Each - Draper Laboratory

estimates may be large enough to preclude the initial use of
an extended Kalman filter, and other means (e.g., particle
filters, multiple-hypothesis filters, information filters) must
be used at least initially to get within the linear range of an
extended Kalman filter.
The form of (16) indicates that accurate estimation of the
multipath parameters {w, c} depends on meeting several
conditions: 1) relatively accurate tag location estimates
over a sufficient length of time, 2) tag motion sufficient to
ensure observability of the parameters, 3) relatively small
variation of the of multipath parameters as the tag moves
through the indoor environment, and 4) persistence of
the sequence of reflections. In the sequel, it is shown for a
representative indoor scenario that the parameter variations
tend to be relatively small as the tag moves through space,
allowing reasonably accurate estimates of the multipath
parameters to be obtained.
Data Association
A generic measurement data association algorithm is
depicted in Figure 4. At any time, data for all current and
past detected indirect paths are stored, both as all past raw
measurement associated with that path and the coefficients
of low-order ordinary least squares regression models of
the path delays. When a new measurement is obtained,
the distance to all current paths is calculated by comparing
the predicted values in the current database with the
new value. If the minimum distance is less than a prespecified
threshold, then the closest current path is updated,
including the regression model. If the distance exceeds the
threshold, a new indirect path is started. Note that new
indirect paths may be started if a new path appears, an old
path reappears, or a current path changes by a relatively
large amount due to tag motion since the last measurement
of that indirect path. The output of the data association
algorithm is the identity of the path associated with the
current measurement.
Step 1
Step 2
New
measurement
(y)
Start new path
Prediction based on
OLS path model
Find distance to current
closest path
Figure 4. Generic measurement data association
algorithm.
8 Innovative Indoor Geolocation Using RF Multipath Diversity
no
d, k
d 0 is used in the filter to model the uncertainty
associated with the unknown control u(i − 1).
From (16), the indirect path length measurements are
modeled as
,
,
(22)
where n(i) is zero-mean Gaussian measurement error.
Updating at a measurement is performed using the extended
Kalman filter update equations (cf., Reference [11])
where
(23)
is the measurement residual and K(i) is the optimal gain
matrix:
where
(24)