1. Why MEMS IMU Requires Precise Calibration
Under the trends of intelligence, informatization, and the Internet of Things, terminal positioning for drones, unmanned ships, and autonomous vehicles has become increasingly important. On urban roads, accurate vehicle positioning is of great significance for reducing traffic congestion, and is also conducive to route planning and lowering transportation costs. To achieve such positioning accuracy, precise MEMS IMU calibration is critical — as the foundation of reliable inertial navigation.
An inertial navigation system can output the carrier’s position, velocity, and other information at high frequency, with the characteristics of autonomy and short-term high precision. With the development of micro-electromechanical system (MEMS) technology, MEMS inertial sensors, featuring small size and low cost, have been increasingly adopted. Their applications range from automotive airbag systems, hard disk detection, and motion analysis, to unmanned aerial vehicle navigation, pedestrian navigation and indoor positioning, and smart weapon systems. Among these, the integrated navigation system combining MEMS accelerometers, MEMS gyroscopes, and GNSS positioning information — referred to as the INS/GNSS integrated navigation system, is attracting growing attention.
The positioning accuracy of an INS/GNSS integrated navigation system depends on the accuracy of the MEMS inertial sensors and the accuracy of GNSS positioning. Since factory MEMS inertial sensors are typically not precisely calibrated, they carry deterministic errors — systematic calibration errors that can be corrected through a proper IMU calibration process. Therefore, high-precision calibration of their parameters before application is critical to reducing operational errors.
2. What Parameters MEMS IMU Needs to Calibrate
MEMS inertial sensors sense the carrier’s inertial physical quantities (angular velocity and acceleration relative to inertial space) and convert them into electrical signals through detection technology. However, these signals cannot be directly used for attitude calculation and position reckoning of the carrier. First, calibration is required to obtain the conversion coefficients between the sensor output signals and the physical quantities, namely the scale factor (also called proportional factor or sensitivity). The scale factor is then used to convert the electrical signals into physical quantities, which can subsequently be used for attitude calculation and position reckoning.
For a micro-inertial navigation system, the inertial sensors consist of three gyroscopes and three accelerometers mounted in an approximately orthogonal arrangement (also called a 6-axis inertial unit). Therefore, the parameters that need to be calibrated in MEMS IMU calibration mainly include the scale factor, bias (requiring zero-offset calibration), non-orthogonal parameters (including orthogonality error and cross-axis sensitivity), and IMU temperature drift.
With the advancement of MEMS technology, MEMS inertial units have evolved from units assembled from six discrete sensors to single-chip integrated inertial units. Correspondingly, MEMS inertial sensor calibration technology has progressed from single-axis to triaxial calibration research.
3. Overview of MEMS IMU Calibration Methods
For MEMS rate gyroscope parameter calibration, traditional methods use the rotational angular velocity of a rate turntable as a reference and apply fitting methods for calibration. For calibration without a rate turntable, the vector cross-product calibration method or system-level calibration methods based on error equations can be adopted.
There is extensive research on MEMS accelerometer calibration methods both domestically and internationally, especially calibration methods that do not rely on a three-axis turntable as a reference. Accelerometer calibration methods without a turntable are also called autocalibration methods. The principle of these methods is to use the fact that the vector magnitude of converted accelerometer output data equals the local gravity value, and then study parameter search methods to obtain calibration parameters. Autocalibration methods for accelerometers include parameter optimization using Genetic Algorithm (GA), Particle Swarm Optimization (PSO), gradient descent-based parameter optimization, variable-gain Newton method parameter optimization, and the Levenberg-Marquardt method for parameter optimization.
Research on MEMS sensor mounting error calibration is divided into two categories: calibration with a turntable and calibration without a turntable. With a three-axis turntable, given its high orthogonality, the least squares method is used to calibrate to the turntable coordinate system. Without a three-axis turntable, the accelerometer’s orthogonal coordinate system is used as a reference, and parameter identification methods based on KF (Kalman Filter) are employed under designed rotation sequences to achieve calibration. Alternatively, the accelerometer can be calibrated first, followed by the gyroscope calibration method without a turntable, thereby achieving mounting error calibration for MEMS inertial sensors.
Research on temperature drift error calibration methods for MEMS inertial sensors can be divided into two experimental approaches: the Soak method and the Ramp method. In the Soak method, the temperature inside the environmental chamber is controlled to stabilize at a specific temperature point. Once the sensor’s internal temperature stabilizes, rotation and data acquisition operations are performed to obtain the data needed for calibration. The calibration parameters at that temperature point are then obtained through multi-position least squares methods, parameter search methods based on the principle of equal vector magnitudes, and so on. The Soak method typically requires acquiring calibration data at N temperature points, yielding N sets of calibration parameters. In the Ramp method, the temperature inside the environmental chamber is controlled to rise or fall at an approximately uniform rate, during which calibration data is collected and parameter calibration is performed.
4. The Six-Position Parameter Correction Calibration Method
4.1 Method Principle
Research on MEMS inertial sensor calibration methods can be divided into two directions: deterministic error calibration at constant temperature and IMU temperature drift calibration. Constant temperature or near-constant temperature parameter calibration can be further divided into three parts: MEMS gyroscope calibration (with rate gyroscopes as the research object), MEMS accelerometer calibration, and MEMS inertial sensor mounting error calibration (referring to mounting errors relative to the orthogonal coordinate system).
To achieve low-cost and high-precision error calibration requirements for MEMS inertial sensors, the six-position parameter correction calibration method — a form of multi-position calibration — is proposed. First, the error model of MEMS inertial sensor data is studied. Then, data characteristics at different positions are analyzed. On this basis, the six-position parameter correction method is proposed for parameter calibration of both accelerometers and gyroscopes.
For MEMS accelerometer calibration, the method without a turntable is also called autocalibration. The principle of these methods is to use the fact that the vector magnitude of converted accelerometer output data equals the local gravity value, then study parameter search methods to obtain calibration parameters.
4.2 Accelerometer Calibration Results
Simulation results show that this method can achieve a scale factor with a relative error of 0.06% (effectively eliminating scale factor non-linearity), a bias error of 0.5 mg, and non-orthogonal transformation matrix off-diagonal element errors of 0.006 (equivalent to an angular error of 0.35°). Repeated calibration experiments also demonstrate the effectiveness of the six-position parameter correction method.
With six-position data, the parameters calibrated by the six-position parameter correction method exhibit consistent accuracy, almost unaffected by the bias to be calibrated. Under the accuracy of a 3D-printed frame (0.2° perpendicularity error), the relative error of the main diagonal elements of the transformation matrix is less than 0.06% (i.e., 600 ppm); the off-diagonal element error is less than 0.005, with parameter variation during repeated calibration of ±0.001; the absolute bias error is less than 0.005 m/s², with parameter variation during repeated calibration of ±0.001 m/s².
4.3 Gyroscope Calibration Results
The six-position parameter correction method is equally effective for MEMS gyroscopes. Compared with attitude updated from raw gyroscope data, the pitch and roll angle errors after attitude update using parameters calibrated by the six-position parameter correction method are significantly reduced. The absolute roll error is reduced from 159 degrees to within 2 degrees, and the absolute pitch error is reduced from 35 degrees to within 1 degree. This demonstrates that the six-position parameter correction method is effective for gyroscope parameter calibration and achieves high precision consistency.
5. Temperature Drift Error Calibration and Compensation for MEMS IMU
5.1 Accelerometer Temperature Drift Calibration
IMU temperature drift calibration for MEMS accelerometers first requires analyzing data drift characteristics under heating conditions. During temperature changes, accelerometer output data exhibits significant drift, with different drift magnitudes across different axes. By analyzing static data during the heating process, the drift pattern of the data with temperature variation can be extracted.
In the experiment, the MEMS inertial sensor was fixed onto a cubic frame, and the cubic frame was placed inside an insulated wooden box. The interior of the insulated wooden box contained heating wires that allowed the temperature inside the box to rise. When collecting sensor data during the heating process at each position, heating was first applied to raise the temperature inside the box. When the temperature approached the target, heating was stopped. After the temperature dropped by a few degrees, the heating wires were alternately turned on and off to control the sensor temperature within a small fluctuation range, creating an approximately constant-temperature environment. Through this operation, the error compensation method — effectively a temperature compensation algorithm — for the heating data drift curve could be used to mitigate the drift caused by the material’s delayed response to temperature.
After obtaining data from the heating process, the sensor was powered off to cool down, and the box door was opened to facilitate cooling. When the temperature inside the box dropped to near ambient temperature, accelerometer data at the next position was collected. This operation was repeated to collect accelerometer data at all six positions. During data collection, the sampling frequency was set to 100 Hz.
Since the parameter accuracy consistency achieved by the six-position parameter correction method ensures relatively small parameter fluctuations during repeated calibration, and given this algorithmic characteristic, when six-position data at each temperature point is acquired, algorithmic calibration can yield a relatively accurate parameter drift trend. By comparing with accurate parameters at a specific temperature, the bias error in the parameter drift curve can be removed, thereby obtaining a more accurate parameter temperature drift curve.
Experimental results show that when the test data temperature rises from 12°C to 47°C, after conversion using the calibrated temperature drift parameters, the data drift of the accelerometer X-axis, Y-axis, and Z-axis changes from -29.2 mg, 18.3 mg, and -28.5 mg before conversion to 0.5 mg, -1.9 mg, and -1.1 mg respectively. The temperature drift errors are suppressed by approximately 98%, 89%, and 96%, respectively.
Because the parameters calibrated by the six-position parameter correction method exhibit small fluctuations, this method can reflect the true parameter drift trend in accelerometer temperature drift error calibration. This provides the basis for the temperature drift calibration method that combines the six-position parameter correction method and the 9-parameter least squares method, and also demonstrates the effectiveness of this approach.
5.2 Gyroscope Temperature Drift Calibration
To address the problem of gyroscope calibration parameters drifting with temperature, a segmented system-level calibration method based on 24 states under heating experimental conditions is proposed. After analyzing gyroscope parameter characteristics, a system-level calibration method based on error equations suitable for low-cost calibration targets is first determined. The system equations with 24 states are then derived, and a segmented system-level calibration method under heating conditions is proposed. This calibration method includes two steps: the first step uses the system-level calibration method under data segmentation to obtain the drift trend of gyroscope parameters versus temperature; the second step removes the bias error in the parameter drift curve using accurate parameters at constant temperature, thereby obtaining a more accurate gyroscope parameter temperature drift curve.
In a 100-second pure inertial navigation test, after conversion using the gyroscope temperature drift parameters, the east, north, and altitude positioning errors changed from -230.8 m, 378.7 m, and -9.1 m to -89.7 m, 203 m, and -5.3 m respectively, with positioning error suppression of approximately 61%, 46%, and 41%. This demonstrates the effectiveness of the proposed method.
6. Conclusion
There are three main factors affecting the positioning error of a vehicle-mounted INS/GNSS integrated navigation system: MEMS inertial sensor errors, changes in GNSS positioning information error characteristics, and GNSS denial (or signal loss). Among these, MEMS IMU calibration — error correction of the inertial sensors themselves is the foundational step for improving the positioning accuracy of the integrated navigation system.
The parameters that need to be calibrated for MEMS inertial sensors mainly include the scale factor, bias, non-orthogonal parameters, and temperature drift error. The six-position parameter correction calibration method can achieve high-precision parameter calibration under low-cost conditions (without requiring an expensive three-axis turntable), with accelerometer scale factor relative error as low as 0.06% and bias error of 0.5 mg. Combined with the temperature drift calibration method, the triaxial temperature drift error of the accelerometer can be suppressed by 89% to 98%, and after gyroscope temperature drift compensation, the pure inertial navigation positioning error can be suppressed by 41% to 61%.
Through precise error calibration and temperature drift compensation, low-to-medium-cost MEMS IMU, when properly temperature compensated, can achieve higher positioning accuracy in INS/GNSS integrated navigation systems, thereby reducing the cost of vehicle-mounted INS/GNSS integrated navigation systems and providing a viable high-precision positioning solution for large-scale applications such as autonomous driving.