Each - Draper Laboratory

indoor environment. The statistical bias model was generated
using ultra-wideband measurements.
In practice, it is important to correctly associate each calculated
delay with the direct path or a specific indirect path
(i.e., a specific sequence of reflections off the same set of
reflecting planes). This is not a straightforward process in
some scenarios with multiple nodes and complex environments
containing many reflecting surfaces of various
orientations and size. The problem is made challenging by
the presence of crossovers between pairs of time delays,
appearance of new paths, disappearance and reappearance
of existing paths, and the presence of noise. In order to be
effective, the data association algorithm should be capable
of detecting path persistence, so that the largest possible
number of measurements for each path are obtained; this
enhances the accuracy of multipath parameter estimation.
All the methods mentioned above rely on a single parameter,
the differential delay, for the multipath model.
Multipath estimation is based on a priori statistical models
of differential delay, typically as a bias (including means to
detect sudden bias changes) or output of a low-order linear
filter. In contrast, the approach suggested here is based on
a geometrical model and the assumption that the indirect
path length is the result of a series of specular reflections
off planar surfaces. This model contains several geometrybased
parameters and does not depend on a priori statistical
models of multipath delay. Thus, use of this model allows
the possibility of inferring geometrical structure within the
indoor environment. We now develop the measurement
model that is appropriate for use in a nonlinear filter that
is capable of joint estimation of tag location and the geometry-based
multipath parameters.
Geometry-Based Measurement Model
In the following, time delays have been converted into
distances using the known signal propagation velocity in
air. The indirect path distance after a sequence of m specular
reflections off planar surfaces is derived as follows.
Referring to Figure 3, the relevant equations are, for i =
1,2,...,m
and
where p i is the specular point on the i th plane, d 1 is the
distance from the source to p 1, {d i ; i = 2,3..., m} is the
6 Innovative Indoor Geolocation Using RF Multipath Diversity
(1)
(2)
(3)
(4)
(5)
(6)
distance from p i−1 to p i , d m+1 is the distance from p m to r, w i
is the unit vector along the incident ray, b i is the distance of
the plane to the origin of the navigation frame, u i is the unit
vector normal to the plane, and d is indirect path length.
From (1), (5), and (6),
Thus,
From (3) and (4),
Thus,
But, from (1) and (2),
p 1
tag r
w m
q 1
q 1
d m+1
u m
d 1
Figure 3. Geometry for m specular reflections.
w 2
u 1
d m
q m
q m
w m+1
w 1
source s
p m
(7)
(8)
(9)
(10)
(11)