Inertial Sensors and Their Applications - Signal Processing Systems - page 82

￿ Difference between the maximum and minimum acceleration of a detected

step [ 11 ]

p 5 ( k )= max a n ( t ) − min a n ( t ) , t s ( k ) ≤ t < t e ( k ) (11)

or

p 6 ( k )= max a v ( t ) − min a v ( t ) , t s ( k ) ≤ t < t e ( k ) . (12)

Also the use of combinations of these signal patterns has been proposed [ 11 , 18 ] ,
as well as slightly different patterns from these [ 21 ] . The empirical step length
model often includes at least one empirically determined parameter. In many cases
a non-linear function, such as raising to a power or extraction of root, has to be
applied to the signal pattern. In the following example, the performance of step
length estimation with different functions applied on different signal patterns is
demonstrated with real pedestrian data.

Example: Comparison of Functions Applied on Signal Patterns

To obtain data for comparison, a straight path of a known length s w was walked ten
times in a straight corridor. The data was collected with a 3D-accelerometer that was
attached to the belt of the test walker and placed on the back. As the step length is a
function of the walking speed, the walker tried to adjust the walking speed to normal,
slower than normal, slow, faster than normal, and fast to obtain step samples with
different step lengths. The test path was walked two times with each target speed.
The steps were detected from the acceleration norms and signal patterns p j ,defined
in ( 7 ) -( 12 ) , were computed from the data. From the signal patterns, square root,
cube root, and 4th root were computed for each step. The step length model

q

Δ s k = K j , q p j ( k ) (13)

was fitted to the data by estimating the scaling factor K j , q that relates Δ s k ,the

q ,where q is the exponent that
defines the function to be applied on the signal pattern p j computed for the k th step.
In this example, values 1, 1

distance traveled during the k th step, with p j ( k )

4for q were tested; these correspond to
the raw signal patterns and their square roots, cube roots, and 4th roots.
The scaling factors were estimated by taking the known total length of the
distance walked during all the ten test walks and dividing it by the sum of the
functions of the signal patterns computed for each detected step in all the test walks:

/ 2, 1 / 3, and 1 /

n w s w

n i
∑
k i =

q

K j , q = (14)

n w
∑

p j ( k i )

i = 1 1

where n w is the total number of test walks, n i is the number of steps observed in the
data set from the i th test walk, and p j

q is the function of the signal pattern p j
during the k i th step detected in the i th data set.

( )

k i