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Magnetic actuation and sensing

Chapter 7. General discussion

In tightly coupled schemes all measurements, for example, the individual GPS-satellites pseudoranges and IMU data, are processed together in the same filter.

The main advantage of this technique is in preserving data availability. Another benefit of this type of integration comes from the fact that poor measurements can be detected and rejected from the solution. However, tightly coupled algorithms require higher computational load in comparison to loosely coupled schemes and usually have a complex system and measurement model.

Another approach, often described in literature to solve non-linear problems, is by means of an extended Kalman filter (EKF). The EKF implements a Kalman filter for a system dynamics that results from the linearization of the original non-linear filter dynamics around the previous state estimates. Theoretically, there is no difference between the EKF and the feedback complementary Kalman fil-ter. Furthermore, the feedforward complementary Kalman filter is identical to the linearized filter [48]. With the increase of computation power over the last years, other solutions for non-linear problems such as particle filters have become a feasible option [41].

7.2. Magnetic actuation and sensing

large approximation errors at distances comparable to the coil dimensions. As a result, the defined coupling matrix Cm in Appendix 5.A of Chapter 5 will not be accurate. The exact field values can be calculated using the Biot-Savart law (Equation 5.1). For each position and orientation, the 9 magnitudes (three pulses sensed by three sensors) can be stored in a look-up table on a suitably defined grid. The effect of errors on one or more of the measured field components can be simulated, which provide confidence intervals of the estimated 6 DOF. These confidence intervals can be used in the models for the fusion with inertial sensors.

The orthogonal arrangement of the coils enabled a straightforward analytical solution to determine 6 DOF. Instead of activating three perpendicular coils, a whole network of (smaller) sources can be used. Coils can be mounted on and around body parts, such as the arms, legs and torso and integrated in clothing.

The relative position and orientation between the coils can vary during movement of the subject and should be measured with inertial sensor modules. An example of body-mounted coils integrated in a belt is given in Figure 7.1. In this asymmetric configuration, the center of the source is not a single point. However, the field coupling can be calculated for each coil, as described in the previous paragraph.

By triangulation of the measured distances from each coil, relative positions can be obtained. Also, a biaxial transmitter can be used as proposed by Paperno and Keisar [85]. However, it will result in some low-resolution regions. Combining the distance of each source with orientation estimates and anatomical knowledge of joints will increase the accuracy and can provide full body tracking.

Figure 7.1 — Prototype of body-mounted magnetic tracking system with coils integrated in a belt.

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Chapter 7. General discussion

In the performed experiments, the current through the coils was equal for each cycle. When the sensor is near the source and the signal-to-noise ratio is more than sufficient, the strength of the magnetic dipole can be decreased. Also, the duty cycle of magnetic updates was fixed. Drift errors of inertial sensors are larger when they are moved. Based on the values of the covariance matrices or estimated errors of the inertial system, the duty cycle of magnetic pulsing can be adapted.

Both options can reduce the energy consumption and increase accuracy. The first feature will also prevent clipping of the magnetometer signals. When multiple users are wearing a magnetic system close to each other, the timing of pulsing should be controlled at a higher level to avoid cross-interference of the emitted magnetic fields.

When measuring weak magnetic fields, like the earth magnetic field, sensor offset and temperature effects can greatly reduce both the sensitivity and accuracy of magnetoresistive sensors. A technique called ’flipping’ was used to cancel these effects. Flipping causes a change in the polarity of the sensor output signal. This can be used to separate the offset signal from the measured signal [106]. The unknown field in the ’normal’ positive direction (plus the offset) is measured in one half of the cycle, while the unknown field in the ’inverted’ negative direction (plus the offset) is measured in the second half. This results in two different outputs symmetrically positioned around the offset value. After filtering and rectifying, the output is free of offset. Although ’flipping’ is necessary for stable magnetic field measurements, oscillations in the output signal may occur during pulsing, due to the large changes in field amplitude. To reduce these effects, timing of ’flipping’

should occur before or after a burst of pulses and can be synchronized using the bus system to which the sensors are attached.

A concern that might arise when sending magnetic fields through the human body are safety issues. We found no signs of increased health risks with the strength of the used magnetic fields based on the studies by the International Commission of Non-Ionizing Radiation Protection [82, 83]. Moreover, magnetic trackers are already commercially available for years and no safety issues have been reported.

Nevertheless, the effect of attaching coils closely to the body should be investigated in more detail. Although no tissue is affected by low-power and low-frequency fields, electronic equipment can be disturbed. For example, pacemaker warnings usually start at 5 Gauss, with manufacturers warning at 10 Gauss. However, the field measured a few cm from the coil was around 1 Gauss. Motion analysis is often combined with recordings of the electric activity of muscles; electromyography (EMG). From several studies which recorded EMG together with magnetic motion trackers, e.g. [25, 71], we found no evidence for the influence of magnetic fields on the EMG. Loops of wire should be avoided since they can cause induced electric fields.

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