Meas. Sci. Technol. 23 (2012) 105104 YLiet al
the accelerometer biases and the sensor scale factors introduce
position errors proportional to the time squared (El-Sheimy
2006). Calibrations are particularly useful for the removal of
the biases and scale factor errors.
However, both the biases and scale factors of the MEMS
sensors will change with time and are highly dependent on
the environmental conditions such as temperature (Aggarwal
et al 2008). Thus a quick and convenient in-field calibration
is needed to mitigate this drift. The calibration process should
be doable by a non-professional user without any specific
equipment.
A novel and efficient hand calibration method is presented
in this paper to meet the above demands. The biases and the
scale factors of both accelerometer triads and gyro triads (i.e.
the whole IMU) can be calibrated within a short period (about
30 s), requiring only motions produced by hands.
The rest of this paper is organized as follows. Section 2
reviews previous relevant works. Section 3 explains the
methodology of this new method, including the basic idea
of the pseudo-observations. Section 4 shows some results with
analysis. Section 5 is the conclusion.
2. Previous works
2.1. Standard calibration methods
‘Calibration is the process of comparing instrument outputs
with known reference information and determining the
coefficients that force the output to agree with the reference
information over a range of output values’ (Chatfield 1997).
The 6-position static method and rate tests are normally used
for this purpose. These tests often require the use of specialized
equipment or special references such as alignment to a given
frame. With these references, each sensitive axis of every
sensor can point alternately up and down precisely, and the
IMU can be rotated around each gyro axis both clockwise and
counter-clockwise with accurately known angles (Titterton
and Weston 1997, El-Sheimy 2006). Based on the idea of
the 6-position method, there are also the 12-position method
and the 24-position method, etc (Xiao et al 2008). Compared
with the 6-position method, the improvement of these methods
lies in that the effects of some error sources can be effectively
eliminated or mitigated through adding a number of specific
position arrangements.
The above methods can be summarized as the standard
calibration methods. Their accuracy depends on how well the
axes are aligned with the reference frame. In order to obtain
accurate results, specialized equipment (i.e. a turntable or a
perfect cube) is always required so as to make IMU attitude
and rotations precisely known. Due to the dependence on
specialized equipment, these standard methods are always
designed for in-lab tests, factory calibration and relatively
high-grade IMU.
2.2. Multi-position calibration methods
For a medium- or low-grade IMU, it is not economical to
utilize the expensive specialized equipment and manpower
that would make the calibration costs even greater than the
value of the sensor or IMU itself. To calibrate an IMU just
with simple devices or even without any specific tool, a
multi-position method was developed. The basic idea of a
multi-position method can be stated as follows: the norms of
the measured outputs of the accelerometer and gyro cluster
are equal to the magnitudes of the given specific force (i.e.
gravity) and rotational velocity inputs (i.e. the Earth’s rotation),
respectively (Shin and El-Sheimy 2002). A major and vital
improvement to the standard calibration methods mentioned
above is that the multi-position method can be performed
without special aligned mounting to the local level frame
(e.g. North–East–Down). This improvement makes the method
more flexible and easier to implement.
The multi-position method was firstly presented to
calibrate biases and scale factors of a tri-axial accelerometer
in the field of medicine (L
¨
otters et al 1998). This proposed
approach was based on the fact that the modulus of the
specific force vector measured with a tri-axial accelerometer
equals 1 g under quasi-static conditions. Based on this fact, the
IMU should be kept static (or quasi-static) at various attitudes
for a period. It takes several minutes to complete the whole
calibration process. To estimate the non-orthogonalities of an
accelerometer triad as well as biases and scale factors, a new
error model was developed (Skog and H
¨
andel 2006, Syed
et al 2007).
For mid- and low-grade IMUs such as MEMS IMUs,
the main drawback in using the multi-position calibration
method is that the gyro reference (Earth rotation rate) is a weak
signal (15 deg h
−1
) which can result in observability problems
when estimating the scale factors and non-orthogonalities. To
solve this problem, a single axis turntable was introduced
to provide a strong rotation rate signal (Skog and H
¨
andel
2006, Syed et al 2007). A remaining problem was that the
inter-triad misalignment between the accelerometer and gyro
triads could not be detected, since gyros and accelerometers
were calibrated independently. Zhang et al (2010) solved
this problem using the rotational axis direction measurements
separately derived from the gyro and accelerometer triads.
Meanwhile an approximately optimal calibration scheme
was proposed by maximizing the sensitivity of the norm
with respect to the calibration parameters. This improved
multi-position approach relaxes the requirement of precise
orientation control, and it can be used to calibrate a navigation
grade IMU. At the same time, Nieminen et al (2010) also
enhanced the standard multi-position calibration method for
consumer-grade IMUs using a rate turntable by exploiting the
centripetal accelerations caused by the rotation of the turntable.
Since the total number of measurements rises, the accuracy
is improved because the method is less sensitive to errors.
Obviously, both these methods have significantly enhanced
the multi-position method.
Generally speaking, the multi-position method and the
improved multi-position methods do not require special
alignment (i.e. accurate angular positions) of the IMU. Thus
they are more flexible and easier to implement. However, these
approaches can only be used in the laboratory due to their
dependence on a turntable (to generate large enough angular
rates).
2