The modern day mobile phone is much more than a machine for voice calls and SMSs. Browsing the Internet, video-calls, gaming, virtual reality and many more use cases have made the smartphone complex machines full of all type of sensors. This article will focus on one of these sensors in mobile phones, the Inertial Measurement Unit (IMU).
IMUs are a core piece of hardware in smartphones, enabling a variety of applications such as gaming apps, fitness apps and many more. Step counting, gesture recognition, picture stabilisation are only a few examples of the uses of an IMU, and are becoming very popular with users.
The development of Microelectromechanical systems (MEMS), and the reduction in their cost, size and power consumption has made IMUs an integral part of not only high-end but also mid-range and low-end smartphones. A good example are the IMUs manufactured by Bosch.
Inertial Measurement Units are just one of the many sensor types relevant for location-based services, which we cover in Chapter 12 of our positioning book. This article completes the information in the book, giving a few details about different types of IMUs and their working principle.
What’s an Inertial Measurement Unit?
An IMU typically consists of three accelerometers and three gyroscopes, measuring acceleration and turn rates accross the three axes or a Cartesian coordinate system. This information that can be combined to generate motion related information, such as in which direction the device is moving and at which speed.
The accelerometers and gyroscopes in the IMU generate electrical signals propotional to the acceleration and angular velocity. These signals are measured with respect to the three axes, X, Y and Z, relative to the frame on which the Inertial Measurement Unit chip is mounted.
The three-dimensional measurements coming from the IMU are processed to correct typical sensor errors (sensor noise, misalignment errors, cross axis coupling errors, …). The inertial computational unit combines these values further and and provides estimates on the position, velocity and orientation of the device.
However, typical commercial sensors in mobile phones are low-cost and not very accurate. The large errors make them suitable for applications such as gesture recognition or dead reckoning, but not as a standalone positioning method. More often than that, they are combined with other measurement sources in a sensor fusion algorithm. For example, IMU measurements can be used to interpolate between known locations computed out of GNSS receivers. We give an introduction to sensor fusion in Chapter 12 of our positioning book.
After having a look at what inertial measurement unit is and how can it be used for location-based services, we will look at different types of accelerometers and gyroscopes that are used inside Inertial Measurement Units.
The different types of gyroscopes available can be broadly divided into three major types: spinning wheel gyroscopes, coriolis vibratory gyroscopes and Sagnac effect gyroscopes.
Typical smartphones Inertial Measurement Units use Coriolis vibratory gyroscopes due to the size and cost factors. Nonetheless, other 5G positioning applications, such as autonomous driving, may require to use high-end Inertial Measurement Units with other type of gyroscopes.
Spinning Wheel gyroscopes
The spinning wheel gyroscopes consist of a vertical post with a very fast rotating wheel supported at the end of a rotating hinge. The wheel rotates with a constant angular velocity w, and the force of gravity causes the wheel to produce a torque, which is perpendicular to the direction of the force applied.
The torque applied causes the whole apparatus to rotate around the vertical axis, creating an angular momentum L that points outwards from the wheel at right angles to the force of gravity.
The wheel does not collapse under the influence of the gravity due to the angular momentum caused by the rotation on the vertical axis, which is in turn caused by the torque.
This phenomena is called precession, and the rotational speed around the vertical hinge is called precession motion. Precession can also be explained based on Newton’s first law of motion, which states that objects tend to maintain their direction of motion until an external force is applied to them. The rotating disk in this case attempts to maintain the direction of rotation around the vertical axis and, as long as the disk rotates at constant speed, the whole apparatus will be balanced, with the wheel pointing in the vertical direction.
Spinning wheel gyroscopes can be used to determine the change in orientation of the object they are placed in by measuring the change in an angular momentum or precession motion. A change in precession motion occurs due to the change in the vector component gravity experienced in the direction perpendicular to the rod.
The spinning wheel gyroscopes are very precise and have wide range of application in Inertial Measurement Units for military guidance systems, aerospace and aeronautic applications. They are however not widely used in commercial applications due to the moving parts involved, which greatly increase production and maintenance costs.
Coriolis vibratory gyroscopes
The Coriolis Vibratory Gyroscopes (CVG) make use of the Coriolis force experienced by an object in motion when it is placed in a rotational plane. The object in the image is subjected to angular momentum along the z-axis. The object will experience a Coriolis force along the y-axis.
This effect is widely used for for commercial sensors in mobile phones, which are small, easy to produce and don’t require large rotating wheels. These gyroscopes consists of two masses which are made to vibrate in opposite directions, as shown in the figure. When this setup is subjected to a rotational velocity, the two masses experience a Coriolis force in opposite direction.
The angular acceleration along the z-axis is calculated by measuring the Coriolis force experienced by the structure on which the two masses are mounted. Due to the vibratory nature of these gyroscopes, they are also called tuning fork gyroscopes.
Sagnac effect gyroscopes
The Sagnac effect gyroscopes work on the principle explained by the experiment conducted by Georg Sagnac.
Consider a rotating disk with two light beams that originate at the same source but travel in opposite directions. The disk is rotating with a certain angular velocity. For an observer in the reference plane outside this system, the observed speed of the system is equal to the speed of light, c. However, for an observer on the rotating disk, the observed speed depends on which beam he is observing.
For example, if observer O1 is looking at the beam travelling in the same direction as the rotation of the disk, the observed velocity is c+v. On the other hand, for the observer O2 observing the beam travelling in opposite direction to the rotation of the disk, the velocity appears to be c-v.
The sagnac effect is used in two types of gyroscopes: the fiber optic gyroscope and the laser ring gyroscope, whose construction is shown in the figure. It consists of a laser source and a beam splitter sending the two beams in different directions. These beams are reflected on three different mirrors and then combined together on the photodetector. In the case that there is no rotation of the plane, the two waves are identical in phase, resulting in a signal with higher amplitude.
When the plane rotates, it creates a phase difference between the two waves, which results in destructive interference and hence reduces the amplitude of the signal. By measuring the amplitude reduction, the corresponding angular velocity can be obtained.
Sagnac effect gyroscopes are much more accurate than MEMS gyroscopes in detecting the angular rotation and are therefore used in high-end Inertial Measurement Units.
Accelerometers are the other type of sensors that are part of Inertial Measurement Units. They can be broadly divided into five major types, mechanical accelerometers, piezo-electric accelerometers, piezo-resistive accelerometers, capacitive accelerometers and thermal accelerometers.
Mechanical accelerometers are typically made of a strain gage, which experiences a change in resistance when a force is applied on it. The measured resistance can be used to calculate the acceleration in a certain direction.
Typically these types of accelerometers are made of a metal structure, where the structure consists of narrow bars connected to each other at the end to form a closed circuit. The orientation of the structure is in the direction where acceleration is measured. The change in resistance is caused by the change in the length of the bar: the sheer on the material changes the crystalline structure of the metal, which changes the resistance. A Wheatstone circuit connection can be used to measure the change in resistance of the structure.
These types of accelerometers are quite accurate but are also relatively expensive due to high production costs.
As the name implies, they are based on the piezoelectric effect; this is the property of some materials that generate electrical signal when they are exposed to external forces. The force created by the acceleration on the mass of the sensor results in an electrical signal that can be measured. This type of sensors has relatively low bandwidth and cannot measure constant accelerations.
They are based on the Piezo-resistive effect, where the resistance of a semi-conducting material is changed by a force applied in a certain direction. They are typically made from silicon and germanium compounds. The advantage compared to Piezoelectric accelerometers is that they can accurately measure constant accelerations. Due to small size and ease of integration, the piezo-resistive accelerometers are very popular MEMS systems and are typical IMU sensors in mobile phones.
Capacitive accelerometers are based on the change of capacitance experienced when the distance between two capacitive plates changes due to an external force. Two capacitors are placed on both sides of the moving plate, attached to the sensor body using springs.
The acceleration causes the sensor body to move and the inertial momentum produces a force in the opposite direction, which stretches the springs and causes the distance between the plates to change. The larger the distance between the moving plate and the capacitors, the greater the capacitance. Consequently, in the figure, C1 is greater than C2. By measuring the difference between C1 and C2 the acceleration can be estimated.
These types of accelerometers are useful to measure very high accelerations accurately and are used in military applications. Capacitive accelerometers are also very popular in MEMS systems and IC modules.
Thermal accelerometers measure the change in temperature of a gas when a force is applied on it. They differ from capacitive and resistive accelerometers in that they have no moving parts and solid masses, making them extremely robust and usable in noisy environments. They are also are very popular in MEMS IC systems.
Their working principle is based on a heated gas bubble that is placed in a cavity filled with cooler gas. The heated gas contains less dense gas molecules compared to the cooler gas in the cavity and when subjected to an acceleration, the heated gas moves in the direction of the acceleration. The temperature sensors at each side of the bubble are used to detect temperature changes and calculate the magnitude of the acceleration. As they are based on gas, these systems are not affected by the resonance that affects mechanical based systems. Hence, they are immune to external vibrations and shock.
Inertial Measurement Units for location-based services
In this article, we have described the major types of accelerometers and gyroscopes that are used to build inertial measurement units. As it was said at the beginning of the article, IMUs are a common sensor in mobile phones nowadays. However, the accuracy of the low-cost inertial measurement units that can be mounted on smartphones is typically low.
The usage of IMUs for location-based services is normally in combination with other positioning sources. For instance, to interpolate between GNSS location fixes during an outage, for example a tunnel. Inertial Measurement Units can be used during short periods of time to keep track of the position of a mobile phone or vehicle using dead reckoning.
Another typical use of Inertial Measurement Units is for sensor fusion. Check our book for more details on how IMUs are used for positioning applications.
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