Instrumentation & Measurement Magazine 23-2 - 70

processing of measured
data. Both distortions and
disturbances are taken
into account. Inverse algorithms provide good and
economic alternatives to
the technical improvement
of the sensor and measurement device. Moreover,
they extend the possibility of being able to measure
physical quantities that
cannot be directly measured by a sensor. The
quality can be further improved by combining the
output of different sensors
by means of sensor fusion.

Fig. 11. Reconstruction in the case of sensor fusion.

Complex Sensors

References

Frequency domain fusion is accomplished at inertial measurement units (IMU) widely used to estimate orientation
of moving objects (flight control, balancing robots, etc.). Accurate measurement is possible with a gyroscope, having a
spinning wheel and several gimbals that provide freedom of
rotation around different axes; however, its cost is extremely
high. A good alternative is its replacement with MEMS based
sensors and the combination of different sensors to provide
acceptable accuracy. 3D accelerometers, rotational speed sensors (so called rate gyro) and 3D magnetometers are usually
applied. None of them alone can accurately measure orientation. An accelerometer is assumed to measure the direction of
gravitational force; however, it is fooled by the acceleration of
the object and is insensitive along one axis of the space. Nevertheless, it provides accurate static information along the other
two axes if the object is still. A magnetometer provides good
orientation in horizontal plane; however, it is not sensitive
along the vertical axis, moreover, every metal object distorts
the magnetic field of earth and thus the measurement. A rate
gyro accurately measures the change of orientation. For angle
measurement, its output needs to be integrated (i.e., high-pass
filtering effect of the sensor regarding the angle information
needs to be compensated). Unfortunately, it requires a reference position; moreover, any offset error of the sensor gets
integrated, fooling the calculation. These three sensors alone
have limited interest but together, with proper fusion algorithm (complementary filter or Kalman filter), provide an
acceptable estimate for the fraction of the price of a real gyro.
Today, every smart phone contains such a MEMS based IMU
for orientation estimation to complement GPS, if from the
change of position (slow motion or still), the orientation of the
map cannot be estimated for navigation.

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[2]	 T. Dabóczi and A. Bódis-Szomorú, "Nonparametric identification
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[7]	 T. P. Dobrowiecki and J. Schoukens, "Linear approximation of
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[8]	 T. B. Bakó and T. Dabóczi, "Reconstruction of nonlinearly
distorted signals with regularized inverse characteristics," IEEE
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[9]	 J. P. Deyst, N. G. Paulter, T. Dabóczi, G. N. Stenbacken and T.
M. Souders, "A fast pulse oscilloscope calibration," IEEE Trans.
Instrum. Meas., vol. 47, no. 5, pp. 1037-1041, 1998.
[10]	O. Aydogmus and M. F. Talu, "Comparison of extended-Kalmanand particle-filter-based sensorless speed control," IEEE Trans.
Instrum. Meas., vol. 61, no. 2, pp. 402-410, 2012.
[11]	J. Cai and Z. Deng, "Initial rotor position estimation and
sensorless control of SRM based on coordinate transformation,"
IEEE Trans. Instrum. Meas., vol. 64, no. 4, pp. 1004-1018, 2015.
[12]	Y. Li and B. Hannaford, "Gaussian process regression for

Conclusions

sensorless grip force estimation of cable-driven elongated

Inverse algorithms have been shown to extend the accuracy
and precision of measurement instruments by numerical post
70	

uncertainty in measurement," Joint Committee for Guides in

surgical instruments." IEEE Robotics and Automation Letters, vol. 1,
no. 3, pp. 1312-1319, Jul. 2017.

IEEE Instrumentation & Measurement Magazine	

continued on page 114
April 2020



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