The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008
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State vector components
(number of states)
Initial Covariance Matrix
Components
Stochastic Model, White Noise
Position (3)
100 m
RC, 0
Velocity (3)
1 m/s
RW, 5 pg
Attitude (3)
Pitch, Roll
1°
RW, 0.001 °/Vhr
Heading
2°
Accelerometer Bias (3)
1 mg
RW, 20 pg/ Vhr
Accelerometer Scale Factor (3)
120 ppm
RC, 0
Gyro Bias (3)
l°/hr
RW, 0.125 °/Vhr
Gyro Scale Factor (3)
10 ppm
RC, 0
Barometer Bias (1)
1 m
RW, 0.1 m
Barometer Scale Factor (1)
1
RC, 0
Magnetometer Compass Bias (3)
1°
RW, 1°
Magnetometer Compass Scale Factor (3)
1
RC, 0
Table 3. State vector components and their stochastic characteristics; (RC): Random constant, (RW): Random walk, (mg) stands for
10
-3
8 , (pg) stands for 10 8 , and ^ is the gravity constant (Grejner-Brzezinska et al., 2007b).
ANN input parameters
Without PCA
With PCA
Training
Mean ± Std [cm]
Testing
Mean ± Std [cm]
Training
Mean ± Std [cm]
Testing
Mean ± Std [cm]
SF, |a|, Varflal), Slope
2.3 ±4.9
7.1 ±5.0
0±0.3
1.5 ± 1.7
Table 4. The effect of PCA transformation on SL determination using ANN in training and testing modes; mean and std of the
differences between the reference (known) SL and ANN-predicted SL; no reduction of the parameter space applied.
Solution type
Mean
Std
Max
End
CEP 50%
CEP 95%
[m]
[m]
Difference [m]
Misclosure [m]
[m]
[m]
DR without PCA
1.7
1.4
4.7
2.3
1.3
4.4
DR with PCA
0.33
0.32
1.07
1.16
0.3
1.0
Table 5. Statistical fit to reference trajectory of DR trajectory generated with SL predicted by ANN with and without PCA
transformation (no parameter space reduction); circular trajectory of ~45 m.
The ANN and FL modules designed for handling the human
locomotion model, form a Knowledge-Based System (KBS).
The ANN component consists of a single-layer network with
Radial Basis Function (RBF) and up to six input parameters that
contain the information about the step length (SL), such as step
frequency (SF), peak-to-peak mean acceleration (|a|), peak-to-
peak variation in acceleration (Var|a|), terrain slope, change in
barometric height during a single gait cycle (Ah Baro ), and
operator’s height; currently, a Gaussian function (G) is used as
RBF. Since the input parameters are correlated, Principal
Component Analysis (PCA) is applied to decorrelate the input
parameters and to determine the minimum sufficient set of
parameters that should be used as input to the ANN. The
accuracy of SL prediction based on this module is at the cm-
level (refer to Tables 4 and 5 for examples of the PCA-
transformation impact on LS modeling results; for more details,
see, Grejner-Brzezinska et al., 2006b, c, and 2007b). This
accuracy of SL prediction allows trajectory recovery well within
the 3-5 m CEP if accurate heading is provided (HG1700
heading is sufficient within a few minute GPS gap). The
trajectory can be recovered in 2D, based on the SL only
n n
( Ax — X SLfc sin Azfc and A_y = X SL^ cos Az£ , where
k=1 k=1
Az is the heading provided by either gyro or magnetometer or
both and n is the number of steps along the trajectory); if
calibrated barometer measurements are used, the solution is
provided in 3D.
Table 6 lists all of the measurements delivered by the sensors
used in the current prototype, which can constitute input
parameters to the KBS to parameterize the body locomotion and
SL approximation functions.
Sensor
Sensor Measurements
Accelerometer
- Step events
l^lxyz, l^lxyj l^lz
-Var(|a| xyz ), Var( |a| xy ), Var(|a| z )
- Max(|a|), Min(|a|)
- Tilt (roll and pitch angles at rest)
Gyroscope
- Angular rate
- Roll, pitch, heading
Compass
- Angular rate
- Heading
Barometer
- Var(Ah)
-Z(|Ah|)
- Altitude
Step sensors
- Step events
External data
- Person’s height, age, weight
Table 6. Sensors and body locomotion parameterization
(Moafipoor et al., 2007a).