their method does not support the precise pose imaging and
the parameters of HMM are difficult to determine.
Inspired by the advantages of RTI, we will explore the
use of RTI based sensing method for fall detection, espe-
cially the older adults or patients living alone. The RSS
measurements would have statistical shadow losses caused
by the obstruction of human body, and the shadow loss is
able to be separated from the value of RSS. We use a
wireless network organized by a group of radio-fre-
quency (RF) sensors for human pose acquisition in the
vertical direction, and then use the non-negative total
variation (TV) minimization for reconstructing the gray
image of body. RTI belongs to the radio imaging tech-
nology and responds only to shadow loss produced by body
obstruction. It has promising advantages in overcoming the
limitations of the traditional camera-based sensing method
as mentioned above, since the body attenuation information
is acquired only, instead of fully sensing redundant back-
ground and chromatic information. Experimental results
demonstrate that the proposed method can benefit the
development of low-cost, low-power and accurate devices
being more suitable than optical countparts for wireless
sensor networks (WSN).
The structure of this article is as follows: Sect. 2 pre-
sents the mathematical formulation of the RTI for human
pose acquisition. Section 3 details the non-negative TV
minimization for image reconstruction. Section 4 describes
the experimental setup and results on actual data. Section 5
gives the conclusion.
2 Measurement model
2.1 Brief review on RTI
The task of RTI is to get the distribution image generated
by shadow fading in a coverage area. However, the shadow
fading can not be acquired from physical measurements
directly. The measurement values of shadow fading need to
be obtained from the separation of RSS. In the architecture
with fixed wireless RF networks, the shadow fading is
approximated by the difference value of measured RSS.
The difference value of measured RSS is calculated based
on the difference between online and baseline RSS value.
The baseline RSS value is the measured RSS that does not
include the information of shadow fading.
Following the general propagation law of narrow-band
RF signal, the RSS from transmitter t to the receiver r has
the following model structure in decibels (dB):
yðr; tÞ¼y
PL
ðd
r;t
Þþy
SH
ðr; tÞþy
MP
ðr; tÞ; ð1Þ
where y
PL
ðd
r;t
Þ is the path loss component only
depending on the link distance d
r;t
, y
SH
ðr; tÞ is the
shadow fading component generated by body’s occlu-
sion, y
MP
ðr; tÞ is the multi-path loss caused by the
environment (Wilson and Patwari 2010). From the per-
spective of sensing the environmental distribution of
shadow fading, y
SH
ðr; tÞ is the component associated
with the shadow fading directly, which can be repre-
sented as the projection vector of attenuation image.
y
MP
ðr; tÞ is the uncertainty interference for the mea-
surement of the shadow fading, which is related to the
deployment of links. y
PL
ðd
r;t
Þ is the component unre-
lated with shadow fading nor multi-path effects.
Based on the above structural characteristic of RSS,
the shadow loss y
SH
ðr; tÞ is the key component to guide
the measurement. Assuming a monitored network region
is given, we can divide it into pixel array according to the
imaging accuracy, as shown in Fig. 1. It should be noted
that the resolution of monitored area is determined by
imaging accuracy. For the task of large-scale person
location, a pixel is usually represented as a region with
50 50 cm. However, for the local pose imaging, higher
imaging accuracy is needed. We will give some test
parameters with different accuracies in the experimental
section. The monitored area in the Fig. 1 is divided into
28 20 pixels, and each pixel is represented as a spatial
region with 7:5 7:5 cm. If we deploy two nodes around
the region and the region is divided into an image vector
of dimension R
NM
, the shadowing loss y
SH
ðr; tÞ for this
link can be expressed approximately as a sum of atten-
uation in each pixel. The mathematical form is denoted
by:
y
SH
ðr; tÞ¼
X
NM
j¼1
M
rt;j
x
j
;
ð2Þ
where x
j
is the attenuation in pixel j, M
rt;j
is the measured
weight for pixel j for the link ðr; tÞ. The measurement
vector M
rt;j
can be approximated by an ellipse with foci at
each pair of nodes locations (Patwari and Agrawal 2008;
Wilson and Patwari 2010), simplified as
M
rt;j
¼ d
1=2
r;t
1; if d
rt;j
ðtÞþd
rt;j
ðrÞd þ k;
0; otherwise:
ð3Þ
where d
rt;j
ðtÞ and d
rt;j
ðrÞ are the distance from pixel j to
the two nodes of link ðr; tÞ respectively , and k is a
tunable width of the ellipse. The elliptical width
parameter k is a tradeoff between modeling error and
imaging quality. In the experiments, we also empirically
specify the parameter k.
If a RF sensor network organized by a group of RF
nodes is given, as illustrated in Fig. 1, the RF signals will
be affected by the occlusion of the targets close to the
wireless links. We can infer the occlusion of the body from
pairwise RSS measurements caused by shadow fading
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