Measuring the Earth’s Rotation Rate Using a Low-Cost MEMS Gyroscope

Accurate measurements of the Earth’s rotation rate can be obtained by using high quality gyroscopes, such as ring laser gyros (RLG) included in tactical grade inertial measurement units. However, such devices are bulky and expensive. As the Micro-Electro-Mechanical System (MEMS) technology has evolved rapidly during the last years, accurate low-cost gyroscopes are now available. Are the new MEMS gyros accurate enough to detect and measure the Earth’s rate? In this paper, we describe a method and algorithm that can be used to answer this question. To test the developed method, we used a modern MEMS gyroscope with specified bias stability less than 2 degrees per hour. The bias stability indicates that it is possible to measure the Earth’s rate. However, in order to do this, all the external factors that affect the gyro bias need to be carefully taken into account. For example, in order to observe the bias the gyroscope needs to be rotated sequentially. In the paper, we present a sequence of rotations that aims to maximize the signal to noise ratio and minimize the time needed to detect the Earth’s rotation rate. Furthermore, the influence of gravity in the bias can be examined with another sequence of rotations. For both cases, we use an accurate stepper motor to switch between different orientations. With this set up, we have successfully determined the Earth’s rotation rate. In addition, by using a Kalman filter we were able to estimate the magnitude of the rate with accuracy better than one degree per hour. The Kalman filter approach was used to improve convergence time and to enable error estimation. The results show that if the factors that affect the bias of the sensor are minimized and correctly modeled, the Earth’s rotation rate can be detected and estimated with new MEMS gyroscopes. This level of accuracy makes MEMS gyroscopes suitable for application areas where traditionally more expensive gyro technologies have been exploited.