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).