Technical note
Simple and efficient thermal calibration for MEMS gyroscopes

https://doi.org/10.1016/j.medengphy.2018.03.002Get rights and content

Highlights

  • An easy protocol to perform a thermal gyroscope calibration is proposed.

  • This calibration procedure is performed without any need for temperature control.

  • The proposed simple calibration method leads to a similar accuracy than those obtained from the manufacturer, known to be performed by controlled rotation on a thermal chamber.

  • An analysis of uncertainty propagation highlights that offsets variability is the major source of error over the computed rate of rotation from the tested sensors. This result leads to a simplified calibration method.

Abstract

Gyroscopes are now becoming one of the most sold MEMS sensors, given that the many applications that require their use are booming. In the medical field, gyroscopes can be found in Inertial Measurement Units used for the development of clinical tools that are dedicated to human-movement monitoring. However, MEMS gyroscopes are known to suffer from a drift phenomenon, which is mainly due to temperature variations. This drift dramatically affects measurement capability, especially that of cheap MEMs gyroscopes. Calibration is therefore a key factor in achieving accurate measurements. However, traditional calibration procedures are often complex and require costly equipment. This paper therefore proposes an easy protocol for performing a thermal gyroscope calibration. In this protocol, accuracy over the angular velocity is evaluated by referring to an optoelectronic measurement, and is compared with the traditional calibration performed by the manufacturer. The RMSE between the reference angular velocity and that obtained with the proposed calibration was of 0.7°/s, which was slightly smaller than the RMSE of 1.1°/s achieved by the manufacturer's calibration. An analysis of uncertainty propagation shows that offset variability is the major source of error over the computed rate of rotation from the tested sensors, since it accounts for 97% of the error. It can be concluded that the proposed simple calibration method leads to a similar degree of accuracy as that achieved by the manufacturer's procedure.

Introduction

Gyroscopes are now required for use in many high-volume applications such as connected objects, vehicle guidance and navigation, and motion control of robots and drones. In the medical field, gyroscopes can be found in inertial measurement units that are used to develop wearable systems dedicated to ecological human-movement monitoring. Such monitoring has many applications, including telehealth, patient follow-ups, and development of new devices (for example, exoskeleton and bionic prostheses and rehabilitation equipment).

However, gyroscopes remain under-produced in comparison with accelerometers or pressure sensors, and as such their cost remains higher [1]. The microelectromechanical systems (MEMS) industry is now facing the challenge of producing low-cost and high-performance gyroscopes.

MEMS technology is particularly adapted to most of the previously cited applications because it enables sensors to be miniaturized, lightweight and cheap. However, MEMS gyroscope performance is known to be much lower than navigation-grade sensors, which are still used in the aeronautics and military fields. For these sensors, which are commonly classified as automotive or consumer grade, it is largely reported in the literature that gyroscope bias is a critical factor [2], [3]. Estimating an angle range by performing a numerical integration over the measured rate of rotation is a common procedure used to gauge the live orientation of human segments for movement analysis [4]. In this case, errors accumulate due to gyroscope bias, which is collectively referred to as drift.

While stochastic sensor errors cannot be fully corrected due to their random nature, many authors suggest removing the majority of the deterministic errors by updating calibration parameters [5], [6], [7]. As reported in the work by Nez and co-workers [8], different measurement models and different calibration methods can be considered. For the gyroscope measurement model, parameters that are commonly taken into account are bias, scale factors and non-orthogonality [5], [6], [9]. Calibration (i.e. the process performed to identify the parameters of the measurement model), is typically done by performing rate tests using a rate-precision turntable [5], [9], [10]. By comparing the outputs of the gyroscope to the precisely known rates of rotation, calibration parameters can be identified. On the other hand, methods that use only the measure of the earth's rotation rate instead of controlled rotation on a turntable have been developed for navigation and tactical grade gyroscopes [11]. However, this rate is too low to be measured by consumer-grade sensors.

The choice of a measurement model and a calibration method is a compromise between resulting accuracy, time constraints, calculation complexity and required equipment [8]. For MEMS gyroscopes, the calibration process is complicated by its dependency on another factor: temperature. It is well known that MEMS gyroscopes are highly sensitive to temperature variation [5], [9]. In the study by Shcheglov et al. [12], it has been shown that temperature fluctuations are a major source of drift for MEMS gyroscopes, particularly for temperatures higher than 20 °C. Temperature also has an impact on noise performance. For example, temperature compensation can improve the gyroscope Allan deviation bias from 0.6°/h to 0.35 °/hr [10]. Hence, the dependence of calibration parameters on temperature must be identified. Consequently, taking the gyroscope temperature into account during calibration requires a temperature-dependent measurement model and a specific calibration process.

Two main approaches to performing this particular process have been described in the literature. The first approach recommends enclosing the sensor in a thermal chamber to stabilize it at a particular temperature before performing calibration rotations. This method of calibrating the sensor at specific temperature points is called the Soak method [5]. The second method, the Thermal Ramp method, which is considered to be faster, consists of performing different calibrations while the sensor temperature is linearly increased or decreased [13]. However, there are two concerns with this method: the temperature differences between the gyroscope and the temperature sensor, and the chamber temperature changes during the calibration test. A faster approach, and a balanced heating-and-cooling strategy, was proposed by Niu and colleagues [9] to improve the original Thermal Ramp method. However, both methods require a costly thermal chamber equipped with a multi-axis turntable.

Since conventional thermal calibration methods are typically time-consuming and costly, this paper proposes including temperature to perform MEMS gyroscope calibration without any need for temperature control. This simple method would enable regular recalibration whenever a defect is detected.

Section snippets

Measurement model

It is generally agreed that the measurement model for a uniaxial gyroscope can be considered as linear when environmental conditions (for example, temperature) are sufficiently steady. Thus the rate of rotation ω can be estimated from the electric potential u given by the sensor, by means of an offset (or bias) b and a scale factor (or sensitivity) s as follows: ω=s.(ub)

When considering triaxial sensors, authors often include non-orthogonal error parameters to take into account the

Materials and method

Before analyzing the effect of calibration during a movement, we highlighted the results on a static acquisition while the sensor temperature was increased from 7°C to 40°C. The rate of rotation was measured from the gyroscopes using the single-value calibration (performed at room temperature: 20°C) described in Section 2.2 and the temperature-compensated calibration described in Section 2.3, respectively. The calibration performed by the manufacturer (which is known to be

Conclusion

After defining a specific measurement model and describing a known high-performance calibration method for gyroscope at one point of temperature, this paper suggests a simple protocol to estimate calibration parameters as a function of temperature. Calibration is performed on a motorized test bench while an auxiliary heater increases the sensor temperature. Results showed that temperature-compensated gyroscope calibration significantly improved the computed rate of rotation, compared to

Acknowledgments

This work has been partially sponsored by the French government research program “Investissements d'Avenir” through the Robotex Equipment of Excellence (ANR-10-EQPX-44).

Conflicts of interest

The authors declare no conflict of interest.

Ethical approval

Not required

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