Adaptive Kalman Filter Approach and Butterworth
Filter Technique for ECG Signal Enhancement
Bharati Sharma
1,1
, R. Jenkin Suji
1
and Amlan Basu
1
1
Department of Electronics and Communication Engineering, ITM University
Gwalior, Madhya Pradesh - 474001, INDIA
bharatisharma30@gmail.com, sujijenkin@gmail.com,
er.basu.amlan@gmail.com
Abstract. About 15 million people alive today have been influenced by
coronary illness. This is a major and critical issue in recent days. There are so
many people have been lost their lives due to heart attack and other heart related
issues. So, early on analysis and proper cure of heart disease is required to
minimize the death rate due to heart disease. For better diagnosis we need exact
and consistent tools for determine the fitness of human hearts to analysis the
disease ahead of time before it makes around an undesirable changes in human
body. For heart diagnosis one of the tools is Electrocardiogram (ECG) and the
obtained signal is labeled ECG signal. This ECG signal contaminated by an
amount of motion artifacts and noisy elements and deduction of these noisy
elements from ECG signal must important before the ECG signal could be
utilized for illness diagnosis purpose. There are various filter methods available
for denoising ECG signal and select the best one on the dependence of
performance parameter like signal to noise ratio (SNR) and power spectrum
density (PSD).
Keywords: Electrocardiogram (ECG), Kalman filter, Butterworth filter,
denoising, signal to noise ratio (SNR), power spectrum density (PSD).
1 Introduction
Observation of the ECG (Electrocardiogram) has quite some time been utilized as a
part of clinical practice. As of late, the relevance area of ECG observation is
extending to regions outer the laboratory [1]. Home observing of patients with rest
apnea is one of an example of such an area. There are various ECG monitoring
technology available, a move in ECG observing applications is occurring. With
advancement in sensor innovation such as material and capacitive terminals, sensors
are fused in pieces of the incubator have ended up accessible [2].
Another sensor technology brings the solace of the patient is enhancing continuously.
While a few years back the patient needed to accommodate itself according to
discomforts of the only available technology, but now a day’s patient used to new
technology for ECG monitoring and goes with a comfortable treatment of heart
diseases [3].
Sometimes these ECG monitoring technologies contaminated due to breathing, and
mismatching measurement and explanation of the signal’s components therefore,
noise artifacts generated into acquired ECG signal and corrupt it. Due to certain stress
test, the noise artifacts vary unpredictably. Elimination of Interference in the ECG
signal by using various filtering method such as, Adaptive filter and Weiner filter are
utilized for removal artifacts from ECG signal [4]. An adaptive Wavelet Weiner
filtering of ECG signals has been proposed with stationary Wavelet Transform (SWT)
and Wavelet Filtering method (WF) compared by different thresholding strategies[5].
This work presents an Adaptive Kalman filter and butter worth filter approach for the
estimation and denoising ECG signal. These IIR methods will be utilized for
approving the proposed Kalman filter approach.
The proposed procedure in this paper is a utilization of the Kalman filter (KF) for the
estimation and evacuation of the noise artifacts in ECG signal. The projected IIR filter
methods based on the frequency selective components [6]. The state space model is
coordinated with Kalman filter so as to approximate the state variables. The proposed
technique recommends an appropriate way for estimation of the noise artifacts of an
ECG signal, and is contrasted with the IIR filter methods which basis on the
performance parameters.
2 Methodologies
2.1 Kalman filter
An adaptive Kalman Filter (KF) is a recursive prescient filter that depends on the state
model and time varying recursive algorithms. An ECG signals complexes that relates
from back to back heartbeats are fundamentally the same yet not indistinguishable.
However, while the recording of ECG, the signal is defiled due to some noise
interference. An adaptive Kalman filter appraises the state of a dynamic system. This
dynamic system can be contaminated by noise. The Kalman filter utilizes estimations
to enhance the estimated state [7].
The KF method consists of the prediction and correction of states of the system.
x
t+1
= x
t
+ v
t
(1)
Yt+1 =
x
t+1
+ w
t+1
(2)
Where x
t+1
is the state input of the system, v
t
is the process noise of the system,
Y
t+1
is the measurement output of the system and w
t+1
is the measurement noise such as
noise artifacts.
The prediction is an initial work of the Kalman filter. The predict state or prior state
is intended by neglecting the noise of the system. In linear case state vector equation
can be represented as:-
X(t) = F. x(t) + n(t) (3)
X(t) = F. x(t) (4)
Where, F is the dynamic grid and is consistent, state vector x(t) and dynamic
interference(t) of the system.
The genuine predicted state is a linear combination of the primary state x
–
(t
0
)
From equation (3) & (4)
x
–
(t ) = A
t
0
x
–
(t
0
) (5)
Where, A
t
0
is called the conversion matrix, which transform the primary state x
–
(t
0
)
to its equivalent x
–
(t ) at point t.
Covariance matrix P
-
( t
i
) of the predicted state vector is attained with the law of error
transmission,
P
-
( t
i
) = A . P(t
i-1
) . A
T
+ Q (6)
Where, covariance matrix of the noise Q is a utility of time.
In a correction process we obtained the improved predicted state with observation
form at time t
i
, thus the posteriori state has form,
x
+
(t
i
) = x
-
(t
i
) + x(t
i
) (7)
And covariance matrix, P
+
(t
i
) = P
-
(t
i
) + P(t
i
)
(8)
x(t
i
) = K(t
i
) . [ l(t
i
)-l
-
(t
i
) ] (9)
K(t) = P
-
H
T
(HP
-
H
T
+ R(t
i
))
-1
(10)
Where, K is called the gain matrix. The difference [ l(t
i
)-l
-
(t
i
) ]is identified the extent
residual. It reproduces the inconsistency between the predicted measurement and
actual extent. At the end corrected state is received by,
x
+
(t
i
) = x
-
(t
i
) + x(t
i
). (11)
The Kalman Filter approach uses to predict and remove the noise artifacts from ECG
signal. Though, the equation given in (11) is repeated over input signal. Equation (11)
is updated for the Kalman filter.
2.2 Butterworth filter
Butterworth filters are having an attribute of maximally level recurrence response and
no ripples in the pass band. It moves of nears zero in the stop band [8]. Its reaction
inclines off directly towards negative infinity on bode plot. For example, other filter
types which have non-monotonic swell in the pass band or stop band, these filters are
having a monotonically changing size capacity with ω. The initial 2n-1 subordinates
for the force capacity as for recurrence are zero. Thus it is conceivable to determine
the formula for frequency response,
(12)
3 Simulations and Result
The proposed approaches implemented in Matlab version 2009. To study the
performance of the planned method numerous standard data sets have been taken
from physio.net, including the MIT-BIH database. This ECG signal corrupted with
some noise artifacts and corrupted ECG signal passes through filter and get noise free
signal.
Fig.1 Typical ECG signal
Fig.2 Noisy ECG signal
a) Graphical representation of Kalman filter method
Fig.3 Kalman filter response of ECG signal
Figure 3 illustrates the Kalman filter response of ECG signal and blue line shows the
true response of the filter and red shows the filtered response of the signal.
Fig.4 Power spectrum density (PSD) of Kalman filter response