Vital Sign Monitoring and Mobile Phone Usage Detection Using IR-UWB Radar for Intended Use in Car Crash Prevention

. 2017 May 30;17(6):1240. doi: 10.3390/s17061240

Algorithm 3: Step by step construction of the vital signal from the best fit signals

(1) Initialization
Find “k” best-fit signals whose R-square values are above certain set threshold, say R-square_min = 0.3.The size of each best-fit signal is 256 samples. So, we have a matrix of

b e s t_f i t_{m a t r i x} (k \times 256) .

In our example, k = 9.
(2) for

i t e r a t i o n s = 1 : l a s t_z e r o_c r o s s i n g

If (iteration == 1)
Then Find the first zero-crossing fast time index (

z e r o_c r o s s i n g s)

of all the “k” best-fit signals. And find the sub-signal component, which has the maximum value of

z e r o_c r o s s i n g s

For our example,

f i r s t_z e r o_c r o s s i n g s

are found to be as follows:

first z e r o_c r o s s i n g s = [234 231 223 231 230 235 224 220];

m a x_z e r o_i n d e x = m a x (z e r o_c r o s s i n g s) = 235;

k_m a x_c r o s s i n g = a r g m a x_{k} (z e r o_c r o s s i n g s) = 6

Construct the vital signal according to the following expression, the result is shown in Figure 8.

c o n s t r u c t e d_v i t a l_s i g n a l (1 : \max_z e r o_i n d e x) = b e s t_f i t_m a t r i x (k_m a x_c r o s s i n g, 1 : m a x_z e r o_i n d e x)

For our example; Figure 8 show the construction of first sub-signal component of the vital signal:

c o n s t r u c t e d_v i t a l_s i g n a l (1 : 235) = b e s t_f i t_m a t r i x (6, 1 : 235);

Else if (iteration > 1) Find the next zero-crossing fast time index (

z e r o_c r o s s i n g s)

of all the “k” best-fit signals
for

i = 1 : k

Append the

i^{t h}

sub-signal component to the previously constructed vital signal.
Find the correlation of the resulting signal

c o r r e l a t i o n (i) = a u t o c o r r ([constructed_vital_signal; i^{th} sub_signal_component]);

end

\max (w i d t h_c o r r e l a t i o n (i)); i = 1 : k

Append that sub-signal component to the previously constructed vital signal, which has maximum correlation as found by the above expression.For our example, when iteration = 2:

s e c o n d z e r o_c r o s s i n g s = [354 359 351 344 347 360 354 351];

After we appended each sub-component to the previously constructed vital signal and found the correlation of each signal, it was found to be:

c o r r e l a t i o n = [17.1 13.3 18.3 9.3 16.2 23.8 18.2 22.8];

k_{m a x_{c o r r}} = a r g m a x_{k} (c o r r e l a t i o n) = 6

\max_c o r r_i n d e x = a r g m a x_{z e r o_c r o s s i n g s} (c o r r e l a t i o n) = 360

Here the 6th signal sub-component shown the maximum correlation with the previously constructed signal. Now we append the next sub-signal component of the 6th signal to the previously constructed vital signal to find the constructed_vital_signal as follows in Figure 9.

c o n s t r u c t e d_v i t a l_s i g n a l (e n d : \max_c o r r_i n d e x) = b e s t_f i t (k_m a x_c o r r, e n d : \max_c o r r_i n d e x)

where

e n d = l e n g t h (p r e v i o u s c o n s t r u c t e d v i t a l s i g n a l) + 1

For our example:

c o n s t r u c t e d_v i t a l_s i g n a l (236 : 360) = b e s t_f i t_m a t r i x (6, 236 : 360);

(3) Check, if: there are further zero crossings, then go to step 2
Else; stop the loop;
Save; the constructed_vital_signalThe final vital signal obtained is given in the Figure 10.
end