Instrumentation & Measurement Magazine 23-2 - 69

the model of the system and try to react to the measured excitation in the same way as the system to be observed. In this
case, both excitation and output signals need to be measured.
First, the distortion of the measurement instruments needs to
be compensated, and then state observers are applied to determine the internal state (Fig. 9c). This case differs from the
previous one in the fact that the model of signal path from internal state to the output of the system might be noninvertible,
and excitation influences the signal to be measured, not just its
measurement.

Application of the Principle for "Sensorless"
Measurement
Dependable systems require high availability even if some
component gets faulty. An embedded or cyber-physical system has strong interaction with the physical world through
its sensors and actuators. Dependability requires some kind
of redundancy in the components (both hardware and software), certainly also for the information acquisition through
sensors and measurements systems. Redundancy can be provided in several ways. The easiest but most expensive way is
the duplication or multiplication of components; after that,
a voting system can check the outputs of the redundant elements and separate the faulty component, or at least identify
the faulty situation (if only duplication can be provided). This
approach is widely used for critical components in highly dependable systems, like power plants or airplanes. The second
way for providing redundancy is repeating the information
in time to overcome temporal outage of a component or communication channel. This approach assumes a short-term
disturbance and cannot handle permanent damage. For acquisition of a physical quantity there is also a third possibility, if
there is an alternative signal path from the physical quantity to
be observed to any other measurable physical quantities. This
is called analytic redundancy that requires the knowledge of
the system (mathematical model) we are going to investigate.
A simple example to demonstrate it: let us assume that we
need the speed of an object. Instead of a speed sensor, we might
measure time and distance, and calculate the speed from the
known dependency between these quantities. The analytic
relationship in general might be much more difficult, requiring several sensors, but the principle is the same. The method
is called "sensorless principle" since we do not use a sensor
to measure that particular quantity. However, generally it requires several sensors. Sensorless principle is nothing other
than the realization of inverse problems shown in Fig. 9b and
Fig. 9c where we measure different quantities having some
relationship with the quantity of interest, and only the set of
measurements together carry the required information. This
approach is advantageous, if the required sensors-instead
of the one measuring directly the quantity we are interested
in-are either already part of the system, because of other
functionality, or are together less expensive than the one just
substituted.
Sensorless principle can be used as a redundant information source for dependable systems but also as a primary
April 2020	

Fig. 10. State of charge of battery of electric vehicles cannot be directly
measured. Analytic redundancy can help to observe it. (photo credit: Creative
Commons Zero).

information source, if the direct measurement of a quantity is
not feasible or economically not reasonable.
This approach is favored for recent control methods of Permanent Magnet Synchronous Motors (PMSM) are similar to
Brushless dc motors (BLDC) or ac motors for both automotive
and avionic applications [10], [11], and robotics [12]. Yet another interesting application from the automotive engineering
area is the estimation of the traveling range of electric vehicles.
This requires the knowledge of the state of charge of the battery. Unfortunately, there is no such sensor that could measure
it. It is easy to measure the charge pumped into the battery and
consumed for use, but the actual state of the battery, determining the efficiency of transforming electrical energy to chemical
one and backwards, the loss of energy because of self-discharge, etc. are not a priori known. However, an electrical and
ion-transport model can be determined, and their parameters
can be identified during operation, that allow the estimation
of state of charge based on voltage, current and temperature
measurements [13].

Case 3: Physical Quantity is Measured
Using Several Sensors Simultaneously
The accuracy of the measurement can be increased if-instead of one measurement-several observations are utilized
by different sensors. In this case, it is worthwhile to select sensors that extend each other with overlapping regions. The
limit can be extended in different domains. One might want to
extend measurement range by selecting sensors with overlapping range specifications. The accuracy in a wide frequency
band might also be of interest. In this case, sensors having different bandwidths or sensors with disturbances at different
frequency bands are beneficial. In all cases, the task is to combine the measurements in a way that provides more accurate
result than any sensors would alone. This is called sensor fusion (Fig. 11).
Often, sensors in different channels differ not only in measurement principle, and thus in range of operation, but also in
the quantity they measure. Sensor fusion needs to take the distortion of the sensor also into account. Distortion might mean linear
or nonlinear distortion of the sensor (or the measurement system) itself, but also the fact that that particular sensor measures
the derivative or integral of the quantity to be observed. Sensor
fusion is treated as inverse problem only if the distortions of the
sensors are taken into account during the fusion. In that case,
sensor fusion acts like a channel equalization for the whole system together, rather than for individual channels, allowing more
freedom to model-inversion at individual channels.

IEEE Instrumentation & Measurement Magazine	69



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