properties. Based on the multimodal parameter combination strategy, test parameters are designed for the boundary factors of the IMU operating environment, and an IMU operating environment test parameter table is generated.

3. The automated calibration method for an inertial measurement unit as described in claim 2, characterized in that, Based on the multimodal parameter combination strategy, test parameters are designed for the boundary factors of the IMU operating environment, generating an IMU operating environment test parameter table, including: Based on the multimodal parameter combination strategy, single-modal and multimodal scene coverage analysis is performed on the boundary of the IMU working environment factors to obtain the environmental factor scene coverage parameter combination; Based on the IMU calibration accuracy requirements, determine the density of environmental test parameters to be selected; According to the selected density of the environmental test parameters, test gradient division is performed on the combination of environmental factor scene coverage parameters to obtain the step size set of environmental factor scene parameters. Based on the set of environmental factor scenario parameter steps, test parameters are designed for the combination of environmental factor scenario coverage parameters to generate an IMU working environment test parameter table.

4. The automated calibration method for an inertial measurement unit as described in claim 1, characterized in that, The IMU multimodal test data is decomposed and quantified using the multimodal reference data to establish an IMU error parameter model, including: The multimodal reference data and the IMU multimodal test data are associated and matched according to timestamps to obtain multimodal reference sequence data and IMU multimodal test sequence data; Define IMU error types, which include deterministic error, random error, and environmental coupling error; The IMU multimodal test sequence data is decomposed into error sources according to the IMU error type to obtain the IMU test error source signal; The IMU test error source signal is quantized and modeled using the multimodal reference sequence data to establish an IMU error parameter model.

5. The automated calibration method for an inertial measurement unit as described in claim 4, characterized in that, The IMU multimodal test sequence data is decomposed according to the IMU error type to obtain the IMU test error source signal, including: Select the signal wavelet basis function based on the characteristic information of the IMU error type; The signal wavelet basis function is used to perform multi-scale decomposition on the IMU multimodal test sequence data to obtain IMU signal approximation coefficients and IMU signal detail coefficients; Error source correlation extraction is performed on the IMU signal approximation coefficients and IMU signal detail coefficients to obtain IMU error source correlation signal coefficients; The error signal is reconstructed sequentially based on the IMU error source correlation signal coefficients to obtain the IMU test error source signal.

6. The automated calibration method for an inertial measurement unit as described in claim 4, characterized in that, The IMU test error source signal is quantized and modeled using the multimodal reference sequence data to establish an IMU error parameter model, including: Based on the IMU test error source signals, deterministic error signals, random error signals, and environmental coupling error signals are obtained; By combining the multimodal reference sequence data, error fitting is performed on the deterministic error signal, random error signal, and environmental coupling error signal respectively to generate deterministic error parameter models, random error parameter models, and environmental coupling error parameter models; The deterministic error parameter model, the random error parameter model, and the environmental coupling error parameter model are fused and optimized to establish the IMU error parameter model.

7. The automated calibration method for an inertial measurement unit as described in claim 1, characterized in that, The IMU error parameter model is minimized based on the calibration multi-objective function to determine the target IMU calibration parameters, including: The IMU error parameter model is calibrated and analyzed, and the calibration parameter particle space is initialized; Based on the calibration multi-objective function, the fitness of the calibration parameter particle space is calculated to obtain the IMU parameter particle fitness set. A neighborhood topology update mechanism is introduced to iteratively update and evaluate the IMU parameter particle fitness set within the calibration parameter particle space, and then minimize the solution until a preset convergence condition is met to determine the target IMU calibration parameters.

8. The automated calibration method for an inertial measurement unit as described in claim 1, characterized in that, The IMU to be calibrated is optimized and corrected using the target IMU calibration parameters through closed-loop optimization, including: The target IMU calibration parameters are used to test, verify, and compare the IMU to be calibrated to obtain the IMU error distribution parameters. A PID controller is used to perform closed-loop optimization and correction of the target IMU calibration parameters based on the IMU error distribution parameters.

9. An automated calibration system for an inertial measurement unit, characterized in that, The steps for implementing the automated calibration method for an inertial measurement unit according to any one of claims 1 to 8, wherein the automated calibration system for the inertial measurement unit comprises: The calibration environment setup module is used to set up an IMU multimodal calibration environment. The IMU multimodal calibration environment integrates a high-precision temperature and humidity control module, a vibration simulation device, an electromagnetic interference device, and a pressure control module. At the same time, multiple sets of reference sensors are deployed in the IMU multimodal calibration environment. The simulation test module is used to design the IMU working environment test parameter table, drive the IMU multimodal calibration environment to perform simulation tests on the IMU to be calibrated according to the IMU working environment test parameter table, and synchronously record the IMU multimodal test data and the multimodal reference data of the multiple sets of reference sensors; The error decomposition module is used to decompose and quantify the error sources of the IMU multimodal test data by combining the multimodal reference data, and to establish an IMU error parameter model. The closed-loop correction module is used to construct a calibration multi-objective function, minimize the IMU error parameter model based on the calibration multi-objective function, determine the target IMU calibration parameters, and perform closed-loop optimization correction on the IMU to be calibrated using the target IMU calibration parameters.

10. An electronic device, characterized in that, include: At least one processor; A memory that is communicatively connected to the at least one processor; The memory stores instructions that can be executed by the at least one processor, which are executed by the at least one processor to enable the at least one processor to perform the steps of the automated calibration method for an inertial measurement unit according to any one of claims 1 to 8.

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