The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B5. Beijing 2008 
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In Table 6, |a| xyz , |a| xy , and |a| z are magnitudes of the 
acceleration vector during a single step in 3D, horizontal, and 
down directions, respectively; Var(|a| xy2 ), Var( |a| xy ), and 
Var(|a| z ) are the corresponding variance of the acceleration 
vector; Max(|a|) and Min(|a|) are the maximum and minimum 
values of the acceleration for each pace. 
An alternative implementation of the SL/SD 
calibration/prediction module is based on FL (see, Moafipoor et 
al., 2007a for details of this algorithm). By incorporating Fuzzy 
Logic to our KBS, better process control is facilitated, as this 
approach allows an easy addition of constraints, such as, for 
example hallway layout for indoor navigation, or digital map 
information, which are difficult to handle in “regular” EKF 
environment. Fuzzy Logic can be described simply as 
“computing with words rather than numbers,” and Fuzzy Logic 
control can be described as “control with sentences rather than 
equations” (Sasiadek and Khe, 2001). Rule-based Fuzzy Logic 
provides a formal methodology for linguistic rules resulting 
from reasoning and decision making with uncertain and 
imprecise information. In fuzzy behavior-based navigation the 
problem is decomposed into simpler tasks (independent 
behaviors), and each behavior is composed of a set of Fuzzy 
Logic rule statements aimed at achieving a well defined set of 
objectives; example rules are: 
Rule (/): If is AND is A^ ,...,AND 
x im is A im THEN y is B i (!) 
where i=l,...,n, and n is the number of rules in a given fuzzy 
rule base; j=l,..,m, and m is the number of antecedents; x ;; are 
V 
the input variables, premise variables, which are the sensor data 
of the mobile user; Ay are the input fuzzy sets; and B- is the 
output fuzzy set, and y is the output variable. Having multiple 
behaviors, which are all running concurrently, leads to 
situations where several command outputs may be produced 
simultaneously. Therefore, the main advantage of using Fuzzy 
Logic for navigation is that it allows for the easy combination of 
various behaviors through a command fusion process instead of 
using fixed parameters in the entire process. 
The design of a Fuzzy Logic controller starts with the definition 
of the membership functions for the output variable, here, SL. 
Currently, seven empirically determined membership functions 
are used for SL in our prototype, as shown in Figure 3. The 
fuzzy language for this fuzzy set is divided into a range of 
quantities such as: Zero, Very Short, Short, Normal, Semi-Long, 
Long, and Very Long; vertical axis in Figure 3 indicates the 
degree of membership of SL in the corresponding fuzzy set 
(fist.)- 
Defining the shape, the membership functions, and the bounds 
of these quantities is a design problem, but the attributes of the 
system will not be changed significantly if the membership 
functions are modified slightly. The value of the membership 
function indicates the degree of membership of SL to the fuzzy 
set. If the membership value is 1 for one of the fuzzy sets, the 
SL is perfectly representative of the set, and if it is 0, the 
quantity is not at all a member of the set. Any value between 1 
and 0 indicates a partial membership. A better way to make SL 
a fuzzy set is to allow the membership functions to change 
gradually from one quantity to the next one. Then, the real 
power of the Fuzzy logic comes from the ability to integrate 
these partial membership values in a way that permits a good 
balance between membership functions. 
For reliable SL/SD results, the KBS system must be sufficiently 
trained, meaning that sufficient amount of calibration data must 
be either stored in the memory or provided during the actual 
navigation task, before the GPS signals are blocked. For the 
ANN module training, different terrains slopes/configuration 
and types of surfaces must be included, for a representative 
number of operators, to derive a reliable predictive model; 
obviously, if the system is calibrated under circumstance totally 
different from the actual navigation task, the results will be 
much worse than the examples provided here. Similarly, the FL 
modules requires a large sample of representative data where 
various human dynamics types are included in various 
environmental conditions and terrain configurations, to derive 
the appropriate fuzzy rules for the membership functions that 
will be used to predict the model parameters once GPS signals 
are blocked. The additional benefit of FL is that the actual 
behavior of the mobile operator can be predicted, that is, if the 
person is running, walking, stumbling, climbing, etc., and that 
might be useful information in particular in combat or 
emergency situation, and can be wirelessly transmitted to an 
operational center (not implemented in our prototype). 
An additional use of FL in our implementation is the adaptive 
Extended Kalman Filter where the adaptivity scheme is based 
on Fuzzy Logic rules (see, e.g., Sasiadek et al., 2000; 
Moafipoor, 2008). In this approach, the pseudorange practical 
1 m j 
covariance, C, = — Y. e, e , and the actual covariance 
k mi=1 k k 
— T 
(covariance of innovation) from the EKF, s k = H k P k H^ , 
are compared, and the level of the difference between them is 
tested using fuzzy rules to decide if the measurement covariance 
matrix R k should be modified (adapted to the current state of 
system sensors). H k is the observation design matrix, P^ is the 
predicted covariance, and e k is the innovation vector. The 
system calibration mode with the KBS module is illustrated in 
Figure 4. 
Figure 3. SL membership function.