International Journal of Electrical and Computer Engineering (IJECE)
Vol. 3, No. 6, December 2013, pp. 713~723
ISSN: 2088-8708



713

The Kalman Filter Performance for Dynamic Change in System
Parameters
Hisham Alrawashdeh, Johnson A sumadu
Department of Electrical and Computer Engineering, Western Michigan University, USA

Article Info

ABSTRACT

Article history:

This paper studies the performance of the simple kalman filter for dynamic
changes of the system variables. The kalman filter was used to detect the
fundamental component of power system signal contained harmonics. First
the performance of the kalman filter was examined for a sudden change in
the amplitude of the fundamental component, then for a frequency variation.
The noise covariance matrices were assumed to be unknown, the values of
these matrices were changed to study the kalman filter behavior in such
circumstances.

Received Jul 8, 2013
Revised Sep 28, 2013
Accepted Oct 15, 2013
Keyword:
Dynamic change
Harmonics
Kalman filter
Noise
Voltage sag

Copyright © 2013 Institute of Advanced Engineering and Science.
All rights reserved.

Corresponding Author:
Hisham Alrawashdeh
Department of Electrical and Computer Engineering, Western Michigan University
1903 Western Michigan Avenue, Kalamazoo, Michigan 49008, United States
Email: hiisham_68@yahoo.com

1.

INTRODUCTION
The kalman filter is an optimal filter under several conditions, one of them is related to the noise
nature, where the noise should be independent white additive Gaussian noise with known covariance
matrices; the measurement noise covariance (R) and the state noise covariance matrix (Q), for that reason
several researches focus on on-line and off-line evaluating of the noise covariance matrices, where they need
a lot of computation time and computation memory.
The effect of the covariance matrices were studied in several previous researches [1-9], There is
strong argument about the effect of the noise covariance matrices on the kalman filter performance, some of
researches concluded that it is necessary to estimate the real values of these matrices to guarantee that the
kalman filter located the optimal solution, otherwise the kalman filter will converges to suboptimal solution.
Some researchers concluded that the real value of these matrices are not important as the relative ratio
between them [3, 4], while other researchers concluded that the knowledge of the ratio between the noise
covariance matrices is not sufficient when the signal to noise ratio exceed 30dB [1], other researchers
concluded the importance of resetting these matrices when a dynamical change occurs [6].
Since it is hard to estimate the noise covariance matrices in many of practical applications or it may
required extra calculations and increase the system complexity, in this paper the covariance matrices were
assumed to be unknown, and the value of these matrices are changed to several values (included the actual
value) to investigate the kalman filter performance, then the kalman filter will be used to detect the amplitude
of the fundamental signal to diagnose the voltage sag problem of a measured signal contains harmonics and
measurement noise under a dynamic change in the fundamental signal amplitude and its frequency.

Journal homepage: http://iaesjournal.com/online/index.php/IJECE

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2.

KALMAN FILTER
Kalman filter is a recursive linear optimal filter, the model of kalman filter can be described as
follows:
X k k  Ak X k k 1  BkU k  Wk
Yk  Ck X k k  DkU k  N k

(1)

Where:
Ak: is the transition matrix
Bk: is the input control vector.
Wk: is the process noise, and it is assumed to be white Gaussian noise with zero mean and
covariance matrix Qk, i.e N (0, Qk ) .
Zk: is observation of the state X k .
Ck: is the observation matrix.
Vk : is the observation noise, and it is also assumed to be Gaussian white noise with zero mean and
Rk covariance matrix, i.e N (0, Rk ) .
The kalman filter calculations can be divided to two stages; predicted stage and updating stage, in
the predicted stage, the state variables and the output are calculated based on the system model, while in
updating stage, the predicted state variables and the output are modified based on the measurement data. The
calculation of each stage as follows:
 Predicted stage:
X k k 1  Ak X k 1 k 1  Bk 1U k 1
Pk k 1  Ak Pk 1 k 1  AkT  Qk



(2)

Updating stage
Yk  Z k  Ck X k

k 1

K k  Pk k 1CkT [Ck Pk k 1CkT  Rk ]1
X k k  X k k 1  K k Yk

(3)

Pk k  [ I  K k Ck ]Pk k 1

Where: PK/K is the estimate covariance matrix.
3.

POWER SYSTEM HARMONICS
The power system signals (voltage and current) have harmonic components due to the nonlinear
devices such as transformer, machines and power electronics devices, the harmonics components may leads
to un correct decision of power system protection devices, for that reason, it is essentially in many
applications to detect precisely the fundamental component, the kalman filter will be useful in such case. One
of the major problem in power system is the voltage sag problem, where the voltage is decreased due to
increasing in load demand, at the beginning, the voltage decreases continuously, then at certain threshold
value the voltage collapse rapidly down to zero, which causes severe problems in power system, the
protection device must detect the voltage and operate before the threshold value to avoid the voltage collapse
problem.
To detect the fundamental component, the system can be modeled in two ways; the first model will
include only the fundamental component and treat the harmonics as noise, while the other model will include
all the harmonics components in the system model.
The two models are as follows:
Model 1:
cos( wT )  sin( wT ) 
Ak  

 sin( wT ) cos( wT ) 

(4)

0
B k    , Ck  1 0 , Dk  [0]
0

(5)

The Kalman Filter Performance for Dynamic Change in System Parameters (Hisham Alrawashdeh)

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Where; w: the angular frequency.
T: the sampling time.
Model 2:
 Ak ,1

Z
Ak  
 

 Z

Z

Z 

Z 
 

 Ak , n 


AK , 2 


Z

(6)

cos( jwT )  sin( jwT )
Ak , j  

 sin( jwT ) cos( jwT ) 

(7)

0 0 
Z 

0 0 

(8)

0
 
0
Bk   

 
 0  n1

Ck  1 0 1 0  01n

(9)

(10)

Where; n: is the order of harmonic to be detected.
The amplitude of the fundamental component can be calculated as follows:
Ampk 

X12,k  X 22, k

(11)

In this paper, model 1 will be used to detect the fundamental components, the exact model of all the
harmonics will be studied in our future works.

4.

SIMULATION RESULTS
Suppose, the electrical signal is given as follows:
x(t )  1.414 cos(100t   6)  0.3 cos(300t   8)  0.1cos(500t )
The signal has the fundamental, first and third harmonic components, the measurement noise
covariance matrix in this experiment is 0.1, the sampling time is 0.1ms, the value of R and Q in the kalman
model, tare assumed to be unknown (the ral value of them will be constant) and they are changed to
investigate their effects in kalman filter performance. Figure 1 shows the measured signal with harmonics
and noise, Figure 2 shows the estimated of the fundamental component using kalman filter for Q =1×10-9
and R = 0.1, which is the real value of the measurement noise covariance .
The error signal, which is the difference between the amplitude of the fundamental signal and the
amplitude of the fundamental signal calculated by the kalman filter, for several values of R and Q are shown
in Figure 3 and Figure 4.
As it is discussed in [10], the value of Q and R matrices in kalman filter represent how much the
kalman filter can trust the predicted and the measurement value to estimate the output, when R in the kalman
filter model is increased this will give indication to kalman filter that the measurement signal is highly noisy,
which cause the kalman filter to trust more the predicted value, where the predicted value is calculated using
the model matrices and it strongly depends on the initial values of the state variables, the model in this
experiment predicted a sinusoidal signal with 1.41 amplitude. When the value of Q is increased, the kalman
filter will trust the measurement signal more than the predicted value, and this will lead the kalman filter to
have a noisy output similar to the input, based on the results shown in Figure 2 and Figure 3, the error signal
goes to zero even though that the noise covariance R is not true, which shows a good response of kalman
filter, so by balancing Q and R matrices, a good response of kalman filter could be achieved.
Based in most researches, the ratio between Q and R is more important than the exact values of
them, Figure 5 shows the error signal for different values of Q/R ratio.

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Q= 1e-009, R= 0.1

the measured data

2
kalman filter
fundemental signal

2
1.9
Amplitude of the fundemental signal

0
-2
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

data without noise including harmonics
2
0
-2
0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

fundemental component
2
0

1.8
1.7
1.6
1.5
1.4
1.3
1.2
1.1

-2

1

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

Figure 1. The measured signal for R =0.1

Q = 1e-009

0.2

0.4
0.6
t [sec]
Q = 1e-007

0.2

0.4
0.6
t [sec]
Q = 1e-006

0

0.2

0.4
t [sec]

0.6

0

0.2

0.4
t [sec]

0.6

0.6

0.7

0.8

Q = 0.0001

0

0.2

0.4
0.6
t [sec]
Q = 0.001

0

0.2

0.4
t [sec]
Q = 0.01

0.6

0.8

0

0.2

0.4
t [sec]

0.6

0.8

1

0.5

0

0.8

0.5

0

0.8

1

0.5

0

0.8

0.5

1

0.5

0

0.8

Error signal

0.5

0

0

1
Error Signal

Error Signal

1

0.4
t [sec]

Q = 1e-005

0.5

0

0.8

0.3

1
Error signal

Error Signal

Error Signal

0.5

0.2

Figure 2. The fundamental signal amplitude of
Kalman filter for Q= 1×10-9 and R= 0.1

1

0

0.1

Q = 1e-008

1

0

0

Error signal

0.01

Error signal

0

0

0.2

0.4
t [sec]

0.6

0.5

0

0.8

Figure 3. The error signal of kalman filter with different values of Q and R= 0.1

0

0.2

0.4
0.6
t [sec]
R = 0.0001

0.2

0.4
0.6
t [sec]
R = 0.001

0.8

0

0.2

0.4
t [sec]

0.6

0.8

0.5

0

0

0.2

0.4
t [sec]

0.6

Error signal
0

0.2

0.4
t [sec]
R=1

0.6

0.8

0

0.2

0.4
t [sec]
R = 10

0.6

0.8

0

0.2

0.4
t [sec]

0.6

0.8

1

0.5

0

0.5

0

0.8

1
Error signal

0.5

1

0.5

0
0

1
Error Signal

Error Signal

1

0

0.5

0

0.8

R = 0.1

1
Error signal

Error Signal

Error Signal

0.5

0

R = 0.01

R = 1e-005
1

Error signal

R = 1e-006
1

0

0.2

0.4
t [sec]

0.6

0.8

0.5

0

Figure 4. The error signal of kalman filter with different values of R and Q= 1×10-9

The Kalman Filter Performance for Dynamic Change in System Parameters (Hisham Alrawashdeh)

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Figure 5. Error signal for several values of Q and R with different constant Q/R ratios

Figure 5 shows the error signal for different values of Q and R matrices with different Q/R ratios,
there is slightly differences in the error signal for different values of Q and R even though that the ratio
between them is still constant, by examining Figure 5 carefully, when the ratio between Q and R is decreased
the kalman filter has the same error signal for the same Q/R ratio.

IJECE Vol. 3, No. 6, December 2013 : 713 – 723

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ISSN: 2088-8708

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Figure 6 shows a dynamic change in the amplitude of the fundamental signal at o.4 sec, first Q and
R matrices are constant, the kalman filter shows a bad performance in this case, then the value of Q and R are
updated to several values listed in the Figure 6, the performance of kalman filter is strongly effected due to
changing in Q and R matrices. Based on these results the best performance of kalman filter was occurred
when both Q and R matrices are changed. Even though that the amplitude of the fundamental signal was
changed at 0.4sec then it returns to its original value at 0.8 sec as it shown in Figure 7, the performance of
kalman filter was poor, in Figure 7 (a) the value of Q and R are constant in the interval 0 sec to 0.4 sec, the
kalman filter detect the fundamental component successfully, then the amplitude of the fundamental
component is changed through the interval 0.4sec to 0.8 sec, Q and R remain constant, the kalman filter
couldn't estimated the amplitude in this interval, then at 0.8sec the signal is returned to its original value
(where the value of Q and R are sufficient to have good performance of kalman filter), the kalman filter is
failed to estimate the fundamental signal correctly in this interval, which points to the importance of
changing Q and R matrices for a dynamic change in the system variables, in Figure 7 (b) the value of Q and
R matrices are modified for the first change and they are kept constant for the second sudden change, the
kalman filter performance was good, when Q and R matrices are changed and poor when they are kept
constant through a dynamical changing of the system variables.
At this point, this will lead to ask , what prevent the kalman filter to detect the amplitude, even
though it did in previous interval, by examining the kalman model matrices, the difference was in the P
matrix (estimate covariance matrix) on interval 0sec to 0.4 sec, the value of P is set to identity matrix, and
through the calculations the kalman filter converges to the solution and the value of P matrix decreases and
approach to zero, for interval 0.4 sec to 0.8 sec, the P matrix is very small at the beginning of this interval, so
in order to investigate the effect of setting the P matrix for a dynamic change, the P matrix is changed in
Figure 8 and Figure 9. The performance of the kalman filter is improved, when the value of the P matrix is
changed, the value of P matrix approaches zero for normal case, as soon as a dynamic change occurs, the P
matrix should be increased to give indication to kalman filter that it doesn’t converge to the solution yet,
based on the results in Figure 8 and Figure 9, the kalman filter estimated the fundamental component
correctly, for different values P matrix.
Up to this point, the kalman filter performance is investigated under constant frequency condition,
while the frequency in power system is usually varied due to the load changing, the control devices in power
system allow the frequency to vary in narrow band limits, since the frequency is assumed to be constant in
the kalman filter transition matrix, which will cause problem in both of the predicted and the estimated
signal, the frequency of the fundamental signal is changed in Figure 10.
Figure 10 shows the state variables of the kalman filter when the fundamental frequency is changed
to different value and the amplitude of the fundamental signal is kept constant, in Figure 10 (a) the
fundamental frequency is changed slightly to 312.9, neither of the noise covariance matrices nor P matrix are
changed, the kalman filter failed to track the amplitude in such case, while in Figure 10 (b) and Figure 10 (c)
the frequency is also changed to 312.9 but in Figure 10 (b) the noise covariance matrices are changed and in
Figure 10 (c) P matrix is changed, the kalman filter shows better performance in these figures, the result
obtained from changing P matrix looks better. In Figure 10 (d) and (e) the fundamental frequency is changed
to 308.7 rad/sec (i.e 49.15 Hz) neither of changing P matrix nor noise covariance matrices improves the
kalman filter capability to detect the amplitude of the fundamental signal, based on the results shown in
Figure 10 the variation of the fundamental frequency has a great effect of the kalman filter performance, in
normal operation of power system, the frequency is usually distinct or changed slightly from the nominal
value due to load changing, so updating P matrix can improve the kalman filter performance, while if the
frequency is changed more, the simple kalman filter failed to detect the amplitude of the fundamental signal,
in this case the frequency should be considered in the kalman filter model which leads to a nonlinear model,
then extended kalman filter and unsecent kalman filter can be used.

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Q=1e-009, R=0.0005
3
2.8
Am
plitudeof thefundem
ental signal

Am
plitudeof thefundemental signal

Q=1e-009, R=0.1
3
2.8
2.6
2.4
2.2
2
1.8
1.6
1.4

2.6
2.4
2.2
2
1.8
1.6
1.4
1.2

1.2
1

1

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

0.5

0.6

0.7

0.8

0.6

0.7

0.8

0.6

0.7

0.8

0.8
Q=1e-009, R=1
3
2.8

Q=1e-010, R=0.1
A
m
p
litu
d
eo
f th
efu
n
d
e
m
e
n
ta
l sig
n
a
l

3

A
m
p
litu
d
eo
f th
efu
n
d
e
m
e
n
ta
l sig
n
a
l

2.8
2.6
2.4
2.2
2
1.8

2.6
2.4
2.2
2
1.8
1.6
1.4

1.6

1.2

1.4

1

0

0.1

0.2

0.3

1.2
1

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.4
t [sec]

0.

Q=1e-009, R=0.0001
3

Q=1e-012, R=0.1
3

2.8
Amplitudeof thefundemental signal

Amplitudeof thefundemental signal

2.8
2.6
2.4
2.2
2
1.8
1.6

2.6
2.4
2.2
2
1.8
1.6
1.4

1.4

1.2
1.2

1
1

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0

0.1

0.2

2.8
Am
plitudeof thefundem
ental signal

Amplitudeof thefundemental signal

3
2.8

2.6
2.4
2.2
2
1.8
1.6

2.4
2.2
2
1.8
1.6
1.4
1.2

1.2

1

0.1

0.2

0.3

0.4
t [sec]

0.5

0.5

2.6

1.4

0

0.4
t [sec]

Q=1e-005, R=0.1

Q=1e-007, R=0.1
3

1

0.3

0.

0.6

0.7

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.8
Q=1e-015, R=0.1
3

Q=1e-011, R=0.001
3

2.8
Amplitude of the fundemental signal

A
m
p
litu
d
eo
f th
efu
n
d
e
m
e
n
ta
l sig
n
a
l

2.8
2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

2.6
2.4
2.2
2
1.8
1.6
1.4
1.2
1

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

Figure 6. Amplitude of the fundamental signal estimated using kalman filter for a sudden change of the
fundamental amplitude for different values of Q and R matrices

IJECE Vol. 3, No. 6, December 2013 : 713 – 723

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Q=8e-018, R=0.0008

3

3

2.8

2.8

2.6

2.6

Amplitude of the fundemental signal

A m plitude of the fundem ental s ignal

Q=1e-015, R=0.1

2.4
2.2
2
1.8
1.6
1.4
1.2
1

720

2.4
2.2
2
1.8
1.6
1.4
1.2

0

0.2

0.4

0.6
t [sec]

0.8

1

1

1.2

0

0.2

0.4

0.6
t [sec]

0.8

1

1.2

Figure 7. The amplitude of the fundamental signal estimated by kalman filter for a sudden change on the
fundamental signal at t=0.4 then its return to its original value, (a) Q and R kept constant, (b) Q and R are
updated at t=0.4 then they are kept constant.

3

3

2.8
Amplitude of the fundemental signal

Amplitude of the fundemental signal

2.8
2.6
2.4
2.2
2
1.8
1.6
1.4

2.4
2.2
2
1.8
1.6
1.4
1.2

1.2
1

2.6

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

1

0.8

0

0.1

0.2

(a)

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

(b)

Figure 8. Amplitude of the fundamental signal using kalman filter for a sudden change of the fundamental
amplitude, Q , R are constant (a) P is reset (b) P is changed to [0.5 0;0 0.5]

2
fundemental signal

fundemental signal

2
1
0
-1
-2

0
-1
-2

0.4

0.42

0.44
t [sec]

0.46

0.48

0.5

2

other state signal

other state signal

1

1
0
-1
-2

0.4

0.42

0.44
t [sec]

0.46

0.48

0.5

0.4

0.42

0.44
t [sec]

0.46

0.48

0.5

2
1
0
-1
-2

0.4

0.42

0.44
t [sec]

(a)

0.46

0.48

0.5

(b)

Figure 9. State signals using kalman filter for a sudden change of the fundamental amplitude, Q, R are
constant and (a) P is reset (b) P is changed to [0.5 0; 0 0.5]

The Kalman Filter Performance for Dynamic Change in System Parameters (Hisham Alrawashdeh)

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W[rad/sec]

316

314

312

Amplitude of the fundemental signal

310

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

3
2.5
2
1.5
1
0.5

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

314

312

310

0.8
Amplitude of the fundemental signal

W[rad/sec]

316

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

3
2.5
2
1.5
1
0.5

(a)

(b)

316

310
Amplitude of the fundemental signal

W[rad/sec]

312

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

3
2.5
2
1.5
1
0.5

310

305

0

Amplitude of the fundemental signal

W[rad/sec]

315

314

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

3
2.5
2
1.5
1
0.5

(c)

(d)

W
[ra
d
/s
e
c
]

315

310

A
m
p
litu
d
eo
fth
efu
n
d
e
m
e
n
ta
ls
ig
n
a
l

305

0

0.1

0.2

0.3

0.4
t [sec]

0.5

0.6

0.7

0.8

0

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t [sec]

0.5

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0.8

3
2.5
2
1.5
1
0.5

(e)
Figure 10. Amplitude of the fundamental signal using kalman filter for a sudden change in the frequency to
(a) 312.9 rad/sec, Q, R and P are constant, (b) 312.9 rad/sec, Q, R are constant and P is changed, (c) to 312.9
rad/sec, Q, R are changed and P is constant, (d) to 307.8 rad/sec, Q, R are constant and P is changed and (e)
to 307.8 rad/sec, Q, R are changed and P is constant

5. CONCLUSIONS AND FUTURE WORKS
the kalman filter was used to detect the fundamental component of a signal contains harmonics and
noise, the measurement noise covariance matrices in the kalman filter model were assumed to be unknown
and the values of these matrices were changed through the research to investigate the kalman filter
performance under the uncertainty of these matrices (the real noise covariance matrix is kept constant), the
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amplitude of the fundamental component is changed several times and it is concluded that, it is necessary to
change the values of both Q and R matrices for the dynamic change, it is also concluded that changing P
matrix in kalman model is also sufficient to improve the kalman filter in such case. The frequency of the
fundamental component is also changed, the frequency is included in the kalman transition matrix, which
caused error in the estimated output of the kalman filter, for a normal operation of power system, the
frequency is changed slightly, changing P matrix can improve the kalman the filter performance, otherwise,
the performance of the kalman filter can be improved by changing the kalman state variables to inclued the
frequency, in such case the system becomes nonlinear , which leads to use extended kalman filter or unsecent
kalman filter.
The covariance noise matrices and P matrix are updated when the amplitude is changed, to
investigate their effect in kalman filter performance, even though, in practical this time is unknown, this
information will be helpful for design adaptive kalman filter, where combining the kalman filter with other
mathematic method to figure the necessary time for updating these matrices or by investigating the kalman
filter converge criteria to set the necessary conditions for updating them, and this will be one of our future
works.
The extended kalman filter could be used to detect the amplitude under a large frequency deviation,
investigating the effects of the covariance matrices in such case could be done. In this paper, transition
matrix includes only the fundamental component, including the harmonic frequencies in the transition matrix
will leads to more accurate model and this may increase the range of the frequency deviation that the simple
kalman filter could be used, even though that the size of matrices will be larger, this can be investigated in
the future works.

REFERENCES
[1]

K Kennedy et al. “Power system harmonic analysis using the Kalman filter”. Power Engineering Society General
Meeting, 2003, IEEE. 2003; 2(2666): 4.
[2] A Routray et al. “A novel Kalman filter for frequency estimation of distorted signals in power systems”. IEEE
Transactions on Instrumentation and Measurement. 2002; 51(3): 469-479.
[3] A Griffo et al. An optimal control strategy for power quality enhancement in a competitive environment.
International Journal of Electrical Power & Energy Systems. 2007; 29(7): 514-525.
[4] S Bittanti and SM Savaresi. “On the parameterization and design of an extended Kalman filter frequency
tracker”. IEEE Transactions on Automatic Control. 2000; 45(9): 1718-1724.
[5] BF La Scala and RR Bitmead. “Design of an extended Kalman filter frequency tracker”. IEEE Transactions on
Signal Processing. 1996; 44(3): 739-742.
[6] KC Kent et al. “An adaptive Kalman filter for dynamic harmonic state estimation and hamonic injection
tracking”. IEEE Transactions on Power Delivery. 2005; 20(2): 1577- 1584.
[7] AA Abdelsalam et al. “Characterization of power quality disturbances using hybrid technique of linear Kalman
filter and fuzzy-expert system”. Electric Power Systems Research. 2012; 83(1): 41-50.
[8] AA Abdelsalam1 et al. “Wavelet, Kalman Filter and Fuzzy-Expert Combined System for Classifying Power System
Disturbances”. Proceedings of the 14th International Middle East Power Systems Conference (MEPCON'10),
Cairo University, Egypt. 2010: 398-403.
[9] G Noriega and S Pasupathy. “Adaptive estimation of noise covariance matrices in real-time preprocessing of
geophysical data”. IEEE Transactions on Geoscience and Remote Sensing. 1997; 35(5): 1146-1159.
[10] H Alrawashdeh et al. “Effect of Noise Covariance Matrices in Kalman Filter Performance of Power System
Harmonics Detection”. IJEECS. 2013; 13(1): 707-717.

BIOGRAPHIES OF AUTHORS
Hisham O. Alrawashdeh received her M.Sc in communication Engineering from Mutah
university, Jordan 2007, and he is now pursing his Ph.D. degrees in Electrical and Computer
Engineering, WMU, USA. Eng. Alrawashdeh is specialized in electronics and communication
engineering. His areas of research include power system harmonics, adaptive filters, fiber optics,
modern control.

The Kalman Filter Performance for Dynamic Change in System Parameters (Hisham Alrawashdeh)

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ISSN: 2088-8708
Johnson A. Asumadu received his B.S. from the University of Science Technology, Ghana, in
1975, his M.S. from Aston University, England, in 1978, his MEE from the Rensselaer
Polytechnic Institute, USA, in 1983, and his Ph.D. from the University of Missouri-Columbia,
USA, in 1987. He is now a faculty member at Western Michigan University, Michigan. He has
published several technical papers and books, has a number of patents and has been involved in
numerous government and industrial-sponsored projects. His current research interests include
power electronics and control engineering including fuzzy logic applications, and
microprocessor / microcontroller embedded applications.

IJECE Vol. 3, No. 6, December 2013 : 713 – 723