Hardware

This section is dedicated to the hardware subsystem. There are two sensors which constitute the foundation of the pocket navigation system: accelerometer and gyroscope. Both together are integrated in a hardware unit called inertial measurement unit (IMU).

What means inertial?

The goal of the sensors is to measure the motion of the pedestrian. However, the motion of any body can only be described relative to something else. The motion is usually described relative to space-time coordinates, namely frame of reference.

I will use the classical physics to describe the movement of a particle. The Newton’s first law says that any particle in a state of rest or of uniform linear motion tends to remain in such a state unless acted upon by an external force. The second law says that the sum of all forces acting on the particle is equal to its mass times its acceleration.

The forces acting on the particle change with the election of the frame of reference. Let’s use a very simple example, a pedestrian standing on a sidewalk while a car is driving in a roundabout:

If the driver is the observer, that means the frame of reference is in the car, he would say that a centrifugal force is acting on him. By entering the roundabout he feels a force pointing outwards which modifies his state of rest.
If the pedestrian is the observer, that means the frame of reference is on the street, he would say that a centripetal force is acting on the driver. By entering the roundabout the driver has to modify his state of uniform linear motion, thus he generates a force pointing towards the center of the roundabout by turning the steering wheel. This force continuously modifies the direction of the velocity of the car.

The centrifugal force is fictitious. Fictitious forces are apparent forces which do not arise from any physical interaction between two particles, but rather from the acceleration of the non-inertial reference frame. These forces disappear if the frame of reference does not accelerate.

However, the pedestrian’s frame of reference is also accelerating because the Earth is rotating. A more detailed analysis includes also the Coriolis and Euler forces as fictitious forces necessary to describe the movement of the driver in the pedestrian’s frame.

Ok, so where can I put the frame of reference for it to be inertial?



In Newton’s time the fixed stars were the inertial reference frame, because they were supposed to be at rest relative to the absolute space. Then E. Halley demonstrated that the fixed stars are not fixed, therefore a new definition of inertial frame was provided. This definition is based on the simplicity of the laws of physics in the frame. Thus, the absence of fictitious forces is their identifying property. In the special theory of relativity A. Einstein wrote:

All physical laws take their simplest form in an inertial frame.

The IMU measures relative to the inertial frame of reference. That means it measures the pedestrian’s movement in the universe due to his specific motion combined with the rotation of the Earth, the translation of the Earth around the Sun, the translation of the Sun around the center of the Milky Way…

The earliest IMU technology is called stabilised platform and it is still in use for ships and submarines. It consists of a platform on which three mutually orthogonal gyroscopes and three mutually orthogonal accelerometers are mounted. This platform is isolated from the angular motion of the casing through gimbals which provide three degrees of rotational freedom. There are motors that rotate the gimbals based on the gyroscopes information in order to maintain the platform stable.

Therefore in a stabilised platform IMU, the accelerometers measure directly relative to the inertial frame because its reference frame is isolated from the angular motion of the casing. Thus, the orientation of the sensors reference frame is stable.

During the World War II the principles of inertial navigation were used in the V1 and V2 rockets (¬¬) and later during the 1960’s inertial navigation systems became standard equipment in military aircraft, ships and submarines with the aforementioned technology. The progress in the miniaturization, accuracy and dynamic range of the sensors enabled the strapdown technology to become a reality during the 1970’s.

In strapdown systems, the sensors are “strapped-down” or fastened to the casing and therefore are not isolated from its angular motion. Unlike the stabilised platform reference of frame, the frame of reference of the sensors of a strapdown IMU is not stable because it moves with the casing.

In a strapdown IMU, before using the accelerometers signal, it is first necessary to know the orientation of the sensors relative to the inertial frame. The orientation of the sensors is computed thanks to the gyroscopes signals. The measurements of the accelerometers are then transformed to the inertial frame. After this transformation, the accelerometer readings for both technologies of IMU are equivalent.

The strapdown technology replaces therefore the mechanical complexity of the stabilised platform technology -intricate mechanical structures for the gimbals, platform connections, etc.- by computational complexity.

The vast majority of the IMUs nowadays use the strapdown technology. However, it was necessary a big technological jump until the IMUs used primarily for aircraft, missiles, ships and submarines could be used for pedestrian navigation.

The governing parameters for pedestrian navigation applications are cost, size and power consumption. The use of silicon as the base material in the manufacture of the sensor components was a step forward regarding the aforementioned parameters with respect to the initial mechanical sensors.

The silicon was a breakthrough in the transition of the micro-electromechanical sensors (MEMS) from research to a mass sensor. It first began with the low cost and miniaturization of the accelerometers for the automobile industry that are used, among others, for the activation of the airbag security system.

The MEMS accelerometers and gyroscopes based on a solid-state architecture and few components, compared to the mechanical sensors, are nowadays the predominant technology embedded also in every smartphone.

The hardware unit of the IMU usually includes other type of sensor: the magnetometer. The magnetometer measures the intensity and direction of the magnetic field of the Earth. This sensor has been used for centuries in the area of navigation, because the knowledge of the direction of the magnetic North helps enormously in navigation. If three orthogonal magnetometers are also present, the hardware is called magnetic and inertial measurement unit (MIMU).

In the following, the most important characteristics of the accelerometer, gyroscope and magnetometer are explained.