Inertial Sensors and Their Applications - Signal Processing Systems - page 86

Tabl e 2 Effect of 1% scale factor error in accelerometer to functions of signal
patterns for step length estimation
Raw

Square root Cube root Fourth root

1 / 2 1 / 3 1 / 4

Function p j ( k ) p j ( k ) p j ( k ) p j ( k )

Step length error (%) 1.00 0.50 0.33 0.25

a b c

Heading error (degrees) y−c oordina te (m)

True
Est

R e lative position error (% of distance traveled)

4

4

30

3

3

20

2

2

10

1

1

0 0 0

0 2 4 6 8 10 0 200 400 600 800 0 2 4 6 8 10

Time (min) x−coordinate (m) Time (min)

Fig. 8 Effect of 25 ◦ / h gyro bias when the pedestrian is walking with constant speed along the
positive x -axis: ( a ) heading error, ( b ) true and estimated coordinates, and ( c ) relative position error

Tabl e 3 Comparison of gyro grade with respect to the effect of uncompensated
bias to the PDR error build-up

Navigation Tactical Consumer

Bias instability ( ◦ / h) 0.0035 1 25

Time to 2% relative position error 27 days 2.3 h 5.5 min

Time to 3% relative position error 41 days 3.4 h 8.3 min

Time to 3 ◦ heading error 35 days 3.0 h 7.2 min

relative to the distance traveled is shown in Fig. 8 . The heading error grows linearly
(Fig. 8 a ), the error in the y -coordinate grows quadraticall y 4 with respect to the x -
coordinate and time (Fig. 8 b ), and the relative position error with respect to the
distance traveled grows almost linearly (Fig. 8 c ). With the best step length models,
the long term average in the relative positioning error is about 2-3%, as can be
seen in Fig. 5 . With the given simulation parameters, the relative positioning error
introduced by the gyro bias is smaller in the beginning, but exceeds 2% in less than
6 min and 3% in less than 9 min.
To compare the gyro grades described in Table 1 , the simulations were also run
with gyro instabilities typical to navigation and tactical grade gyros. The results are
shown in Table 3 .
The effect of the gyro scale factor error is simulated by using a scenario where
the pedestrian first makes a 180 ◦ turn and then walks with a constant step length of
0 . 75 m and a constant frequency of 2 steps/s along the positive x -axis. The gyro scale

4 The growth is almost quadratic with small heading errors; however, with larger heading errors,
the sine and cosine functions in ( 19 ) bound the error growth.