Method and wearable electronic system for predicting the heart rate of a user during a physical activity, and, non-transitory computer readable storage medium
A method for predicting heart rate (HR) of a user during a physical activity, comprising: monitoring the user during the physical activity with an wearable electronic device comprising a photoplethysmography (PPG) sensor, an accelerometer, a memory and a processor; wherein the memory is configured to store user demographic data, PPG data and accelerometer data detected by the PPG sensor and the accelerometer, respectively. The method includes computing a PPG heart rate estimation and a PPG quality flag using the PPG data and accelerometer data, wherein the PPG quality flag indicates whether the PPG data is reliable or not; computing an exponential heart rate estimation by applying the PPG heart rate estimation, the PPG quality flag and the user's demographic data on an exponential approximation model; if the PPG quality flag is reliable, outputting the PPG heart rate estimation; otherwise, outputting the exponential heart rate estimation.
1. A method for predicting heart rate (HR) of a user during a physical activity using a wearable electronic device, the method comprising:
monitoring the user during the physical activity with the wearable electronic device, the wearable electronic device including a photoplethysmography (PPG) sensor to detect changes in blood volume of the user during the physical activity, an accelerometer to capture acceleration of the user during the physical activity, a memory to store demographic data of the user, data from the PPG sensor and data from the accelerometer and a processor to process the data obtained from the PPG sensor and the data from the accelerometer;
computing, using the data from the PPG sensor and the data from the accelerometer, a PPG heart rate estimate and a PPG quality flag;
computing an exponential heart rate estimate by applying the PPG heart rate estimate, the PPG quality flag and the demographic data of the user in an exponential approximation model;
the exponential approximation model being determined by:
HR
(
t
+
1
)
=
-
[
-
HR
(
t
)
]
×
e
-
1
τ
where, HR (t+1) is the exponential estimate of heart rate,
is a parameter that indicates an increase or decrease in that heart rate calculated in a previous iteration, and T is a constant that determines the increase or decrease in rate,
where, is determined by:
= D S ×W T +{b low ,b high }
where D s is a matrix that defines [AL, BMI, age, male, female], AL is a normalized raw activity level, BMI is a body mass index and male or female assumes 1 or 0, the parameter determined according to intensity of the physical activity of the user and W T is transposition of a matrix of weights that affect behavior of the exponential approximation model;
outputting, provided the PPG quality flag indicates that the data captured from the PPG sensor is reliable, the PPG heart rate estimate; and
outputting, provided the PPG quality flag indicates that the data captured from the PPG sensor is unreliable, the exponential heart rate estimate.
2. The method according to claim 1 , further comprising:
determining a level of movement and an intensity of the physical activity of the user using the data from the accelerometer.
3. The method according to claim 2 , wherein the determining the level of movement and the intensity of the physical activity of the user using the data from the accelerometer comprises:
filtering the data from the accelerometer to reduce noise and aggregating an accelerometer signal using a norm function to produce an aggregated accelerometer value,
computing a raw value of activity level, AL raw , by integrating the aggregated accelerometer value,
computing a normalized raw activity level, AL, and
computing the intensity of the physical activity of the raw value of activity level upon a comparison with a defined threshold.
4. The method according to claim 3 , wherein the accelerometer signal is aggregated with a norm function defined by:
α gg (α x ,α y ,α z )=α x 2 +√{square root over (α y 2 +α 2 2 )}
where a x , a y and a z , represent the 3-axis coordinates of the accelerometer.
5. The method according to claim 4 , further comprising:
integrating the aggregated signal with a sliding window of time to obtain a raw value of the activity level ALraw; and
approximating the aggregated signal with a trapezoidal rule:
AL
raw
=
∫
t
1
t
2
agg
(
a
)
≈
Δ
a
∑
k
=
1
N
-
1
agg
(
a
k
)
+
agg
(
a
n
)
+
agg
(
a
0
)
2
where a=[a x , a y , a z ] and N is a number of data points within the sliding window of time, which depends on a sampling frequency of the accelerometer signal.
6. The method according to claim 5 , further comprising:
applying a clipping operation to ensure that the raw value of activity level is within [0, 1],
integrating the raw value of activity level, and
normalizing the integrated raw value of activity level by dividing the integrated raw value of activity level by a size of the sliding window of time.
7. The method according to claim 3 , wherein the raw value of activity level assumes a low and a high state, which is determined by a threshold φ i , and
provided AL raw <φ i for a predefined period of time, the raw value of activity level assumes a low state; otherwise, the raw value of activity level assumes a high state.
8. The method according to claim 1 , wherein provided the PPG quality flag is reliable, the exponential approximation model parameters are fine-tuned in real-time as a personalization model for the user.
9. The method according to claim 8 , further comprising:
performing a gradient descent algorithm using derivatives of a mean absolute error (MAE) throughout time, wherein the MAE is defined by:
MAE
(
y
,
y
^
)
=
1
N
∑
i
=
0
N
❘
"\[LeftBracketingBar]"
y
i
-
❘
"\[RightBracketingBar]"
wherein y is the PPG heart rate estimate, is the exponential heart rate estimate.
10. The method according to claim 9 , wherein a gradient descent strategy is used with a module definition to compute the derivatives for y i − >0 with respect to Θ={W, τ, b low , b high }:
∂
MAE
(
y
,
y
^
)
∂
Θ
=
∂
∂
Θ
[
1
N
∑
i
=
0
N
(
y
i
-
)
]
=
1
N
∑
i
=
0
N
∂
(
y
i
-
)
∂
Θ
=
1
N
∑
i
=
0
N
∂
y
i
∂
Θ
-
∂
∂
Θ
=
1
N
∑
i
=
0
N
-
∂
∂
Θ
;
when y i − >0, signals of the derivatives are inverted; and
the derivatives of HR (t+1) are given by:
∂
HR
(
t
+
1
)
∂
Θ
=
∂
∂
Θ
-
∂
∂
Θ
[
(
-
HR
(
t
)
)
e
-
1
τ
]
=
∂
∂
Θ
-
[
∂
(
-
HR
(
t
)
)
∂
Θ
e
-
1
τ
+
∂
e
-
1
τ
∂
Θ
(
-
HR
(
t
)
)
]
=
∂
∂
Θ
[
(
∂
∂
Θ
-
∂
HR
(
t
)
∂
Θ
)
e
-
1
τ
+
∂
e
-
1
τ
∂
Θ
(
-
HR
(
t
)
)
]
=
∂
∂
Θ
-
[
∂
∂
Θ
e
-
1
τ
+
∂
e
-
1
τ
∂
Θ
(
-
HR
(
t
)
)
]
.
11. The method according to claim 10 , wherein the exponential approximation model comprises parameters update rules:
W
t
+
1
=
W
t
-
α
(
D
s
e
-
1
τ
t
-
D
s
)
{
b
t
+
1
low
,
b
t
+
1
high
}
=
{
b
t
low
,
b
t
high
}
-
α
(
e
-
1
τ
t
-
1
)
τ
t
+
1
=
τ
t
-
α
-
e
-
1
τ
t
τ
t
2
[
D
s
×
W
t
⊤
-
HR
(
t
)
]
wherein α is a learning rate of the exponential approximation model.
12. The method according to claim 1 , further comprising:
managing a transition between the PPG heart rate estimate and the exponential heart rate estimate when the PPG quality flag changes from reliable to unreliable, or vice-versa.
13. The method according to claim 12 , wherein the managing of the transition comprises applying a stabilization equation given by:
(
t
)
=
HR
Target
-
(
HR
Target
-
(
t
-
1
)
)
×
e
-
Δ
t
σ
wherein (t) is the transition HR; (t−1) is the heart rate obtained right before the transition starts, HR Target is a target heart rate in which (t) must stabilize; Δt is one step of time that depends on the PPG signal frequency; and σ controls how fast or slow the transition should happens.
14. The method according to claim 1 , further comprising:
counting a personalization timer indicating a period which indicates for how long the exponential approximation model was personalized using data of the user,
comparing the personalization timer with a threshold time, τt, indicating a minimum required training time, and
provided the personalization timer is lower than the threshold time, outputting the PPG heart rate estimate.
15. The method according to claim 1 , wherein a new heart rate estimate is estimated every second.
16. A wearable electronic system for predicting heart rate (HR) of a user during a physical activity, comprising
a processor;
a memory comprising computer readable instructions that, when executed by the processor, causes the processor to perform the method of claim 1 .
17. A non-transitory computer readable storage medium which stores computer readable instructions that, when executed by a processor, causes the processor to perform the method of claim 1 .