IEEE Signal Processing - May 2018 - 66
a door that blocked the direct LOS path between the Wi-Fi
devices. For a fixed false-positive rate of 0.15%, the truepositive rate increased from 75% at a 40-MHz effective
bandwidth to 76.38%, 87.12%, and 95% at the 120-, 240-,
and 360-MHz effective bandwidths, respectively. We can
see from the experiment that a large effective bandwidth
not only enhances the positioning accuracy but also boosts
the robustness of indoor positioning against random environmental perturbations [33].
TR (h T, Rv 0, h T, Rv ) =
/
Given a large enough bandwidth, the multipaths in a rich-scattering environment can be resolved into multiple taps in discrete time. Let h T, Tv " Rv 0 [k] be the kth tap of the time-domain
v 0, where Tv and
channel impulse response (CIR) from Tv to R
v
R 0 are the coordinates of the transmitter and receiver, respectively. Then we denote the time-reversed and conjugated version of the captured CIR as h *T, Rv 0 " Tv [-k], where * indicates
complex conjugation. With channel reciprocity, the received
v when the TR waveform h *T, Rv 0 " Tv [-k]
signal at any location R
is transmitted can be written as
h T, Tv " Rv 0 [l] h *T, Rv 0 " Tv [l - k],
(3)
l =0
where N tap is the number of taps resolved in the CIR. When
v =R
v 0 and k = 0, s Rv [k] = R lN=tap0-1 h T, Tv " Rv 0 [l] 2, with all of
R
the multipaths added up coherently; i.e., the signal energy is
refocused on the particular spatial location at a specific time
instance. This phenomenon is called the TR spatial-temporal
resonating effect [30].
To study the TR resonating effect in the spatial domain, let
us fix the time index k = 0 and define the TRRS between the
v 0 and R
v as the normalized energy of
CIRs of two locations R
v 0 is
the received signal when the TR waveform for location R
transmitted as shown in (4), where h T, Rv is an abbreviation of
h T, Tv " Rv [l], l = 0, g, N tap - 1, when Tv is fixed.
66
/
h T, Tv " Rv (t) =
,
h T, Tv " Rv [l 2]
2
(4)
/
G (~) q (t - x (~))
~!X
v
v
# e i (2rf0 (t -x (~)) -z (~) -k (~)·R),
/
T
T
x (~) ! 8lT - , lT + j
2
2
Distance estimation based on TRRS spatial distribution
/
2
N tap - 1
l2 = 0
h T, Tv " Rv [l] =
The reliability of the centimeter-accuracy IPS discussed
previously depends on whether the CSI fingerprints in the
offline database are up to date or not. If the environmental
changes affect the CSI and thus degrade the positioning
accuracy, the CSI database needs to be updated, which will
increase the IPS overhead. To avoid having to recalibrate the
CSI fingerprints, we analyze the TRRS spatial distribution
and present a mapping-free TR-based indoor tracking system (TRITS) that can achieve decimeter accuracy. As the
TRITS tracks a moving object based on its previous location
and current location displacement, which consists of a moving distance and a moving direction, and the moving direction
can be estimated through an inertial measurement unit (IMU),
we focus on the moving distance estimation. Then, we discuss a map-based position correction technology to reduce
the accumulated tracking error.
N tap -1
h T, Tv " Rv 0 [l 1]
l1 = 0
Mapping-free indoor tracking
with decimeter accuracy
s Rv [k] =
2
s Rv [0]
N tap - 1
(5)
G (~) q (Dx (l, ~))
v
v
# e i (2rf0 Dx (l, ~) -z (~) -k (~)·R),
N tap
s Rv [0] = /
/
l = 1 x ! 6lT - T2 , lT + T2 h
(6)
G (~) q (Dx (l, ~))
2
# e i (2rf0 Dx (l, ~) -z (~)) .
(7)
A more detailed illustration of the multipath propagation is
displayed in Figure 1(b), where each multipath is represented
by the total traveled distance of the multipath r, the direction
of arrival of the multipath i, and the power gain G (~), with
v in a source-free region with con~ = (r, i). For any point R
stant mean electric and magnetic fields, the CIR, when a deltalike pulse is transmitted, can be written as (5) [48], where X is
the set of multipaths, q (t) is the pulse shaper, x (~) = r/c is the
propagation delay of the multipath ~, f0 is the carrier frequency,
z (~) is the change of phase due to reflections, and kv (~) is the
wave vector of amplitude k = c/f0 . Accordingly, the lth tap of a
v can be expressed as in (6), where T
sampled CIR at location R
is the channel measurement interval and Dx (l, ~) = lT - x (~)
for l = 0, 1, f, N tap - 1. When the TR waveform h *T, Rv 0 " Tv [-l]
is transmitted, the corresponding received signal at the focal
v 0 can be written as (7), which shows that the multipaspot R
ths with propagation delays x (~) ! [lT - T2 , lT + T2 ) would be
merged into the lth tap in an incoherent way, while the signals
coming from different taps would add up coherently. Therefore, the larger the bandwidth, the larger the TR focusing gain
that can be achieved, since more multipaths can be aligned and
added up coherently. When the bandwidth is sufficiently large,
v can be approximated as
the received signal at each point R
N tap
s Rv [0] .
/
2
v
v
v
G (~) q (Dx (l, ~)) e -ik (~)·(R -R 0) .
(8)
l =1
Without loss of generality, the energy distribution of each
multipath in a rich-scattering environment can be assumed
uniform in i; i.e., the distribution of G (~) is only a function
of r. Then, the energy of the multipaths coming from different directions would be approximately the same when there is
a large number of them. When a rectangular pulse shaper is
used, i.e., q (t) = 1 for t ! [-(T/2), T/2), and q (t) = 0 otherwise, under the above assumptions, the received signal s Rv [0]
can be approximated as
IEEE Signal Processing Magazine
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May 2018
|
Table of Contents for the Digital Edition of IEEE Signal Processing - May 2018
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