HỘI NGHỊ KHOA HỌC TOÀN QUỐC VỀ CƠ KHÍ – ĐIỆN – TỰ ĐỘNG HÓA
(MEAE2021)
Kalman Filter and MPU6050 Sensor in Positioning Issue for
one-axis Solar Tracking System
Dao Hieu 1,*, Khong Cao Phong 1
1 Faculty of Electro-mechanics, Hanoi university of Mining and Geology, Hanoi, Viet nam, e-mail:
daohieu@humg.edu.vn
ARTICLE INFO ABSTRACT
Article history:
th Gyroscope and accelerometer are widely used in applications that have to
Received 15 Jun 2021 estimate the motion of object

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t. The motion, velocity and position of an
Accepted 16th Aug 2021 object are determined based on the principle of integrating one or two
Available online 19th Dec 2021 layers from the acceleration. That causes cumulative errors in the results
Keywords: to increase rapidly over time due to noise of sensors. Therefore, noise is a
big issue in control systems. Theories and experiments have proved that
MPU6050, Solar Tracking, noise filter is a solution to solve the issue. Kalman filter is the most common
filter which is suitable to reduce sensor noise problem. This paper
Kalman filter, accelerometer, introduces the process of designing a Kalman filter to improve the
gyro, gyroscope. accuracy of MPU6050 data which is used to determine motion trajectory
and position of a solar tracking system. Quality of unfiltered data, filtered
data and the simulation, testing results will be detailed in the article.
Copyright © 2021 Hanoi University of Mining and Geology. All rights reserved.
1. Introduction light source in real time. With these tracking
systems, the efficiency can be improved by 20-
The gradual depletion of fossil fuels (oil, coal,
30% compared to fixing systems (J.Rizk et al
...) and the disasters that hydropower and
2008 and K.Tseng et al 2019). The solar tracking
nuclear power hide are driving the global energy
system has two types: track on one axis and track
trend towards renewable energy sources. And
on two axes.
there, the supply from solar energy is a big part
(Nadarajah et al 2016). Photovoltaic cells are With a moving mechanical system, tracking
used to convert energy from sunlight into and monitoring requirements are indispensable.
electrical energy. They are integrated called That contributes to ensure the system works
solar panels. The efficiency is the highest when correctly and efficiently. The most importance
the surface of the panel and the direction of light parameter of the system is the position
form a certain angle (Frank Dimroth et al 2007). (orientation) of the panel. This information and
Due to the relative displacement of the earth and the direction of the light is the basis for tracking
the sun, in each region of the earth, at each time control (East-West rotating).
of the year, the sun's orbit is different (Sidek et al
In this study, the authors employ a widely
2014). Therefore, tracking systems are used to
used and low-cost sensor to determine the
drive the solar panels to the position of the best
position for one-axis solar tracking system. It is
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an integrated sensor that includes a gyroscope
and 3-axis accelerometer. The 3-axis
accelerometer is a type of sensor specialized in
determining position systems for moving objects
in space. Due to its very high mechanical
sensitivity, its measurement signal have a lot of
noise. A Kalman filter is used to accurately
determine measurement and control results. The
processing, data filtering and results are
presented in detail in the following sections.
2. MPU6050 sensor in solar tracking system
The sensor MPU6050 is proposed in this
study. This is a low-cost sensor, which is widely
used in applications to determine the position of
objects in space. The sensor is integrated on the
where the sensor
blue board (Figure 24). This board can is located
communicate with a controller via I2C
communication standard by SCL and SDA pins. It
is equipped with a gyro measuring angular
Figure 36. The MPU6050 sensor is fixed on the
velocity around 3 axes, and an accelerometer
test solar tracking system
measuring linear acceleration in the same axes
(InvenSense Inc 2013). 2.1. The gyroscope
Gyro works based on the direction of gravity and
the earth’s magnetic field. It is the natural sensor
to use for estimating an angle (as it measures the
derivative of an angle). It has some problems.
The gyro measurements can give us angles
relative to initial orientation, then we can simply
VCC 3-5 Vdc in calculate the angular velocity. In many
GND Ground applications, we are interested in the absolute
SCL, SDA I2C Bus interface angle of the object, such as knowing if the object
XDA, XCL I2C Bus for external sensor
ADD I2C Slave Address (High/Low) is standing straight up or not. In addition, the
INT Interrupt digital output sensor has bias errors, meaning that the angle
Figure 35. MPU 6050 board (module) estimate will drift. Experients showed that any
bias in the angular velocity measurement will
The measurements are placed on the test lead to a growing error in the angle estimate
solar tracking system as indicated in Figure 36. (Lund university 2018). In this application, the
The sensor is fixed on the rotating shaft (driven tracking system only rotates in one axis.
by motor), which rotates the solar panel to an Consequently, we are only interested in
angle according to the direction of sunlight. rotations around the x-axis (rotations in the y-z
plane) and thus only use one of the gyro
measurements .
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2.2. The accelerometer developed extensively (Youngjoo Kim et al 2018;
The accelerometer might seem unrelated to and Phạm Duy Dưởng 2019) and is incorporated
the orientation of the device, as it measures the in many different applications (Haykin 2001; Lê
three linear accelerations of the object. However, Ngọc Duy et al 2018; and Trịnh Tuấn Dương
the acceleration is measured relative to free-fall, 2019).
meaning that when the device is kept still, there The Kalman filter uses discrete-time
should be an acceleration of magnitude modeling to estimate the states of a system using
2 2 2 2 a linear stochastic equation (Kalman 1960):
√푎푥 + 푎푦 + 푎푧 = 9.8 푚/푠 . The way this
magnitude is distributed on the three body-fixed 푥푘 = 퐹푥푘−1 + 퐵푢푘−1 + 푤푘−1 (1)
accelerations ax(t), ay(t) and az(t) will give us In addition, at the time k, it is possible to exactly
information about the absolute orientation. In measure and observe the state of the system by
practice the tracking system is never completely some method. It is represented by a linear
still when balancing, because of the effects of equation:
wind on the solar panels. So that, ay and az will
always contain parts that come from actual 푧푘 = 퐻푥푘 + 푣푘 (2)
movements, which will influence the computed
Here: F is the transition matrix, it is applied to
angle, i.e., there are noises on the angle estimate.
the previous state x ; B is the input control
Another problem is that the accelerometer can k-1
matrix, it is applied to the control vector u ; H is
have slant states along with the solar panel, k
the observation matrix, it converts the measured
which will give us a bias in the accelerometer
state into the observed state; w and v are two
signal (Lund university 2018). k k
random variable vectors representing the
2.3. Combine accelerometer and gyro to reduce system noise and the measurement noise, they
noise were assumed to follow Gauss distribution with
When the object moves, the gyro gives the mean value is 0 and covariance matrices are Q
result with a smaller error than the and R ( wk ~ N(0,Qk) ; vk ~ N(0,Rk) ).
accelerometer. When the object is stopped, the The matrices Q, R, F, H can be changed over
value of the gyro is not as stable as the time (according to step k), but here, we assume
accelerometer. In applications, that they do not that they are constant to make the calculation
need high accuracy of measurements, low speed more convenient.
response and allow large control errors, we often
use a combination of both these sensors. Tests The Kalman filter consists of two processes:
and experiments show that, the percentages of 1 – estimate prior state; 2 – based on the
two sensors can vary depending on specific measurement results to correct the prediction.
system conditions. Estimate prior state
3. Processing data by Kalman filter Estimate prior state is the process for
3.1. Kalman filter estimating a prior state value and a prior
The Kalman filter was introduced in 1960 by covariance matrix. We must first initialize the
R.E. Kalman (Kalman 1960). Later, it is re- initial value of the estimated posterior state
introduced by a other documents (Greg Welch et 푥̂푘−1|푘 , and error correlation matrix Pk-1|k. The
al 1997; and Simon Haykin 2001). Today, it is
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process of predicting the prior state and prior the smallest amplitude of variation of the
covariance matrix is determined as follows: measurement result (when not using the Kalman
algorithm, it was determined by experiment). In
푥̂ = 퐹푥̂ + 퐵푢 (3)
푘|푘−1 푘−1|푘 푘 which, the Gyro is error-corrected by the bias
푇 determined from the initial 1000 measurements
푃푘|푘−1 = 퐹푃푘−1|푘퐹 + 푄 (4)
performed when the MPU is stability. The final
Here: 푥̂푘|푘−1 is the prior state estimated at time result is the average of 50 consecutive results. In
k; 푥̂푘−1|푘 is the posterior state estimated at time addition, after a certain period, the MPU is soft
k-1; Pk|k-1 is the prior error correlation matrix; reset and reconfigured to increase the stability of
and Pk-1|k is the posterior error correlation the sensor, and to reduce measurement errors.
matrix. This processing algorithm is depicted in Figure
37.
Correction of estimate
The data is recorded by the CPU and sent to
Correction of estimate is the process based computer. The system is tested in three different
on the measurement value to correct the prior modes: When the system is stable at a certain
estimate, thereby getting the correct posterior angle; When the system moves from small angle
estimate. This result is the output of Kalman to large angle; and When the system moves from
filter. The estimate process is done as follows: a large angle to a small angle. The measurement
results show that the data still has errors and
푥̂푘|푘 = 푥̂푘|푘−1 + 퐾푘 ∗ (푧푘 − 퐻 ∗ 푥̂푘|푘−1) (5)
oscillation (Figure 38).
푇 푇 −1
퐾푘 = 푃푘|푘−1퐻 (퐻푃푘|푘−1퐻 + 푅) (6)
Start
푃푘|푘 = (퐼 − 퐾푘퐻)푃푘|푘−1 (7)
Init, config MPU
Here: Kk is the gain of Kalman filter, it is changed
for each estimate of k and is chosen so that the Determine
correlation of the posterior estimate error is Gyro_offset
minimal; I is the unit matrix; 푥̂푘|푘 is the estimatex Time to read
posterior state at time k, and also is the output data
Time++
value of the Kalman filter. Get Gyro_Angle
3.2. Read and pre-process MPU6050’s data Time to Get Accel_Angle
reset
This study uses microcontroller Pic16f1938
to connect and read data from MPU6050 via I2C Sum=Sum + 0.8Gyro + 0.2Accel
Reset
communication (Microchip 2011). This MPU
microcontroller is also the center process unit Count=50
(CPU) to control the tracking system. The Count++ Angle=Sum/50
selected MPU6050 address is the high address
(InvenSense Inc 2013). Because of the track Count=0, Sum=0
system is particularly rotate around one-axis, so
the x-axis is select and the system move in y-z Figure 37. Algorithm for reading and pre-
plane. Data is pre-processed by combining the processing MPU6050’s data
measurement data of Gyro and Accelerometer at
the respective rate of 80%-20%. This ratio gives
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in the overall results. When the system is stable
at an angle, the measurement results oscillate
around the stable corner point (Figure 38a).
When the system moves from a small angle to a
large angle, the measurement results have
increased trend, but lower (smaller) than
desired (Figure 38b). When the system moves
from a large angle to a small angle, the
measurement results have also increased trend,
but slower (larger) than desired (Figure 38c).
(a) From that reason, The authors have continued to
use the Kalman filter towards better stability.
3.3. Kalman filter for data and result
Pre-processing data based on proportional
sum of gyro and accelerometer measurement
results did not meet the requirements.
Therefore, these data are used to build Kalman
filter on Matlab2013 software. The filter
construction process is depicted in Figure 39.
Begin
(b)
Init parameters
for system
Create Kalman filter
parameters
Load data
N Y
i < endPoint
True(i)
GyroMeasure(i)
AccelMeasure(i)
(c) Plot graphs
Figure 38. Pre-processed data graph is plotted of data
Kalman filter:
by Matlab2013 uk = gyroMeask1;
zk = accelMeask1;
xk1Minus = phi * xk + psi * uk;
End pk1Minus = phi * pk * phi' +0;
The characteristics in Figure 4 indicate that, S = H * pk1Minus * H' + R;
K = pk1Minus * H' + inv(S);
even though, the measured value has been xk1 = xk1Minus + K*(zk - H*xk1Minus);
processed to reduce noise by combining multiple pk1 = (eye(2,2) - K*H)*pk1Minus;
methods (summarizing the results of the gyro
and accelerometer, averaging of multiple Figure 39. Building Kalman filter on Matlab
results). However, the results are still
misleading. The noise still appears, sometimes The processing of building Kalman filter had
there are some large noises that make big falses selected R = 0.01, the matrices Q = [0.00001 0 0
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0]; and H = [0.8 0]. Following that, the system. Experiments show that, the allowable
characteristic that describes the data after limits can be up to +-2 degrees, which is the error
filtering is the blue line. It follows the desired value of mechanical system. The code segment
characteristic (the green line) and has a much describing Kalman filter in the Pic16f1938
smaller error than the pre-processing data (the microcontroller is shown in Figure 41.
red line) (Figure 40).
float32 Kalman(float32 newAngle, float32
newRate)
{
//angle = X_Raw_Gyro_Angle;
rate = newRate - bias;
angle += dt * rate;
P_00 += dt * ( dt*P_11 - P_10 - P_01 +
Q_angle);
P_01 -= dt * P_11;
P_10 -= dt * P_11;
P_11 += Q_bias * dt;
S = P_00 + R_measure;
K_0 = P_00 / S;
K_1 = P_10 / S;
y = newAngle - angle;
angle += K_0 * y;
bias += K_1 * y;
P_00 -= K_0 * P_00;
P_01 -= K_0 * P_01;
P_10 -= K_1 * P_00;
P_11 -= K_1 * P_01;
}
Figure 41. Kalman code in CPU Pic16f1938
4. Conclusion
This paper presents the method and process
of building Kalman filter applied to MPU6050
sensor data processing in 1-axis solar tracking
test system. Simulation and testing results have
demonstrated the quality of the designed
Kalman filter. Responses and errors are
completely within the allowable limits of the test
Figure 40. Data graph with Kalman filter system. The test results also show that, even with
From the designed Kalman filter in Matlab, systems that do not need high accuracy, and
the selected coefficients and filters have been set quick respond such as solar tracking systems,
on the Pic microcontroller (CPU). Testing results the measurement data of the accelerometer is
for good response, stable measurement still unstable. Therefore, the use of filtering
parameters. System control error is +-1 degree, solutions to remove noise is unavoidable. And
within the allowable limits of the solar tracking the final optimal solution is still to use the
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Kalman filter algorithm. This research is done on R. E. Kalman. (1960). A new approach to linear
a small model, under test conditions. With actual filtering and prediction plobems.
solar farms, the sources of noisy may be more Transaction of the ASME-Journal of Basic
and stronger, so in order to use the MPU6050 Engineering, 82 (Series D): 35-45.
sensor, the filter parameters may have to be
Sidek M.H.M., Hasan W.Z.W., Ab. Kadir M.Z.A.,
adjusted to be more suitable. Shafie S., Radzi M.A.M. (2014). Ahmad S.A.,
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