Each - Draper Laboratory

North (m)
Node 1 Node 2
30
25
20
15
10
5
0
x1t1spr
0 10 20 30
East (m)
Figure 6. Conditions after particle filter initialization.
Available measurements were processed every 0.5 s. Tag
speed was held constant at 0.5 m/s. No dead reckoning
sensors were employed, so that the geolocation estimates
calculated by both filters were not propagated between
measurements; however, the error covariance matrices
were increased within both filters using (21). The process
noise covariance matrix Q(i) = v(i)I was calculated using
sequential differencing of the position estimates to estimate
the variance v(i).
The simulation was run for 94 s at a time step of 0.5 s.
The time delay (in meters) for the direct and indirect paths
are plotted in Figure 7. The two indirect paths from Node
1 have a single crossover point at 20 s. The two indirect
paths from Node 2 have a single crossover point at 70 s,
with a near-crossover at 17 s. The data association algorithm
given in the previous section was employed using
quadratic regression models and produced no data association
errors.
The true and estimated paths over time for both filters
are shown in Figure 8. True tag location is shown by the
solid black line. The estimated path for the multipath filter
(MP) is shown by the solid colored line, while the estimated
path for the conventional filter (CV) is shown by the
dotted colored line. While both direct paths are detected
(for the first 55 s), the MP filter and the CV filter produce
identical geolocation estimates (blue line). After the direct
path from Node 2 is lost at 55.5 s, the CV filter is able to
navigate off the direct path from Node 1 only, while the MP
filter, in addition, is able to navigate off the indirect path
from Node 1 reflected off the bottom wall and the indirect
path from Node 2 reflected off the West wall. The MP
filter estimate (solid red line) produces very small tracking
errors, while the CV filter errors (dotted silver line) start to
grow. When both direct paths become undetected at 73.5
s, the CV filter can no longer track at all; its geolocation
estimate remains constant for the remainder of the simulation.
In comparison, the MP filter is able to navigate off the
10 Innovative Indoor Geolocation Using RF Multipath Diversity
m
m
North (m)
70
60
50
40
30
20
Node 1
10
0 20 40 60 80 100
60
50
40
30
20
Time (s)
x1dy
10
0 20 40 60 80 100
30
25
20
15
10
5
0
Node 2
Time (s)
Figure 7. Measurement delay vs. time.
Node 1 Node 2
x1tag
0 10 20 30
East (m)
Figure 8. Comparison of true and estimated paths.
detected indirect paths. Between 73.5 and 77.5 s, the MP
filter navigates off the indirect path from Node 1 reflected
off the bottom wall and both indirect paths from Node 2.
At 78 s, the indirect path from Node 2 reflected from the
West wall becomes undetected, and the MP filter is reduced
to using both indirect path measurements off the bottom
wall. At 84 s, all four indirect paths become detectable and
are used by the MP filter until the end of the simulation.