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Albena Tchamova, Jean Dezert
IICT, Bulgarian Academy of Sciences, ”Acad.G.Bonchev” Str., bl.25A, 1113 Sofia, Bulgaria.
ONERA, The French Aerospace Lab, F-91761Palaiseau, France.
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IEEE INISTA 2013 International Symposium on INnovations in Intelligent SysTems and Applications, Albena, Bulgaria
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Tracking Applications
with fuzzy-based Fusion Rules
Outline
Introduction
Basics of Dezert-Smarandache Theory based Proportional Conflict Redistribution fusion rule no.5 (PCR5)
Basics of TConorm-Norm fusion rule (TCN)
Alarms classification approach
Simulation scenario
TCN rule performance for danger level estimation
Comparison between TCN / PCR5 /Dempster’ rules based results
Target Type Tracking Approach
TTT algorithm
Simulation scenario
Comparison between TCN / PCR5 /Dempster’ rules based results
Conclusions
Introduction
Alarms Classification Approach:
The overflowing amount of alarms could become a serious source of confusion indangerous cases. The critical delay of the proper response could cause significantdamages.
Critical cases arisen : high priority danger - incorrectly interpreted as false alarm, increasing the chance to be ignored
lower danger’s priority - incorrectly interpreted as a high priority, deflecting the attention from the existing real dangerous source
The cause: Multiple suspicious signals generated in the observed area
The uncertainty and conflicts in/between sound signals emited
The effect /Result : Weaken or even mistaken decision about the degree of danger
Assigning a wrong steering direction to the surveillance camera
Target Type Tracking Approach:
Supports the process of targets’ identification and consequently improves the quality of generalized data association
Critical case: complicated situations characterized with closely spaced or/and crossing targets
The effect /Result : weaken or even mistake the surveillance system decision
That is why a strategy for an intelligent, scan by scan, combination/updating of data generated is needed in order to provide the surveillance system with a meaningful output.
Basics of Dezert-Smarandache Theory based PCR5 rule
To combine two distinct and equally-reliable sources of evidences anddefined on one and the same frame PCR no.5 fusion rule is defined
on the power set :
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Conjunctive consensus result
The general principle of DSmT based Proportional Conflict Redistribution (PCR) rules :
to calculate the conjunctive consensus between the sources of evidences;
to calculate the total or partial conflicting masses;
to redistribute the conflicting mass (total or partial) proportionally on non-empty sets
involved in the conflict according to the model of the problem under consideration.
Basics of TCN fusion rule
Under Shafer’s model of the frame, TCN rule for two sources of information is:
Conjunctive consensus:
Normalization:
Advantages : satisfying the impact of Vacuous Belief Assignment; commutative, convergent
to idempotence, reflects majority opinion, adequate data processing in case of partial and
total conflict between the sources; easy to implement.
Drawback: lack of associativity, which is not a main issue in temporal data fusion.
Alarms classification approachThe task: to estimate the proper degree of danger, associated with the a priori defined
dangerous directions, in order to declare direction for steering the video camera.
The frame of expected hypotheses according to the degree of danger :
Shafer’s model holds:
Signals’ frequencies of intermittency are utilized.
Rule base – to map the input sounds’ observations into non-Bayesian bba, considering the degree of danger.
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at the a priori bba (history) set to be a vacuous bba
for each scan, for each source - updating history by the new observation via
TCN(PRC5/DS) fusion rules :
decisions - For each scan, for each source.
Pignistic probabilities, associated with all the considered modes of danger are
estimated:
Flag Emergence is taken having maxBetP(Emergency).
X 2
X YY 2 BetP(Y) m(X)
X
Simulation scenario and results
A set of three sensors located at different distances from the microphone array are installed in an observed area for protection purposes, together with a video camera.
The sensors are assembled with particular alarm devices.
In case of alarm events, the devices emit powerful sound signals with various duration and frequency of intermittence depending on the nature of the event.
Degree of danger associated with the sound sources: Emergency – for Sensor 1, Alarm - for Sensor 2, Warning– for Sensor 3.
The decisions are governed at the video camera level, periodically, depending on time duration needed to analyze correctly and reliably the sequentially gathered information. Decisive scans -10th, 20th, and 30th
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PCR5 rule performance for danger level estimation
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PCR5 rule prevents to produce a mistaken decision, that way prevents to avoid the
most dangerous case without immediate attention.
A similar adequate behavior of performance is established in cases of lower
danger priority.
TCN rule performance for danger level estimation
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TCN rule shows a stable, quite proper and effective behavior, following the performance of PCR5
fusion rule.
Special feature of TCN performance – smoothed estimates and more cautious decisions taken at
the particular decisive scans.
Dempster’s rule performance
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Emergency case - ungrounded decision - DST rule does not respond to the new observations
coming.
Alarm and Warning case – DST rule causes false alarms and can deflect the attention from the
existing real dangerous source by assigning a wrong steering direction to the surveillance
camera.
An emblematic example – detecting the fundamental flaw of DST
The Target Type Tracking Problem
Formulation of the Problem
time index
M possible target types
for example
at each instant a target of true type
(not necessarily the same target) is observed by a sensor
The attribute measurement of the sensor (for example noisy Radar Cross
Section) is then processed through a classifier which provides a decision
on the type of the observed target at each instant
The sensor is in general not totally reliable and is characterized by a
confusion matrix
The Question is:
How to estimate
classifier up to time
from the sequence of declarations done by the unreliable
i.e. how to build an estimator
Principle Algorithm of the Target Type Tracker
Initialization step:
The principle of our estimators is based on the sequential combination of the current
basic belief assignment (drawn from classifier decision, i.e. our measurements) with the
prior bba estimated up to current time from all past classifier declarations by using TCN
(PCR5 /Demspter’s) rules.
Select the target type frame
Set the prior bba as VBA
Generation of the current bba from the current classifier declarationbased on attribute measurement
the unassigned mass is committed to total ignorance
Combination based on TCN, (PCR5/Dempster’s )fusion rules:
Estimation of True Target Type is obtained from by taking the singleton of
i.e. a Target Type, having the maximum of belief (or eventually the maximum
Pignistic Probability)
Set do and go back to step 2
Simulation Scenario
simple scenario for a 2D Target Type frame
Classifier:
Our goal is to investigate the adaptive reactions of two attribute’s estimators, based
on TCN (Dempster’s and PCR5) fusion rules in case when the true Target Type
sequence (Groundtruth ) changes over the time (120 scans)
The simulation consists of 1000 Monte Carlo runs to compute and show in the
sequel the averaged performance of both fusion rules.
At each time step the target type’s decision is randomly generated according
to the corresponding row of the classifier’s confusion matrix.
Estimation of Belief Assignment for Cargo Type
TCN fusion rule shows a stable and adequate behavior, characterized with more smoothed process of re-
estimating the belief masses in comparison to PCR5.
TCN fusion rule with t-conorm=max and t-norm=bounded product reacts and adopts better than TCN
with t-conorm=sum and t-norm=min, followed by TCN with t-conorm=max and t-norm=min.
Estimation of Belief Assignment for Fighter Type
Conclusions:
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Two tracking applications of a particular fuzzy fusion rule, based on fuzzy
T-Conorm/T-Norm operators are presented:
Alarms identification and prioritization in terms of degree of danger relating
to a set of a priori defined, out of the ordinary dangerous directions.
Tracking Object’s Type Changes, supporting the process of identification;
The ability of TCN rule to assure coherent and stable way of identification
and to improve decision-making process in temporal way are
demonstrated.
Different types of t-conorm and t-norms, available in fuzzy set/logic theory
provide us with richness of possible choices to be used applying TCN
fusion rule.
The attractive features of TCN rule is it’s easy implementation and adequate
data processing in case of conflicts between the information granules.
References:
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