Rapid Gyroscope Calibration: A Deep Learning Approach

TL;DR

This work tackles rapid zero-order calibration of low-cost gyroscopes by combining real and virtual multi-gyro data within a CNN-based framework to estimate and compensate deterministic bias. Two complementary strategies are explored: increasing input channels (multi-gyro inputs) and expanding training data with real and virtual measurements, trained under an MSE objective with Adam optimization. Across six real and virtual datasets from four brands, the approach achieves substantial reductions in calibration time (up to ~88% in some setups) and improved bias estimates, with robustness demonstrated across device types. The method enables fast deployment of inertial navigation systems in time-sensitive applications, while acknowledging a trade-off where model-based calibration remains superior when unlimited calibration time is available; virtual data further enhances scalability and data efficiency. The technique shows strong practical potential for robotics, autonomous systems, and related fields where rapid sensor readiness is critical.

Abstract

Low-cost gyroscope calibration is essential for ensuring the accuracy and reliability of gyroscope measurements. Stationary calibration estimates the deterministic parts of measurement errors. To this end, a common practice is to average the gyroscope readings during a predefined period and estimate the gyroscope bias. Calibration duration plays a crucial role in performance, therefore, longer periods are preferred. However, some applications require quick startup times and calibration is therefore allowed only for a short time. In this work, we focus on reducing low-cost gyroscope calibration time using deep learning methods. We propose an end-to-end convolutional neural network for the application of gyroscope calibration. We explore the possibilities of using multiple real and virtual gyroscopes to improve the calibration performance of single gyroscopes. To train and validate our approach, we recorded a dataset consisting of 186.6 hours of gyroscope readings, using 36 gyroscopes of four different brands. We also created a virtual dataset consisting of simulated gyroscope readings. The six datasets were used to evaluate our proposed approach. One of our key achievements in this work is reducing gyroscope calibration time by up to 89% using three low-cost gyroscopes. Our dataset is publicly available to allow reproducibility of our work and to increase research in the field.

Figures (14)

• Figure 1: Example of a running average applied to measurements over time of a stationary gyroscope until convergence is achieved, approximately after 63 seconds.
• Figure 2: Raw and calibrated gyroscope signals. The blue signal presents the raw stationery gyroscope measurements, the orange line being the deterministic bias. The calibrated gyro measurements are shown in the green signal.
• Figure 3: MG convergence over time as a function of the number of gyroscopes. (Left): Using a single gyroscope. (Center): Using 4 gyroscopes. (Right): Using 10 gyroscopes.
• Figure 4: Block diagram of our proposed approach to increasing the number of input channels. The upper diagram depicts a setup with three gyroscopes while the lower has $3\dot N$ gyroscopes. The figure shows the differences in the training data size, input channels, and output. N is the number of IMUs, M is the number of samples recorded by each gyroscope, and S is the window size.
• Figure 5: Block diagram illustrating our approach for increasing the training data. The upper diagram depicts a setup with three gyroscopes; the lower diagram shows $3\dot N$ gyroscopes. The figure shows the differences in the training data size. N is the number of IMUs, M is the number of samples recorded by each gyroscope, and S is the window size.