Soft-thresholding Alternating Minimization Optimization Algorithm for Turntable-free Calibration Based on the Miniature Inertial Measurement Unit

The micro inertial measurement unit (MIMU) is widely used in various fields such as aerospace, automotive industry, smartphones, and wearable devices. Field calibration is the key to ensuring measurement accuracy and reliability. To address the complex problem of solving calibration parameters for MIMU system errors in nonlinear optimization calibration methods, an alternating minimization algorithm based on soft thresholding updates was proposed in this paper. An accelerometer error model was established regarding gravity, and the gyroscope error model was established on the basis of the calibrated acceleration and rotation angular velocity in this method. Finally, the error models were used in convex optimization to design a simplified solution process. Compared with the Gauss‒Newton algorithm, the scale factor calibration accuracy was improved by one order of magnitude, and in the nonorthogonal error and bias error calibration, the accuracy was improved by one to two orders of magnitude. Compared with the calibration method using a high-precision turntable with an accuracy of 0.001 °/s, the proposed method achieved an accuracy of 10−3 through manual calibration. It can still maintain stability with initial values of different orders of magnitude, and ultimately, the global optimal solution for the error was obtained.