Timing jitter occurs in different practical situations for a
variety of reasons. The first presentation of the problem was
given in [1]. Later, the sampling time jitter was discovered in
many practical applications and standardized in [2], [3].
Regular blood sugar monitoring is conducted in diabetic
patients to timely reflect the influence of diet, exercise, stress,
and drugs on the blood glucose level [4]. This also gives the
necessary data for evidenced-based clinical decision-making
by healthcare professionals. Monitoring is provided at least
once per day for type 2 diabetes and more than 4 times per
day for type 1 diabetes [5]. Although glucose monitoring is
usually assigned at a certain time, real time may differ by
several hours due to human factors – thus random timing jitter.
It is worth noting that during glucose measurements, jitter may
take several hours [6].
Of importance is that timing jitter does not depend on the
sampling interval, is often normally distributed, and makes the
model uncertain that requires robust approaches [7]–[9]. The
robust H2filter has several distinctive features: it becomes the
Kalman filter (KF) in white Gaussian environments and gives
robust estimates for maximized errors. The H2filter appears
from the transform domain, where the squared Frobenius
norm of the error-to-error transfer function Tis minimized
for maximized errors, and the solution can also be found
numerically using a linear matrix inequality (LMI) [14]–[17].
The robustness can also be improved using batch finite
impulse response (FIR) structures [18], which are bounded
input bounded output stable and can work with full (not
diagonal) block error matrices and discard errors beyond the
averaging horizon. The first receding horizon H2-FIR filter
was developed in [18] for disturbed systems and the envelope-
constrained H2-FIR filter proposed in [19]. Some other FIR
solutions can be found in [20]–[24], and it is important that
the H2-FIR filter can be as robust as the H∞filter [25].
Even so, the H2-FIR approach is still poorly developed for
uncertain systems, and its robustness to timing jitter still
remains unknown.
In this paper, we develop the H2optimal FIR (OFIR)
filter for blood sugar monitoring in diabetic persons taking
into account timing jitter. Based on glucose measurements
in diabetic patients, we investigate the effect of timing jitter
on the H2-OFIR filter performance in a comparison with the
OFIR filter [26], [27].
We represent the blood sugar dynamics with a linear time-
invariant (LTI) continuous-time state-space equations
d
dtx(t) = Ax(t) + Lw(t),(1)
y(t) = Cx(t) + v(t),(2)
where x(t)∈RK,y(t)∈RM,w(t)∈RP, and v(t)∈RM.
The matrices A∈RK×K,L∈RK×P, and C∈RM×Kare
constant and known. The glucose measurements are provided
with the sampling time τk=tk−tk−1, where kis the discrete-
time index. We assume that τkis random and uncertain due to
human factors. We represent τkas τk=τ+ ˜τk=τ(1 + δτ k),
where τis the known mean, ˜τkis the zero mean random jitter,
and δτ k =˜τk
τis the fractional jitter.
To go to discrete time, we integrate (1) from tk−1to tkand
write the solution as
x(tk) = eAτkx(tk−1) + Ztk
tk−1
eA(tk−θ)Lw(θ)dθ , (3)
y(tk) = Cx(tk) + v(tk).(4)
Substituting xk∼
=x(tk),yk∼
=y(tk), and vk∼
=v(tk)gives
xk= (F+ ∆Fk)xk−1+ (B+ ∆Bk)wk,(5)
yk=Hxk+vk,(6)
Robust Blood Sugar Monitoring in Diabetic Patients
with Timing Jitter due to Human Factors
ELI G. PALE-RAMON, JORGE A. ORTEGA-CONTRERAS, KAREN J. URIBE-MURCIA,
YURIY S. SHMALIY
Department of Electronics Engineering, Universidad de Guanajuato, Salamanca, 36855, MEXICO
Abstract: Blood sugar monitoring in diabetic patients is commonly provided with timing jitter caused by human
factors. In this paper we address the problem by developing the robust H2 optimal finite impulse response
(OFIR) filter under under possible disturbances, initial errors, and measurement errors. The filter is applied to
data collected daily before breakfast from diabetic patients. It is shown that the robust H2-OFIR filter improves
the accuracy of the OFIR filter by the factor of less than the fractional time jitter. That is, for large fractional
timing jitter of 10% the improvement would be less than 10% that is small. Otherwise, it is worth using robust
estimators.
Keywords: blood sugar level, diabetic patients, timing jitter, robust filter, optimal filter
Received: March 15, 2021. Revised: March 26, 2022. Accepted: April 27, 2022. Published: May 19, 2022.
1. Introduction
2. Model and Problem Formulation
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where H=C,F=eAτ,∆Fk=eA˜τk, the disturbance wk
is defined by the stochastic integral
Bkwk=Ztk
tk−1
eA(tk−θ)Lw(θ) dθ ,
where Bk=B+ ∆Bk, and the data error vk=
1
τkRtk
tk−1v(t) dtis supposed to be zero mean and bounded.
For white Gaussian wk∼ N (0,Qk), the covariance Qk
is given by Qk=E{wkwT
k}∼
=τkLSwLT, where Swis the
power spectral density (PSD) of w(t), and we maximize it as
¯
Q=τ+ max |˜τk|
τQ= (1 + ¯
δτ)Q,(7)
where Q=τLSwLTand ¯
δτ= max |δτ k |=max |˜τk|
τis
the maximized fractional jitter. For vk∼ N (0,Rk), the
covariance Rk=E{vkvT
k}is defined as Rk=1
τkSv, where
Svis the PSD of v(t), and we similarly have
¯
R=1
1 + ¯
δτ
R∼
=(1 −¯
δτ)R.(8)
The robust H2-OFIR filter can be developed for timing jitter,
if we reorganize the model (5) and (6) as
xk=Fxk−1+ξk,(9)
yk=Hxk+vk,(10)
where the zero mean error vector ξkis given by
ξk= ∆Fkxk−1+ (B+ ∆Bk)wk.(11)
Next, we follow [26] and extend (9) and (10) to the averaging
horizon [m, k]of Npoints, where m=k−N+ 1, as
Xm,k =FNxm+ˆ
FNΞm,k ,(12)
Ym,k =HNxm+GNΞm,k +Vm,k,(13)
where Xm,k = [ xT
mxT
m+1 ... xT
k]T,Ym,k =
[yT
myT
m+1 ... yT
k]T,Ξm,k = [ ξT
mξT
m+1 . . . ξT
k]T,
Vm,k = [ vT
mvT
m+1 ... vT
k]T, and the partitioned matrices are
FN=hI FT... FN−2TFN−1TiT
,(14)
ˆ
FN=
I 0 ... 0 0
F I ... 0 0
.
.
..
.
.....
.
..
.
.
FN−2FN−3... I 0
FN−1FN−2... F I
,(15)
HN=¯
HNFN,GN=¯
HNˆ
FN, and ¯
HN= diag( H H ... H
| {z }
N
).
The extended uncertain vector Ξkis
Ξm,k =F∆
m,kxm+ ( ¯
BN+D∆
m,k)Wm,k ,(16)
where ¯
BN= diag( B B ... B
| {z }
N
),F∆
m,k and D∆
m,k are given by
F∆
m,k =
0
∆Fm+1
.
.
.
∆Fk−1˜
Fm+1
k−2
∆Fk˜
Fm+1
k−1
,(17)
D∆
m,k =
0 0 ... 0 0
∆Fm+1 0... 0 0
.
.
..
.
.....
.
..
.
.
∆Fk−1˜
Fm+1
k−2∆Fk−1˜
Fm+2
k−2... 0 0
∆Fk˜
Fm+1
k−1∆Fk˜
Fm+2
k−1... ∆Fk0
,
(18)
and matrix ˜
Fg
rof uncertain products is specified as
˜
Fg
r=
Fu
rFu
r−1...Fu
g, g < r + 1 ,
I, g =r+ 1
0, g > r + 1
.(19)
Finally, we write the extended state equation as
Xm,k = (FN+˜
Fm,k)xm+ (ˆ
FN+˜
Dm,k)Wm,k ,(20)
where ˜
Fm,k =ˆ
FNF∆
m,k and ˜
Dm,k =ˆ
FND∆
m,k. The state xk
can now be taken as the last row vector in (20),
xk= (FN−1+¯
˜
Fm,k)xm+ (¯
ˆ
FN+¯
˜
Dm,k)Wm,k ,(21)
where ¯
˜
Fm,k,¯
ˆ
FN, and ¯
˜
Dm,k are the last row vectors in ˜
Fm,k,
ˆ
FN, and ˜
Dm,k, respectively.
Similarly, we obtain the extended observation equation
Ym,k = (HN+˜
Hm,k)xm+(GN+˜
Tm,k)Wm,k +Vm,k,(22)
where ˜
Hm,k =MNF∆
m,k,˜
Tm,k =MND∆
m,k, and MN=
¯
HNˆ
FN.
The FIR filtering estimate can be defined as [23]
ˆ
xk=HNYm,k
=HN(HN+˜
Hm,k)xm+HNVm,k
+HN(GN+˜
Tm,k)Wm,k ,(23)
where HNis the filter gain, and ˜
Hm,k and ˜
Tm,k are uncer-
tain matrices specified after (22). The unbiasedness condition
E{ˆ
xk}=E{xk}applied to (21) and (23) gives the unbiased-
ness constrain
FN−1=HNHN,(24)
and the estimation error εk=xk−ˆ
xkcan be written as
εk= (FN−1− HNHN+¯
˜
Fm,k − HN˜
Hm,k)xm
+(¯
ˆ
FN− HNGN+¯
˜
Dm,k − HN˜
Tm,k)Wm,k
−HNVm,k .(25)
3. Extended Model
4. Robust H2-Ofir Filter
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DOI: 10.37394/232014.2022.18.16
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E-ISSN: 2224-3488
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Next, we generalize εkin the form
εk= (BN+˜
Bm,k)xm+ (WN+˜
Wm,k)Wm,k
−VNVm,k ,(26)
where BN=FN−1−HNHN,WN=¯
ˆ
FN−HNGN, and VN=
HN,˜
Bm,k =¯
˜
Fm,k −HN˜
Hm,k and ˜
Wm,k =¯
˜
Dm,k −HN˜
Tm,k.
This generalises (26) as
εk= ¯εxk + ¯εwk + ¯εvk + ˜εxk + ˜εwk ,(27)
where the sub errors are defined as
¯εxk =BNxm,¯εwk =WNWm,k ,
¯εvk =−VNVm,k ,
˜εxk =˜
Bm,kxm,˜εwk =˜
Wm,kWm,k .(28)
We now have five sub transfer functions: T¯x(z)for εx-to-
¯εx,T¯w(z)for εw-to-¯εw,T¯v(z)for εv-to-¯εv,T˜x(z)for εx-to-˜εx,
and T˜w(z)for εw-to-˜εw, and can proceed with the derivation
of the batch H2-OFIR filter.
2
To derive the batch H2-OFIR filter, we need a lemma.
Lemma 1: Given the model (9) and (10), Then the ξ-to-y
transfer function on [m, k]is T(z) = Cw(Iz−Aw)−1zBw,
where the strictly sparse matrices Awand Bware defined as
Aw=
0 I 0 ... 0
0 0 I ... 0
.
.
..
.
..
.
.....
.
.
0 0 0 ... I
0 0 0 ... 0
,Bw=
0
0
.
.
.
0
I
(29)
and Cwis a real matrix. The squared Frobenius norm of the
weighted transfer function ¯
T(z)is
k¯
T(z)k2
F=1
2πZ2π
0
tr [T(ejωT )ΞT∗(ejωT )] dωT(30)
= tr(CwΞCT
w),(31)
where T∗is complex conjugate of Tand Ξis a symmetric
positive definite weighting matrix.
Proof: The proof can be found in [31].
Using lemma 1 and introducing χm=E{xmxT
m},
QN=E{Wm,kWT
m,k}, and RN=E{Vm,kVT
m,k},
we obtain the squared Frobenius norms k¯
T¯x(z)k2
F=
tr(BNχmBT
N),k¯
T¯w(z)k2
F= tr(WNQNWT
N), and
k¯
T¯v(z)k2
F= tr(VNRNVT
N). For εx-to-˜εx, we obtain
k¯
T˜x(z)k2
F= ˜χF
m= trE{ ˜
Bm,kxmxT
m˜
BT
m,k}
= trE{¯
˜
Fm,kxmxT
m¯
˜
FT
m,k},(32)
and, for εw-to-˜εw, we have
k¯
T˜w(z)k2
F= tr E{ ˜
Wm,kWm,kWT
m,k ˜
WT
m,k}
= tr( ˜
QD
N−˜
QDT
NHT
N− HN˜
QT D
N
+HN˜
QT
NHT
N),(33)
where ˜
QD
N=E{¯
˜
Dm,kWm,kWT
m,k ¯
˜
DT
m,k},
˜
QDT
N=E{¯
˜
Dm,kWm,kWT
m,k ˜
TT
m,k},˜
QT D
N=
E{˜
Tm,kWm,kWT
m,k ¯
˜
DT
m,k}, and ˜
QT
N=
E{˜
Tm,kWm,kWT
m,k ˜
TT
m,k}.
The following theorem states the batch a posteriori H2-
OFIR filter for data with timing jitter.
Theorem 1: Given model (21) and (22) with zero mean
and mutually uncorrelated timing jitter and other errors. The
batch a posteriori H2-OFIR filtering estimate ˆ
xk=HNYm,k
specified by (23) has the gain
HN= (FN−1χmHT
N+ατ¯
ˆ
FNQNGT
N+˜
QDT
N)
×(HNχmHT
N+ατGNQNGT
N
+βτRN+˜
QT
N)−1,(34)
where ατ= 1 + ¯
δτ,βτ= 1 −¯
δτ, and ¯
δτ.
Proof: Consider (27) and represent the trace trP=
{εT
kεk}of the error matrix Pas
tr P=E{(¯εxk + ¯εwk + ¯εvk + ˜εxk + ˜εwk )T(...)}
=E{¯εT
xk ¯εxk}+E{¯εT
wk ¯εwk}+E{¯εT
vk ¯εvk }
+E{˜εT
xk ˜εxk}+E{˜εT
wk ˜εwk}
=k¯
T¯x(z)k2
F+k¯
T¯w(z)k2
F+k¯
T¯v(z)k2
F
+k¯
T˜x(z)k2
F+k¯
T˜w(z)k2
F.(35)
Solve the minimization problem
HN= arg min
HN
trP
= arg min
HN
tr(BNχmBT
N+WNQNWT
N
+VNRNVT
N+k¯
T˜x(z)k2
F+k¯
T˜w(z)k2
F)(36)
by considering ∂
∂HNtr P= 0. Substitute Qand Rwith (7) and
(8), arrive at (34), and complete the proof.
Finally, compute the error matrix associated with (23) by
P=BNχmBT
N+ατWNQNWT
N+βτVNRNVT
N
+˜
Px+˜
Pw,(37)
where ˜
Px= ˜χF
mand ˜
Pw=k¯
T˜w(z)k2
F.
We now need to specify the uncertain matrices ˜
QDT
Nand
˜
QT
Nin (34) for timing jitter. For the two-state polynomial
model, we write the system matrix Fk=F+ ∆Fkas
Fk=F+ ˜τk¯
Fk=1τ
0 1+ ˜τk0 1
0 0(38)
and the uncertain error ξkis given by (11).
To provide the averaging in ˜
QDT
Nspecified after (33), we
start with ˜
Dm,k =ˆ
FND∆
m,k, where FNis given by (14) and
4.1 Batch H2-Ofir Filter
5. Two-state Glucose Level Model
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D∆
m,k by (18). For small jitter and other errors, we neglect the
products of their values and obtain
D∆
m,k =
0 0 ... 0 0
˜τm+1 ¯
F 0 ... 0 0
.
.
..
.
.....
.
..
.
.
˜τk−1¯
FFN−3˜τk−1¯
FFN−4... 0 0
˜τk¯
FFN−2˜τk¯
FFN−3... ˜τk¯
F 0
.(39)
This gives ¯
˜
Dm,k =¯
ˆ
FND∆
m,k. Similarly we obtain ˜
Tm,k =
¯
HNˆ
FND∆
m,k and arrive at ˜
QDT
N=¯
ˆ
FNQ∆
Nˆ
FT
N¯
HT
N, where
Q∆
N=E{D∆
m,kWm,kWT
m,kD∆T
m,k}.(40)
This gives ˜
QT
N=¯
HNˆ
FNQ∆
Nˆ
FT
N¯
HT
N.
Now, we assume that ˜τk,wk, and vkare small, zero mean,
and mutually uncorrelated white Gaussian processes with the
standard deviations στ,σw, and σv, and first transform matrix
D∆
m,k as follows. The key product in (39) is ¯
FFn=1
0. We
thus assign a matrix ˜
Tn=˜τn
0and obtain
D∆
m,k =
0 0 ... 0 0
˜
Tm+1 0... 0 0
.
.
..
.
.....
.
..
.
.
˜
Tk−1˜
Tk−1... 0 0
˜
Tk˜
Tk... ˜
Tk0
.(41)
Looking into (40), we notice that its key component
is E{˜τ2
kw2
n}. Then for X= ˜τ2
kand Y=w2
nthe
Cauchy-Schwartz inequality E{XY }6pE{X2}E{Y2}
gives E{˜τ2
kw2
n}6pE{˜τ4
k}E{w4
n}. Since for Gaussian vari-
ables we have E{˜τ4
k}= 3σ4
τand E{w4
k}= 3σ4
w, after some
transformations we obtain Q∆
N63σ2
τσ2
wQN
N, where QN
N=
diag( J1J2...JN), in which Ji=i0
0 0,i∈[1, N].
The gain (34) can now be written as
HN= (FN−1χmHT
N+ατ¯
DNQNGT
N
+3σ2
τσ2
w
¯
ˆ
FNQN
Nˆ
FT
N¯
HT
N)(HNχmHT
N
+ατGNQNGT
N+βτRN
+3σ2
τσ2
w¯
HNˆ
FNQN
Nˆ
FT
N¯
HT
N)−1.(42)
and we notice that under the assumption of small errors, the
terms with σ2
τσ2
wcan be omitted and (42) becomes
HN= (FN−1χmHT
N+ατ¯
DNQNGT
N)(HNχmHT
N
+ατGNQNGT
N+βτRN)−1.(43)
Note that, since the batch OFIR filtering estimate [27] can
be computed iteratively using Kalman recursions [32], the
batch (43) can also be computed using Kalman recursions.
We finish the derivation of the robust H2-OFIR filter with the
iterative algorithm, which pseudo code is listed as Algorithm
1. The algorithm requires a maximized value max |˜τk|of the
time jitter in order for the estimate of the blood sugar level to
be robust.
Algorithm 1: Robust H2-OFIR Filtering Algorithm
Data: yk,uk,ˆxm,Pm,Q,R,max |˜τk|
1begin
2ατ= (1 + max |˜τk|
τ);
3βτ= (1 −max |˜τk|
τ);
4for k= 1,2,··· do
5m=k−N+ 1 if k > N −1and m= 0
otherwise;
6for i=m+ 1, m + 2,··· , k do
7P−
k=F Pk−1FT+ατBQBT;
8Sk=HP −
kHT+βτR;
9Kk=P−
kHTS−1;
10 ˆxk=Fˆxk−1+K(yk−HF ˆxk−1);
11 Pk= (I−KkH)P−
k;
12 end for
13 end for
Result: ˆxk,Pk
14 end
Analyzing (42), the following conclusions can be made.
There are two types of corrections: the first-order corrections
by the terms ατand βτand the second-order corrections
by the terms σ2
τσ2
w. The fractional jitter ¯
δτaffects the blood
sugar measurements in the opposite directions, as in (7) and
(8), which is favorite for jitter reduction. The estimation error
matrix (37) does not directly indicate the robustness of the H2-
OFIR filter, and the best is to prove the effect experimentally.
In this section, we apply the filter designed to daily glu-
cose measurements in diabetic patients. We use the above-
considered two-state model and assume that all errors are
Gaussian. Since the glucose measurement error reaches ±20%
in the upper range, we set σv= 20 mg/dl. The scalar
disturbance wkis unknown, and we set σwthat gives the
best estimate for each smoothing window. We next consider
the diabetes data available from [6]. Deliberately, we choose
several databases related to monitoring at 8:00 before breakfast
and apply a two-state UFIR smoother [33] on 3 days, one
week, and two week horizons to obtain a pseudo ground truth.
To investigate the blood sugar level dynamics, we use the H2-
OFIR, OFIR, Kalman, ML-FIR, and UFIR filters and minimize
errors relative to the pseudo ground truth in the MSE sense.
The time jitter in “data-01” obtained over 134 days is shown
in Fig. 1a. As we can see, the time variations are about ±2
hours that corresponds to ¯
δτ= 3.79%. The daily glucose
measurements, a pseudo ground truth obtained by 14-days
smoothing, and the filtering estimates are sketched in Fig.
1b. First we notice that the robust H2-OFIR filter produces
the smallest RMSE of 19.78 mg/dl. The OFIR filter is less
accurate (20.01 mg/dl), and the ML-FIR (28.00 mg/dl) and
UFIR (27.92 mg/dl) filters give more errors.
5.1 Effect of Time Jitter on the Filter
Performance
6. Glucose Monitoring in Diabetic Patients
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Volume 18, 2022
050 100
3
-
2
-
1
-
0
1
2
3
k
Time ji! er, hours
(a)
050 100
0
100
200
300
400
k
(b)
Blood glucose, mg/dl
H2-OFIR UFIR OFIR
ML-FIR Data
Pseudo ground truth
Fig. 1. Daily glucose measurements (“data-01”) at 8.00 before breakfast in
a diabetic patient: (a) timing jitter and (b) filtering estimates for a pseudo
ground truth (14-days smoothed).
The time jitter in another “data-29” obtained over 148 days
is shown in Fig. 2a. Instantly we notice that its mean is not
050 100
4
-
3
-
2
-
1
-
0
1
2
k
Time ji! er, hours
(a)
0 50 100
0
100
200
300
400
k
H2-OFIR UFIR OFIR
ML-FIR
Data
Pseudo ground truth
Blood glucose, mg/dl
(b)
Fig. 2. Daily glucose measurements (“data-29”) at 8.00 before breakfast in
a diabetic patient: (a) timing jitter and (b) filtering estimates for a pseudo
ground truth (14-days smoothed).
zero and that the time variations range from −3to 1 hours that
corresponds to ¯
δτ= 2.29%. The filtering estimates along with
TABLE I
ACCURACY IMPROVEMENT (IN %) BY ROBUST H2-OFIR FILTER FOR
DIFFERENT SMOOTHER WINDOWS AS FUNCTION ON THE FRACTIONAL
TIME JITTER ¯
δτ(IN %)
¯
δτ,%3 days 7 days 14 days
3.79 0.224 0.143 1.144
4.77 5.362 4.014 4.581
9.53 8.044 8.223 9.161
a pseudo ground truth (14-days smoothing) are sketched in
Fig. 2b. Again we notice that the robust H2-OFIR filter gives
the smallest RMSE (19.14 mg/dl), while the OFIR filter (19.22
mg/dl), UFIR (23.82 mg/dl), and ML-FIR (25.64 mg/dl) filters
are less accurate.
Now we wonder how robust the H2-OFIR filter is compared
to the OFIR filter, which does not have the tuning option to
mitigate timing jitter. To find out, we compute the difference
between the H2-OFIR and OFIR estimates, relate the result
to the OFIR estimate, and plot in percents in Fig. 3. What
0 2 4 6 8 10
0
2
4
6
8
10
Es!ma!on accuracy improvement, %
Frac!onal !me ji"er, %
t= 24 hours
t= 12 hours
t= 6 hours
Fig. 3. Improvement of the OFIR filter accuracy (in %) by the robust H2-
OFIR filter as function of the fractional time jitter ¯
δτ(in %).
follows is that, for the maximum observed ¯
δτ= 3.8% related
to τ= 24 hours, the filtering accuracy is improved only by
1.14%. Next, we assume that monitoring is conducted each
τ= 12 and τ= 6 hours and infer that the estimation
accuracy is improved proportionally to ¯
δτ. Note that these
projections do not accurately apply to glucose monitoring as
blood sugar levels are higher during the day and lower at
night. Nevertheless, it gives an idea of the effect of fractional
time jitter on the accuracy of a robust filter. This is supported
by Table I, from which we also deduce that the accuracy
improvement does not depend on the smoother window.
Finally, we look at the estimated second state and compute
the average rate of the blood sugar level. The most accurate
robust H2-OFIR filter reveals a low rate of 0.089 (mg/dl)/day
in “data-01” and a high rate of 0.45 (mg/dl)/day in “data-29”.
Other rates obtained by different filters are listed in Table II.
WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2022.18.16
Eli G. Pale-Ramon, Jorge A. Ortega-Contreras,
Karen J. Uribe-Murcia, Yuriy S. Shmaliy
E-ISSN: 2224-3488
120
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TABLE II
BLOOD SUGAR LEVEL RATES IN (MG/DL)/DAY DETECTED IN “DATA-01”
AND “DATA-29” BY DIFFERENT FILTERS
Data set H2-OFIR OFIR KF ML-FIR UFIR
“data-01” 0.089 0.058 0.103 0.039 0.129
“data-29” 0.451 0.449 0.557 0.271 0.418
To provide accurate monitoring of glucose level in diabetic
patients under timing jitter caused by human factors, we
have developed the robust a posteriori H2-OFIR filter and
compared its performance to the a posteriori OFIR filter.
It turned out that under the maximum observed fractional
daily jitter in glucose measurements of 4%, the accuracy
improvement by the robust filter is less than 4%, which is
small. In this case, the jitter can be ignored and the standard
filters used. However, more frequent measurements result in
larger fractional jitter that require robust estimates.
This work was supported by the Consejo Nacional de
Ciencia y Tecnolog´ıa (CONACyT) of Mexico Project A1-S-
10287, Funding CB2017-2018.
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7. Conclusions
Acknowledgements
References
WSEAS TRANSACTIONS on SIGNAL PROCESSING
DOI: 10.37394/232014.2022.18.16
Eli G. Pale-Ramon, Jorge A. Ortega-Contreras,
Karen J. Uribe-Murcia, Yuriy S. Shmaliy
E-ISSN: 2224-3488
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DOI: 10.37394/232014.2022.18.16
Eli G. Pale-Ramon, Jorge A. Ortega-Contreras,
Karen J. Uribe-Murcia, Yuriy S. Shmaliy
E-ISSN: 2224-3488
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