Figure 3.2 Top view of a simplified accelerometer sensor from ADXL50 [49] datasheet. Anchor points move with the device frame, while inertia of the proof mass causes the distance between fixed plates to vary, changing the capacitance [20].

      Source: Courtesy of Jarchi, D., Pope, J., Lee, T.K.M., Tamjidi, L., Mirzaei, A. and Sanei, S.

      where M is the mass of proof mass, E and D are the distances travelled by the proof mass with respect to the earth and to its anchors respectively, b is the damping factor, and k the spring constant. The differentiation is with respect to time t. In addition, there are electrostatic forces between the fixed and moving plates to be considered. In order to measure the speed of movement, consider the relative motion between the stationary plates and the moving proof mass which changes the capacitance between them.

However, to measure the acceleration, the transfer of charge is amplified electronically by mixing with a high-frequency signal using a double sideband suppressed carrier modulation technique. Finally, the amplitude-modulated signal is synchronously demodulated and amplified.

There are several ways to evaluate the movement resulting from the changes in capacitance. Early methods used closed loop feedback by impressing a voltage on the capacitor plates so the proof mass stays at its original position [25]. Changes in this voltage thus reflect the change in position. More recent methods are open loop, where the capacitance is obtained using switched-capacitor techniques.

      Despite the widespread use of accelerometers, there are limitations of current devices which prevent them from being used in even more applications. A prime example is that of deriving the speed and distance moved by performing mathematical integration of the measured acceleration. In practice, the measurements drift and the integration causes accumulation of these errors rendering the readings useless. To overcome this, it is necessary to periodically recalibrate the accelerometer readings. One popular method is zero-velocity update point (ZUPT). Other schemes depend on the instances where an external event indicates an instantaneous null in the movement pattern, for example in between footsteps [25].

      Another source of accelerometer disturbance is the noise arising from mechanical sources due to the proof mass being subjected to Brownian motion. Nevertheless, electronic sources themselves generate considerable noise. The conversion of minute capacitance changes to usable voltages requires high electronic gain and, with that, an increase in noise. A widely used method benefits from switched-capacitor techniques, and the oscillation frequency can be superimposed to the main signal, resulting in an aliasing effect. This may be worsened when using chopper amplification with synchronous demodulation, often applied to moderate the effect of drift.

      3.2.1.2 Accelerometers in Practice

      Accelerometers have gained even wider use by being part of consumer devices like smartphones and tablets. It is useful to differentiate between such installed units and those available as standalone units, where the accelerometer integrated circuit has settings for force sensitivity. The external components may filter part of the operating frequencies too. These units are small in size and consume little current but need to have proper packaging.

      By way of contrast, in ready-to-use consumer devices, there is no control over how an accelerometer is mounted in its physical environment. This affects its operating conditions in terms of temperature, humidity, and electronic interference. In addition, inevitable smoothing of the measurements by means of digital filtering and processing may introduce further latencies. Nevertheless, in many situations, in order to achieve device independence [26], the accelerometer is treated as a ‘black box’, where the digital readout is assumed to be a measure of the acceleration. Then, the imperfections are treated statistically and data calibration would need to be employed for demanding applications. In spite of this, the use of accelerometers in consumer devices has proven to be adequate for many clinical purposes, mainly due to their compatibility with many computing systems and microcontrollers and also their flexibility in terms of price, size, and application as seen in various publications, such as [27]. In such applications the measurements are compared with gold standard equipment like motion capture cameras and accelerometers built in instruments designed for clinical use.

      The use of accelerometry for gait analysis has been significantly increased due to their ease of use, portability, compatibility, and the capability to be integrated into low-powered wireless embedded platforms. However, in addition to accelerometers, there are other popular existing wearable technologies for gait analysis which are briefly described here.

      3.2.2 Gyroscope and IMU

The gyroscope is arguably the next most commonly used motion detector after the accelerometer. It can be attached to the feet to measure the angular velocity of the foot for detecting different gait phases [28]. The MEMS technology used in accelerometers is used to drive down the cost of gyroscopes, so they are often featured alongside accelerometers in many devices and in IMUs. In contrast to accelerometers, which can directly measure linear acceleration, gyroscopes measure the angular movement about a given axis.

      Accelerometers by themselves can measure angular rotation but they cannot give as good a result as gyroscopes, as shown in [29]. Thus, the gyroscope can be used to correct the accelerometer readings, or have its output fused with those of accelerometer when deployed together, such as in an IMU.

      The miniaturisation technologies for fibre optic and MEMS progresses quickly. Except for gyroscopes working on optical principles, what the other types have in common is a mass that is constantly moving within the device in order to measure the angular motion. This motion causes the gyroscope to consume more current than an accelerometer. An example of MEMS gyroscope technology is that based on Coriolis acceleration [30]. As opposed to centrifugal acceleration, which is always present in rotation, Coriolis acceleration occurs whenever there is motion along the radius of the rotation.

Figure 3.3 shows the schematic of a single axis of a gyroscope which rotates clockwise, together with its semiconductor substrate. The gyroscope has capacitive fingers fabricated as part of its structure [20]. To this substrate a frame with a set of capacitive fingers is tethered with springs. In addition, a mass, also tethered to this frame with springs, is driven into mechanical resonance and constrained to move in one direction. On the left of the figure, the mass is considered as it moves to the top of the figure along the radius of rotation. The Coriolis force acts on the frame, which deflects to the left as shown. On the right of the figure, as the mass resonates it moves to the bottom of the figure; in this case the Coriolis force causes a deflection to the right. The varying distance between the capacitive fingers is picked up as a voltage representing a measure of the angular speed. From [29], it can be shown that the displacement of the frame relative to the substrate is [20]:

Figure 3.3 A simple diagram of a gyroscope rotating clockwise. On the left, resonating mass is moving upwards, whereas, on the right, it is moving downwards. Direction of Coriolis force is also shown [20].

      Source: Courtesy of Jarchi, D., Pope, J., Lee, T.K.M., Tamjidi, L., Mirzaei, A. and Sanei, S.

      where Ω is the angular velocity of the gyroscope (towards the right) and v the velocity of the resonating mass along the radius of rotation,

---

Скачать книгу