Velocity measurement based on inertial measuring unit

TELKOMNIKA, Vol.17, No.4, August 2019, pp.1898~1906
ISSN: 1693-6930, accredited First Grade by Kemenristekdikti, Decree No: 21/E/KPT/2018
DOI: 10.12928/TELKOMNIKA.v17i4.11826 ◼ 1898
Received June 30, 2018; Revised March 5, 2019; Accepted April 12, 2019
Velocity measurement based on
inertial measuring unit
Waru Djuriatno*1
, Eka Maulana2
, Hasan3
, Effendi Dodi Arisandi4
, Wijono5
1,2,5
Department of Electrical Engineering, Brawijaya University, Indonesia
1,2,5
Collaborative Research Center for Advanced System and Material Technology
3
Master Program in Telecommunication Engineering, National Sun Yat-sen University
4
Lembaga Penerbangan dan Antariksa Nasional, Indonesia
*Corresponding author, e-mail: warudj@ub.ac.id
Abstract
Vehicles technology have been a priority area of research over the last few decades. With the
increasing the use of electronic components in the automotive industry to measure conditions around the
vehicle, the focus of automotive technology development is now leading to the development of active
technology. Information on the speed of conventional vehicles is generally still obtained based on the
rotation of the wheel, but there are weakness in the system that is the diference between wheel and road
through vehicle also changes wheel radius of the vehicle due to wind tube air preasure that can change at
any time. In this research used Inertial Measuring Unit (IMU) 6 axis (accelerometer and gyroscope) which
have been done filtering by using Kalman filter in order to make output sensor value more stable, results
obtained at the test of 0 m/s had an RMS error of 0.8696 m/s when elevation is +450; 0.0393 m/s when
elevation is 00; and 0.3030 m/s when elevation is -450. this research is expected to be an exploration for
the development of a decent system that is suitable to be used as vehicle speed estimator which is as
reliable as it is by using an existing speedometer on a ground vehicle generally regardless of slippage and
changes in wind capacity on wheels.
Keywords: inertial measuring unit, Kalman filter, velocity
Copyright © 2019 Universitas Ahmad Dahlan. All rights reserved.
1. Introduction
Vehicles technology have been a priority area of research over the last few decades.
With the increasing of electrical components in the automotive industry to sense conditions
around the vehicle, the focus of automotive technology development is now leading to
the development of active technology [1]. The speed information on conventional vehicles is
obtained from the rotational speed of the wheels. But there is a shortage in this system which is
the slip between the wheels and the road through which the vehicle passes [2]. In this study
used inertial measuring unit (IMU) 6D (6 axes) consisting of 3 axes acceleration sensor and
3 axis angular velocity sensor [3-5]. This study is expected to be an exploration for
the development of a viable system to use as a reliable vehicle speed estimator as well as using
an existing speedometer on a ground vehicle generally regardless of slippage and changes in
wind capacity on wheels [6-8].
2. Research Method
The system is designed by 3 main components consist of IMU sensor, Microcontroller
and Display. The functional block diagram is shown in Figure 1. In this design desired final
specifications such as the following points:
- Vehicles acceleration of 0.2-10 m/s2.
- Vehicle speed of 0-140 km/hour.
- The speed rating is updated maximally within 1 meter once.
- The system can only be used on public streets
According to the Figure 1, there are 5 main blocks to obtain the velocity value:
- IMU to obtain linear acceleration value (ɑ) and angular velocity value (ω), this section works
as an Input of system.
- IMU output containing noise by using Kalman filter so that noise will be muffled.

TELKOMNIKA ISSN: 1693-6930 ◼
Velocity measurement based on inertial measuring unit (Waru Djuriatno)
1899
- Integrate angle velocity value towards time by Midpoint Riemann Sum method to obtain
angle position value.
- Calculate the dynamic acceleration value of a vehicle parallel to the earth's surface by using
angle position value and acceleration sensor value.
- Integrate dynamic acceleration value towards time by Midpoint Riemann Sum method to
obtain velocity value.
- The whole process will be repeated with t intervals.
Figure 1. Functional block diagram of the system
2.1. Dynamic Acceleration
To eliminate the effect of earth gravitational acceleration, the following equations are
made based on acceleration vector diagram shown on Figure 2. Obtain angle position value θ0
(initiation value)
Dynamic acceleration is the acceleration value which is unaffected from the static acceleration
caused by gravity of the earth, so that the readable is pure acceleration parallel to the surface of
the earth [9, 10].
a=acceleration parallel to the surface of the earth
Figure 2. Accelerometer sensor vector
2.2. Using Kalman Filter to Filter Acceleration and Angle Velocity Value
Kalman filter in this study serves to reduce the disturbance due to lack of precision
sensors to obtain optimal and stable results [11-18]. In this process is divided into covariance
calculations (3 stages) and state calculations (2 stages). The calculation of covariance passes
through three stages:

◼ ISSN: 1693-6930
TELKOMNIKA Vol. 17, No. 4, August 2019: 1898-1906
1900
a.Calculate Kalman gain:
b.Calculate estimation:
c. Calculate covariance error:
The calculation of state passes through two stages:
a. Save last estimation valuee:
b. Save last covariance error value:
For the initial process before there is the last state value there will be an error, with
the passage of time the filter process is repeated continuously so it will establish iteration then
deviation value will be reduced to near reality value.
2.3. Acceleration and Angular Velocity Value Integrate
The output of the IMU sensor is the angular velocity and acceleration, to get speed value
it must be done integrating process. The correlaton between position, velocity and acceleration
can be seen in Figure 3. There are various methods that can be used to integrate.
Midpoint Riemann Sum is a single step method that is more accurate than the Euler method
[19, 20]. This method estimates the derivative at the interval points, which are then summarized
as shown in Figure 4. The Midpoint Riemann Sum method is the embryo of
the integral. which integral can certainly be done by the approximation of the sum of
the multiplicity of f(x) multiplied by Δt. The smaller the value Δt results in more
accurate readings [21, 22].
Figure 3. Corelation between acceleration, velocity,
and position [19]
Figure 4. Integration using
Midpoint Riemann Sum [20]
In the specification it has been determined that the speed rating will be updated a
maximum of 1 meter once. Then it can be determined how the maximum time interval value for
integration using Midpoint Riemann Sum method. The parameters in the specification are a
maximum renewal range of 1 m and maximum speed is 140 km/h or can be written
38,888 m/sec. So it can be calculated for the maximum time interval as follows:

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with Supdate_max is the maximum distance to update the speed and vmax is the maximum speed
that the system can measure. The equation for the angular position can be written
as follows :
with . The equation for the velocity can be written as follows:
with
2.4. Flowchart of System
Flowchart of the system used as reference of program making for IMU sensor value
conversion until becoming speed value is shown in Figure 5. The flowchart consists of data
retrieval process, digital filter process, angle position calculation, acceleration and speed value.
3. Results and Analysis
Testing is needed to analyze the performance of the system that has been made.
The system has been made can be known performance by analyzing the output values in
each sub-system.
3.1. Kalman Filter Test
Kalman filter here serves as a frequency damper due to noise that can be used to
smooth the signal readings [23-25]. In this filter applied here has 2 control variables that are R
and Q which have values between 0 to 1. Where R is the measurement noise covariant, while Q
is the covariance of the process noise. The purpose of selecting the value of R and Q is as a
parameter of determining the frequency attenuation, if attenuation is low then the signal still
contains noise, if the damping is too high the noise decreases but the filter output readout is not
too accurate. Based on Figure 6 can be seen that the output sensor still contains a lot of noise
so impressed not too stable, therefore Kalman filter serves as a noise filter due to instability
sensor output. Here is an unfiltered sensor output plot that has been through a fourier
transformation so that it can be viewed in the frequency domain. From Figure 7 the output of
the unfiltered sensor can be seen that the frequency distribution is between 10 Hz to 500 Hz.
Figures 8 (A), (B) and (C) and 9 (A), (B) and (C) show the sensor output plot using
kalman filter that has been through a Fourier transformation so that it can be viewed in the
frequency domain. In the data processing here there will be 2 variables in the test that is
Q (0.1; 0.01; 0.001), shown in Figure 8 (A), (B) and (C), and R (0.0; 0.5; 1.0), shown in
Figure 9 (A), (B) and (C). From this test can be concluded that the smaller value of Q then the
frequency will be more muffled. From this test can be concluded that the greater value of R then
the frequency will be more muffled.

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Figure 5. Flowchart of the system
Figure 6. Corelation between output sensor and after pass the filter
Figure 7. Sensor output frequency response without filter

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Figure 8. Output kalman filter with R value is 0,5 and Q independent variabel,
(A) Q=0.1; (B) Q=0.01; (C) Q=0.001
Figure 9. Output kalman filter with Q value is 0,01 and independent variabel R,
(A) R = 0.0; (B) R = 0.5; (C) R = 1.0
3.2. Angular velocity integral
The angular velocity integral aims to obtain angular position values. In this integral
processing use the midpoint Riemann sum method using AVR computation ie Atmega328 has
been tested to perform data retrieval to bring up the angle position, the process takes ± 2,4 ms
as shown in Figure 10.
Figure 10. The time taken for data retrieval
Here is a comparison of test graph of integration value of angle velocity value to time
with t value t=5 ms; 10 ms; 20 ms. From the graphs in Figures 11, 12 and 13, the integral result
with midpoint rieman sum method, it can be seen that the smaller value of Δt generate
integration resolution and data acquisition from the system will have a high accuracy value, but
due to data acquisition processing until it appears angular position value take ± 2.4 ms then the
smallest value for integration also has the smallest capability limit should be above

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processing time. From the three graphs integral result with midpoint rieman sum method can be
seen the smaller value of Δt generate integration resolution and data acquisition from the
system will have a high accuracy value, but due to data acquisition processing until it appears
angular position value take ± 2.4 ms then the smallest value for integration also has the smallest
capability limit should be above processing time.
Figure 11. Angle velocity integration with Δt=5ms
3.3. Eliminate Value of Static Acceleration due to Earth Gravity
The dynamic acceleration readings aim to eliminate static acceleration readings caused
by earth gravity so that the readable value is a pure acceleration parallel to the earth's surface.
Here is a correlation graph between the x-axis acceleration sensor to the static acceleration
value, which aims to accelerometer output values will display dynamic acceleration. According
to the Figure 14 in a stationary state dynamic acceleration has a value of 0 m/s even though the
IMU changes its angular position, the static acceleration captured by the x-axis sensor will be
eliminated by dampening the value using angular readings on the sensor.

1905
Figure 14. Comparation between ax and static acceleration
3.4. RMSE in the State of Speed 0 m/s
The system has been made is not the ideal system it is necessary to test the error value
of root mean square to know the error value in the state of speed 0 m/s. Tests take 500 data in
the state of the stationary to obtain the identical treatment, in this test the independent variable
is a θ value ( θ=+450; 0; -450). Based on Figure 15, when the angle value of sensor is +450
obtained RMSE 0,8696 m/s and based on Figure 16 and Figure 17, when the angle value of
sensor is 00 and -450 can be obtained the RMSE of 0,0393 m/s and 0.3030 m/s, respectively.
Figure 15. Value of 0 m/s captured by the
sensor when the angle value is +450 in 5
seconds
Figure 16. Value of 0 m/s captured by the
sensor when the angle value is 00 in 5 seconds
Figure 17. Value of 0 m/s captured by the sensor when the angle value is -450 in 5 seconds
4. Conclusion
After the research done by taking data and calculation of parameters and analysis, it
can be concluded that static acceleration can be eliminated by a mathematical equation with

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utilize gyroscope. Results obtained at the test of 0 m/s had an RMS error of 0.8696 m/s when
elevation is +450; 0.0393 m/s when elevation is 00; and 0.3030 m/s when elevation is -450.
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Velocity measurement based on inertial measuring unit

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