4 SIGNAL PROCESSING
Signal processing stack in Hermes is composed of
pre-processing and processing stages. Signal con-
ditioning, filtering and segmentation is part of pre-
processing stage, while in processing stage temporal,
spatiotemporal and consistency features are extracted
based on which the measure for instability can be es-
tablished.
We define the spatial and temporal parameters ac-
cording to (Whittle, 2007) as following: Step length is
the distance from a point of contact with the ground
of one foot to the following occurrence of the same
point of contact with the other foot. This can gener-
ally be thought of as the distance one foot moves for-
ward in front of the other. Step time is the time taken
for each step. Cadence is the number of steps taken
per second. Stride length is defined as the distance
between successive points of initial contact point of
the same foot. It consists of two steps lengths, left
and right. Gait speed is the product of stride length
and cadence. Stance-to-swing ratio, where the stance
phase is the time from heel-down to toe-off, and the
swing phase is the time between toe-off and heel-
down. Dual stance is the time that both feet are in
contact with the ground. Pressure correlation is the
correlation of the pressures recorded in each step with
the previous steps.
Temporal parameters are extracted through pres-
sure signal analysis. The extraction of left and right
stance phase, left and right swing phase, and dual-
support phase features is done by by processing a
minimum of four signals, which are most closely as-
sociated to the point of pressure for the toe and heel.
We process discretized and sanitized signals that
represent the input pressure signals. These sig-
nals represent occurrences of pressure-contact-on and
pressure-contact-off. Given these occurrences, we
know exactly where the following occur: right heel
on, right toe off, left heel on, and left toe off. For
a single step cycle, these are the only events that we
need to detect in order to generate all temporal fea-
tures. Temporal features are calculated as follows:
Left/Right stance phase is the time between the heel
on and toe off, left/right swing phase is the time be-
tween toe off and heel on again, dual support is the
time between right heel on and left toe off. Any other
temporal parameter that is later decided to be useful,
can be added in a similar manner.
Spatial parameters are extracted through both
pressure and non pressure signal analysis. The sig-
nals acquired from pressure sensors are used to com-
pute step consistency by computing the correlation of
consecutive steps in real-time. We also use the sig-
nal reading from the accelerometer and gyroscope to
compute the stride and step length using techniques
described in (S. Bamberg, 2007).
Step consistency is calculated in real-time by
computing the difference of two consecutive signals
by taking the difference of their integral over the time
according to Equation 1, where k is the operation
window, S is the max number of steps taken, es and bs
are the beginning and end point of the step and P(x)
is the function of recorded sensor value over the time.
We keep track of the median difference over the win-
dow of 5 most recent steps (K = 5).
C = 1/k
S−1
∑
i=S−k
(
Z
es
i+1
bs
i+1
P(t)dt −
Z
es
i
bs
i
P(t)dt) (1)
The trend we define as the true behavior or activ-
ity that is observable. It is important to distinguish
between trend and variance, trend is the true tendency
of the variation, while the variance is deviation of the
data from the trend. To develop our trend for a given
data, we use a multi-pass interpolation with a prede-
fined window to determine the relative average path.
Trend analysis is important because it is an accu-
rate predictor of behavior. Accurate predictions of the
behavior of a patient at any given time is a key com-
ponent in the instability analysis model.
The next step in the data flow model is variance
analysis. After the features are computed for each
step cycle, and the trend function is computed for the
signal in each segment, we compute the variability of
each feature using equation 2, where p
i
is the value
of the features’ variance relative to the trend as de-
scribed in equation 3. γ is the trend function that is
constructed as specified. If a patient is attempting to
increase their speed, but are having difficulty doing
so consistently, they are generally at a higher risk of
falling. This is why the variance analysis is important
for the instability model. In general, stronger variance
in a feature implies a higher instability.
Var
feature
k
=
s
1/n− 1
t+k
∑
i=t
(p
i
− ¯p)
2
(2)
p
i
= s
i
− γ(s
i
) (3)
Once the trends and the variability of each fea-
ture relative to trend is computed, for each feature
the measure for instability can be established for each
segment of input signal based on equation4, where V
T
and V
ST
are the variance of temporal and spatiotem-
poral parameters in the segment. V
T
and V
ST
are com-
puted based on equation 4, where τ
i
is the variance of
temporal feature i and σ
j
is the variance of spatiotem-
poral feature j. α
i
and γ
j
are the coefficients which in-
dicate the importance of a particular feature and they
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