FASTRAK MANUAL
Rev. G
E-3
JUNE 2012
FILTER RESPONSE (LAG)
FASTRAK has optional filters that are intended to smooth the receiver’s calculated
position and orientation in mechanically or magnetically noisy environments. The degree of
filtering is user selectable from very heavy to none at all, or the degree of filtering can be
automatically selected in real time by the tracker as it adapts to “noise”. Filtering can introduce
lag in response; the sync-to-output latent period remains unchanged (recall that latent period is
defined as “a first indication” and not a final settled response), but the data that is output may not
correspond to where the receiver was recently.
To help understand the response of the optional filters, the filter algorithm is described
and analyzed in the following paragraphs.
FASTRAK coordinate filters are exponential filters as described by the following
equation.
>
x
<
)
-
(1
+
x
=
>
x
<
1
-
k
k
α
α
Equation E-1
In this equation “x” is the unsmoothed receiver coordinate measured at time “k”; it may
be a coordinate of position or orientation. The variable “<x>
k
” is the filter output at
discrete time “k” and “<x>
k-1
” is the smoothed value at time “k-1”. The filter parameter
“
α
“ controls the degree of filtering and must be within the range 0 <
α
< 1. Small values
of
α
produce heavy filtering; large values produce light filtering; in the limit as
α
→
0 the
filter output never changes; and in the limit as
α
→
1 the output exactly follows the input.
The filter parameter
α
can be set to a specific value through system commands, or a
range of values can be specified which allows the system to choose its own optimum
value automatically adapting to environmental noise.
expresses the steady state filter response for zero acceleration in receiver
coordinates and for a constant filter parameter
α
. In the derivation of the equation, the
coordinate “x” is assumed to be of the general form “x = vt”, where “v” represents a
constant velocity (in either position or orientation), “t” is time, and “
∆
t” is the tracker’s
cycle time (the inverse of update rate).
t
v
-
1
-
x
=
>
x
<
k
∆
α
α
Equation E-2
can be reformulated to express the filter time delay for a constant rate of
change (“v”) in input.
t
-
1
=
v
>
x
<
-
x
k
∆
α
α
Equation E-3