Dezert-Smarandache theory applied to highly conflictual reports for

Transcription

Dezert-Smarandache theory applied
to highly conflictual reports for
i d e n t i f i c a t i o n a n d re c o g n i t i o n
Illustrati ve example of ESM associations in
dense environments
Pascal Djiknavorian
Université Laval
Pierre Valin
DRDC Valcartier
Dominic Grenier
Université Laval
Defence R&D Canada – Valcartier
Technical Report
DRDC Valcartier TR 2008-537
February 2009
Dezert-Smarandache theory applied to
highly conflictual reports for identification
and recognition
Illustrative example of ESM associations in dense environments
Pascal Djiknavorian
Université Laval
Pierre Valin
DRDC Valcartier
Dominic Grenier
Université Laval
Technical Report
February 2009
Principal Author
Original signed by Pierre Valin
Pierre Valin
FC2CS Group Leader
Approved by
Original signed by Eloi Bossé
Eloi Bossé
C2DSS Section Head
Approved for release by
Original signed by Christian Carrier
Christian Carrier
Chief Scientist
© Her Majesty the Queen in Right of Canada, as represented by the Minister of National Defence, 2009
© Sa Majesté la Reine (en droit du Canada), telle que représentée par le ministre de la Défense nationale,
2009
Abstract ……..
Electronic Support Measures (ESM) consist of passive receivers which can identify emitters
coming from a small bearing angle, which, in turn, can be related to platforms that belong to 3
classes: either Friend, Neutral, or Hostile. Decision makers prefer results presented in STANAG
1241 allegiance form, which adds 2 new classes: Assumed Friend, and Suspect. DezertSmarandache theory is particularly suited to this problem, since it allows for intersections
between the original 3 classes. In this way, an intersection of Friend and Neutral can lead to an
Assumed Friend, and an intersection of Hostile and Neutral can lead to a Suspect. Results are
presented showing that the theory can be successfully applied to the problem of associating ESM
reports to established tracks, and its results identify when miss-associations have occurred and to
what extent. Results are also compared to Dempster-Shafer theory which can only reason on the
original 3 classes. Thus decision makers are offered STANAG 1241 allegiance results in a timely
manner, with quick allegiance change when appropriate and stability in allegiance declaration
otherwise.
Résumé ….....
L’écoute électronique au moyen des émissions radar (Electronic Support Measures, ou ESM) se
fait avec des récepteurs passifs qui peuvent permettre d’identifier les émetteurs radar provenant
d’un petit angle d’azimut, lequel peut être relié à des plate-formes émettrices de trois classes :
Ami, Neutre, ou Ennemi. Par contre, les décideurs préfèrent recevoir les résultats sous la forme
prescrite par le STANAG 1241 qui ajoute deux nouvelles classes : Présumé Ami et Suspect. La
théorie de Dezert-Smarandache est particulièrement appropriée pour ce problème, parce qu’elle
permet une intersection non nulle entre les trois classes originelles. Ainsi, une intersection d’Ami
avec Neutre peut donner Présumé Ami, et une intersection d’Ennemi avec Neutre peut donner
Suspect. On présente des résultats démontrant que la théorie s’applique bien à l’association de
contacts ESM avec des pistes déjà établies, et que ses résultats indiquent quand les mauvaises
associations ont été faites et dans quelle mesure. Les résultats sont aussi comparés à la théorie de
Dempster-Shafer, laquelle ne peut raisonner que sur les trois classes originelles. Les décideurs ont
donc accès aux résultats sous la forme requise par le STANAG 1241, pour une prise de décision
rapide, qui permet des changements rapides d’allégeance le cas échéant, mais qui demeure stable
autrement.
i
This page intentionally left blank.
ii
Executive summary
Dezert-Smarandache theory applied to highly conflictual reports
for identification and recognition: Illustrative example of ESM
associations in dense environments
Pascal Djiknavorian; Pierre Valin; Dominic Grenier; DRDC Valcartier TR 2008537; Defence R&D Canada – Valcartier; February 2009.
Introduction or background: Electronic Support Measures (ESM) consist of passive receivers
which can identify emitters coming from a small bearing angle, which, in turn, can be related to
platforms that belong to 3 classes: either Friend, Neutral, or Hostile. Decision makers prefer
results presented in STANAG 1241 allegiance form, which adds 2 new classes: Assumed Friend,
and Suspect. Dezert-Smarandache theory is particularly suited to this problem, since it allows for
intersections between the original 3 classes. In this way, an intersection of Friend and Neutral can
lead to an Assumed Friend, and an intersection of Hostile and Neutral can lead to a Suspect.
Results: Dezert-Smarandache theory is successfully applied to the problem of associating ESM
reports to established tracks, and its results identify when miss-associations have occurred and to
what extent. Results are also compared to Dempster-Shafer theory which can only reason on the
original 3 classes.
Significance: Decision makers are offered STANAG 1241 allegiance results in a timely manner,
with quick allegiance change when appropriate and stability in allegiance declaration otherwise.
Future plans: Other means of achieving STANAG 1241 allegiance results can be explored, such
as in missions of war. The results presented in this report correspond to surveillance missions,
when war is not foreseen.
iii
Sommaire .....
Dezert-Smarandache theory applied to highly conflictual reports
for identification and recognition: Illustrative example of ESM
associations in dense environments
Pascal Djiknavorian; Pierre Valin; Dominic Grenier; DRDC Valcartier TR 2008537; R & D pour la défense Canada – Valcartier; Février 2009.
Introduction ou contexte: L’écoute électronique au moyen des émissions radar (Electronic
Support Measures, ou ESM) se fait avec des récepteurs passifs qui peuvent permettre d’identifier
les émetteurs radar provenant d’un petit angle d’azimut, lequel peut être relié à des plate-formes
émettrices de trois classes : Ami, Neutre, ou Ennemi. Par contre, les décideurs préfèrent recevoir
les résultats sous la forme prescrite par le STANAG 1241 qui ajoute deux nouvelles classes :
Présumé Ami et Suspect. La théorie de Dezert-Smarandache est particulièrement appropriée pour
ce problème, parce qu’elle permet une intersection non nulle entre les trois classes originelles.
Ainsi, une intersection d’Ami avec Neutre peut donner Présumé Ami, et une intersection
d’Ennemi avec Neutre peut donner Suspect.
Résultats: On présente des résultats démontrant que la théorie s’applique bien à l’association de
contacts ESM avec des pistes déjà établies, et que ses résultats indiquent quand les mauvaises
associations ont été faites et dans quelle mesure. Les résultats sont aussi comparés à la théorie de
Dempster-Shafer, laquelle ne peut raisonner que sur les trois classes originelles.
Importance: Les décideurs ont donc accès aux résultats sous la forme requise par le STANAG
1241, pour une prise de décision rapide, qui permet des changements rapides d’allégeance le cas
échéant, mais qui demeure stable autrement.
Perspectives: Il y a d’autres manières d’arriver à des résultats dans le langage de STANAG 1241
par exemple dans des situations de guerre. Les résultats présentés dans ce rapport correspondent à
des missions de surveillance lorsque la guerre n’est pas imminente.
iv
Table of contents
Abstract …….. ................................................................................................................................. i
Résumé …..... ................................................................................................................................... i
Executive summary ....................................................................................................................... iii
Sommaire ....................................................................................................................................... iv
Table of contents ............................................................................................................................ v
List of figures ................................................................................................................................ vi
List of tables ................................................................................................................................. vii
1
Background ............................................................................................................................... 1
1.1
Definition of the problem .............................................................................................. 1
1.2
Some solutions .............................................................................................................. 1
An Interpretation of STANAG 1241 ............................................................................. 2
1.3
1.4
Another Interpretation of STANAG 1241 ..................................................................... 3
2
Dezert-Smarandache Theory .................................................................................................... 4
2.1
Formulae for DST and DSmT ....................................................................................... 4
A typical simulation scenario ........................................................................................ 6
2.2
3
Results for the simulated scenario ............................................................................................ 8
3.1
DST results .................................................................................................................... 8
3.2
DSmT results ................................................................................................................. 9
PCR5 results .................................................................................................................. 9
3.3
3.4
Decision-making threshold .......................................................................................... 10
4
Monte-Carlo results ................................................................................................................ 11
DST results .................................................................................................................. 11
4.1
4.2
DSmT results ............................................................................................................... 11
4.3
PCR5 results ................................................................................................................ 12
4.4
Effect of varying the ESM parameters ........................................................................ 13
5
Conclusions............................................................................................................................. 16
References ..... ............................................................................................................................... 17
List of symbols/abbreviations/acronyms/initialisms .................................................................... 19
Distribution list ............................................................................................................................. 21
v
List of figures
Figure 1: Venn diagram for the STANAG allegiances. .................................................................. 2
Figure 2: Another possible Venn diagram for the STANAG allegiances. ...................................... 3
Figure 3: Chosen scenario. .............................................................................................................. 7
Figure 4: DST result for the chosen scenario. ................................................................................. 8
Figure 5: DSmT result for the chosen scenario. .............................................................................. 9
Figure 6: PCR5 result for the chosen scenario. ............................................................................. 10
Figure 7: Decision thresholds. ....................................................................................................... 10
Figure 8: DST result after 100 Monte-Carlo runs. ........................................................................ 11
Figure 9: DSmT result after 100 Monte-Carlo runs. ..................................................................... 12
Figure 10: PCR5 result after 100 Monte-Carlo runs. .................................................................... 13
Figure 11: DST result after 100 Monte-Carlo runs and input filter. .............................................. 14
Figure 12: DSmT result after 100 Monte-Carlo runs and input filter............................................ 14
Figure 13: PCR5 result after 100 Monte-Carlo runs and input filter. ............................................ 15
vi
List of tables
Table 1: Cardinalities for DST vs. DSmT. ...................................................................................... 4
vii
viii
1
1.1
Background
Definition of the problem
coming from a small bearing angle, but cannot determine range (although some are in
development to provide a rough measure of range). The detected emitters can be related to
platforms that belong to 3 classes: either Friend (F=1), Neutral (N=2) or Hostile (H=3), heretofore
called ESM-allegiance, within that bearing angle.
In the case of dense targets, ESM-allegiance can fluctuate wildly due to miss-associations of an
ESM report to established track. Hence, decision makers would like the target platforms to be
identified on a more refined basis, belonging to 5 classes: Hostile (or Foe), Suspect (S), Neutral,
Assumed Friend (AF), and Friend, since they realize that no fusion algorithm can be perfect and
would prefer some stability in an allegiance declaration, rather than oscillations between
extremes. This will heretofore be referred to as NATO Standardization Agreement, a.k.a.
STANAG 1241 allegiance (or STANAG-allegiance for short) [1].
With this more refined STANAG-allegiance, a decision maker would probably take no aggressive
action against either a friend or an assumed fiend (although he would monitor an assumed friend
more closely). Similarly a decision maker would probably take aggressive action against a foe
and send a reconnaissance force (or a warning salvo) towards a suspect. Neutral platforms would
correspond to countries not involved in the current conflict, or to commercial airliners.
All incoming sensor declarations correspond to a frame of discernment of 3 classes, and several
theories exist to treat a series of such declarations to obtain a fused result in the same frame of
discernment, like Bayesian reasoning and Dempster-Shafer (DS) reasoning [2, 3] (often called
evidence theory). However, when the output frame of discernment is larger that the input frame of
discernment, an interpretation has to be made as to what this could mean, or how that could be
generated. This is the subject of the section 1.3.
1.2
Some solutions
It should be noted that Bayes theory is implemented in a very complex form in STANAG 4162
[4], and that DS theory is found on board many platforms, such as the German F124 frigates [5],
the Finnish Fast Attack Craft Squadron 2000 [6], and the Light Airborne Multi-Purpose System
(LAMPS) helicopters of the US Navy [7]. The translation from DS to Bayes can be performed via
the pignistic transformation [8] and the result broadcast via tactical data links.
In all these implementations, the emitter detected is first correlated to a platform, and then to an
allegiance. According to [9], recognition of a platform can range from a very rough scale (e.g.
combatant/merchant) to a very fine one (e.g. name of contact/track), whereas identification refers
to the assignment of one of the 6 standard STANAG 1241 identities (for which we adopt the word
“allegiance” in this report) to a track. The extra identity is “unknown”, which we disregard in this
report, assuming that all detected emitters are identifiable.
1
Therefore, this report investigates an alternative method of achieving STANAG-allegiances,
which does not aim to compete with the above implementations, but rather can be seen as an
expert advisor to the decision maker. Since Dezert-Smarandache theory was only developed
extensively after the publications of the STANAGs, this could not have been foreseen by NATO,
and is thus worthy of experimentation.
1.3
An Interpretation of STANAG 1241
Both Bayes and DS assume that the universe of discourse remains fixed (at 3 singletons
“Hostile”, Neutral”, and “Friend”), and is the same for the input declarations and the fused output
results, after repeated use of their respective combining rules.
However, there exists a new theory called Dezert-Smarandache theory which can coherently, with
well-defined fusion rules, lead to an output amongst 5 classes, even though the input classes
number only 3, because the theory allows for intersections. For example,
• “Suspect” might be the result obtained after fusing “Hostile” with “Neutral” (although other
possibilities also exist), and
• “Assumed Friend” might be the result obtained after fusing “Friend’ with “Neutral”
(although again other possibilities also exist).
This illustrated in the Venn diagram of Figure 1, where Friend (F=1), Neutral (N=2) or Hostile
(H=3).
Figure 1: Venn diagram for the STANAG allegiances.
2
1.4
Another Interpretation of STANAG 1241
The interpretation in the preceding sub-section is a conservative one, namely that there is only
one easy way to become suspect. This could correspond to a decision maker being in a nonthreatening situation due to the choice of mission, e.g. peace-keeping. There could be situations
where there is a need for a more aggressive response. In the case of a combat mission for
example, the appropriate Venn diagram might be the one of Figure 2, where there are many more
ways to become suspect, namely all the intersections bordering Hostile.
Figure 2: Another possible Venn diagram for the STANAG allegiances.
Note that for Figure 1, the intersection of Friend = 1 and Hostile = 3 is empty (i.e. not allowed, or
1^3 = φ, the null set), and this corresponds to an interesting constraint situation in DezertSmarandache theory, as we shall see. It also corresponds to a more likely mission for Canadian
Forces (CF), namely peace-keeping, or general surveillance.
On the other hand, Figure 2 corresponds to a combat situation more appropriate for the USA, or
to the CF as long as they play an active role in the Kandahar region of Afghanistan. For this
reason, and also because all of the features of Dezert-Smarandache theory will be exercised,
without the additional complexity of keeping all the intersections of Figure 2, the situation of
Figure 1 will correspond to the one implemented in this technical report.
3
2
2.1
Dezert-Smarandache Theory
Formulae for DST and DSmT
Since Dempster-Shafer (DS) Theory (DST) has been in use for over 40 years, the reader is
assumed to be familiar with it [2, 3]. Only a brief review will be provided here, in order to stress
the difference between it and Dezert-Smarandache (DSm) Theory (DSmT). DSmT encompasses
DST as a special case, namely when all intersections are null. Both use the language of masses
assigned to each declaration from a sensor (in our case, the ESM sensor). A declaration is a set
made up of singletons of the frame of discernment Θ, and all sets that can be made from them
through unions are allowed (this is referred to as the power set 2Θ). In DSmT, all unions and
intersections are allowed for a declaration, this forming the much larger hyper power set DΘ. For
our special case of cardinality 3, Θ = {θ1, θ2, θ3}, with |Θ| = 3, DΘ is still of manageable size:
For larger cardinalities, the hyper power set makes computations prohibitively expensive (in
calculational time) as the following table summarizes (the cardinal of DΘ follows the Dedekind
sequence, and includes the null set):
Table 1: Cardinalities for DST vs. DSmT.
Cardinal of Θ
2 3
4
5
6
Cardinal of DΘ 5 19 167 7,580 7,828,353
This is one of the reasons why this application is well suited to DSmT, because a low cardinality
of Θ in DST (three) generates a cardinality in DSmT which is computationally feasible
(nineteen).
In DST, a combined “fused” mass is obtained by combining the previous (presumably the results
of previous fusion steps) m1(A) with a new m2(B) to obtain a new fused result as follows:
The renormalization step using the conflict K∩ , corresponding to the sum of all masses for which
the set intersection yields the null set, is a critical feature of DST, and allows for it to be
4
associative, whereas a multitude of alternate ways of redistributing the conflict (proposed by
numerous authors) lose this property. The associativity of DST is key when the time tags of the
sensor reports are unreliable, since associative rules are impervious to a different order of reports
coming in, but all others rules can be extremely sensitive to the order of reports. This is the main
reason we concentrate only on DST vs. DSmT, but another one is the proliferation of alternatives
to DST, which redistribute the conflict in various fashions (for a review, see [10]).
In DSmT, the hybrid rule (called DSmH in [10]) appropriate for constraints such as described
previously (corresponding to Figure 1) turns out to be much more complicated:
The reader is referred to a series of books [10, 11] on DSmT for lengthy descriptions of the
meaning of this formula. A three-step approach is proposed in chapter 5 of [11], which is used in
this technical report. From now on, the term “hybrid” will be dropped for simplicity.
If the incoming sensor reports are in DST-space Friend (F=1), Neutral (N=2) or Hostile (H=3),
then Figure 1 has the interpretation in DSmT fused space (allowing intersections) are:
Friend = {θ 1 – θ1∩θ2}
Hostile = {θ 3 – θ3∩θ2}
Assumed Friend = {θ1∩θ2}
Suspect = {θ2∩θ3}
Neutral = {θ 2 – θ1∩θ2 – θ3∩θ2}
5
As expected, all STANAG-allegiances (masses assigned to the sets mentioned above) sum up to
1. Hence the first line, which is the sum for all 5 classes, yields the second line after using the
DSmT cardinality criterion (with a multiplying factor of -1 for each non-null intersection).
θ 1 – θ1∩θ2 + θ 3 – θ3∩θ2 + θ1∩θ2 + θ2∩θ3 + θ 2 – θ1∩θ2 – θ3∩θ2
= θ 1 + θ 2 + θ 3 – θ1∩θ2 – θ3∩θ2 = 1
(since θ1∩θ3 = 0 by construction of Figure 1).
2.2
A typical simulation scenario
In order to compare DST with DSmT, one must list the pre-requisites that the scenario must
address. It must:
1. be able to adequately represent the known ground truth
2. contain sufficient countermeasures (or miss-associations) to be realistic and to test the
robustness of the theories
3. only provide partial knowledge about the ESM sensor declaration, which therefore contains
uncertainty
4. be able to show stability under countermeasures, yet
5. be able to switch allegiance when the ground truth does so
The following scenario parameters have therefore been chosen accordingly:
1. Ground truth is FRIEND for the first 50 iterations of the scenario and HOSTILE for the last
50.
2. the number of correct associations is 80%, corresponding to countermeasures appearing 20%
of the time, in a randomly selected sequence.
3. the ESM declaration has a mass (confidence value in Bayesian terms) of 0.7, with the rest
(0.3) being assigned to the ignorance (the full set of elements, namely Θ).
Items 4 and 5 of the first list would translate into stability (item 4) for the first 50 iterations and
eventual stability (item 4) for the last 50 iterations after the allegiance switch at iteration 50 (item
5).
This scenario will be the one addressed in the next section, while a Monte-Carlo study is
described in the subsequent section. Each Monte-Carlo run corresponds to a different realization
using the above scenario parameters, but with a different random seed.
The scenario chosen is depicted in Figure 3 below.
6
Figure 3: Chosen scenario.
The vertical axis represents the allegiance Friend, Neutral, or Hostile. Roughly 80% of the time
the ESM declares the correct allegiance according to ground truth, and the remaining 20% is
roughly equally split between the other two allegiances. There is an allegiance switch at the 50th
iteration, and the selected randomly selected seed in the above generated scenario generates a
rather unusual sequence of 4 false Friend declarations starting at iteration 76 (when actually
Hostile is the ground truth), which will be very challenging for the theories.
7
3
Results for the simulated scenario
Before presenting the results for DST, it should be noted that the original form of DST tends to be
overly optimistic. Given enough evidence concerning an allegiance, it will be very hard for it to
change allegiances at iteration 50. This is a well-known problem, and a well-known ad hoc
solution exists [12], and consists in renormalizing after each fusion step by giving a value to the
complete ignorance which can never be below a certain factor (chosen here to be 0.02).
Comparison will be made with DSmT and the Proportional Conflict Redistribution (PCR) #5
(PCR5) preferred by Dezert and Smarandache [11].
3.1
DST results
The result for DST is shown in Figure 4 below with Friend (1), Neutral (2) and Hostile (3).
Figure 4: DST result for the chosen scenario.
DST never becomes confused, reaches the ESM-allegiance quickly and maintains it until iteration
50. It then reacts reasonably rapidly and takes about 6 reports before switching allegiance as it
should. Furthermore after being confused for an iteration around the sequence of 4 Friend reports
starting at iteration 76, it quickly reverts to the correct Hostile status. Note that a decision maker
could look at this curve and see an oscillation pointing to miss-associations without being able to
clearly distinguish between a miss-association with the other two possible allegiances. This fairly
quick reaction is due to the 0.02 assigned to the ignorance, which translates to DST never being
more than 98% sure of an ESM-allegiance, as can be seen by the curve topping out at 0.98. The
Figure 4 shows the mass, which is also the pignistic probability for this case, with the latter being
normally used to make a decision.
8
3.2
DSmT results
For the hybrid DSmT [10], it was suggested to use the Generalized Pignistic Probability in order
to make a decision on a singleton belonging to the input ESM-allegiance. This seems to cause
problems [13]. Since the whole idea behind using DSmT was to present the results to the decision
maker in the STANAG-allegiance format, the result of Figure 5 would be shown to the decision
maker.
Figure 5: DSmT result for the chosen scenario.
The decision maker would clearly be informed that miss-associations have occurred, since
Assumed Friend dominates for the first 50 iterations and Suspect for the latter 50. DSmT is more
susceptible to miss-associations than DST (the dips are more pronounced), but it has the
advantage of giving extra information to the decision maker, namely that the fusion algorithm is
having difficulty with associating ESM reports to established tracks.
Just like DST, the 4 Friend declarations starting at iteration 76 cause confusion, as it should. The
change in allegiance at iteration 50 is detected nearly as fast as DST. What is even more
important is that F and AF are clearly preferred for the first 50 iterations and S and H for the last
50, as they should.
3.3
PCR5 results
PCR5 shows a similar behaviour, but is much less sure of what’s going on (the peaks are not as
pronounced), as seen in Figure 6. Again, F and AF are clearly preferred for the first 50 iterations
and S and H for the last 50, as they should.
9
Figure 6: PCR5 result for the chosen scenario.
3.4
Decision-making threshold
Because of the sometimes oscillatory nature of some combination rules, one has to ask oneself
when to make a decision or recommend one to the commander. This is illustrated in Figure 7 for
DST although the same is applicable for all the others. A threshold at a very secure 90% would
result in a longer time for allegiance change, and result in a longer period of indecision around
iteration 76, compared to one at 70%.
Figure 7: Decision thresholds.
10
4
Monte-Carlo results
Although a special case such as the one described in the previous section offers valuable insight,
one might question if the conclusions from that one scenario pass the test of multiple MonteCarlo scenarios. This question is answered in this section. In order to sample the parameter space
in a different way, the simulations below correspond to 90% correct associations (higher than the
previous 80%), an ESM confidence at 60% (lower than the previous 70%) and an ignorance
threshold at 0.02 as before. The number of Monte-Carlo runs was set to 100.
4.1
DST results
The result for DST is shown in Figure 8. As expected, since DST reasons over the 3 input classes,
Suspect and Assumed Friend are not involved.
Figure 8: DST result after 100 Monte-Carlo runs.
Naturally, since Assumed Friend and Suspect do not exist in DST, these are calculated as zero.
Friend, Neutral, and Hostile have the expected behaviour. One sees the same response times, after
an average over 100 runs, as was seen in the selected scenario of the previous section.
4.2
DSmT results
The similar result for DSmT is shown in Figure 9 below. In this case, AF dominates for the first
50 iteration, on average (over 100 runs) and S for the last 50, confirming that the chosen scenario
was representative of the behaviour of DSmT. The response times are similar on average also.
11
DSmT is slightly less sure (plateau at 70%) than DST (plateau at 80%), but this can be adjusted
by lowering the decision threshold accordingly.
Figure 9: DSmT result after 100 Monte-Carlo runs.
4.3
PCR5 results
Finally, the PCR5 result is shown in Figure 10 below.
In this case also, AF dominates for the first 50 iterations, on average (over 100 runs), and S for
the last 50, confirming that the chosen scenario was representative of the behaviour of PCR5. The
response times are similar on average also. PCR5 is slightly less sure (plateau at 60%) than DST
(plateau at 80%) or DSmT (plateau at 70%).
12
Figure 10: PCR5 result after 100 Monte-Carlo runs.
4.4
Effect of varying the ESM parameters
In order to study the effects of varying the ESM parameters, the simulations below correspond to
an ESM confidence at 80% (higher than the previous 60%) and an ignorance threshold at 0.05
(higher than the 0.02 used previously). The number of Monte-Carlo runs was again set to 100.
A filter was also applied to the input ESM declarations over a window of 4 iterations than assigns
lesser confidence to ESM reports which are not well represented in the window. The results are
shown in Figure 11 for DST, Figure 12 for DSmT and Figure 13 for PCR5. From these figures,
one can see the smoothing effect of the filter, but more importantly the all of the conclusions of
the previous Monte-Carlo runs, as well as the selected scenario of the previous section hold in
their totality.
13
Figure 11: DST result after 100 Monte-Carlo runs and input filter.
Figure 12: DSmT result after 100 Monte-Carlo runs and input filter.
14
Figure 13: PCR5 result after 100 Monte-Carlo runs and input filter.
15
5
Conclusions
Because of the nature of ESM which consists of passive receivers that can identify emitters
coming from a small bearing angle, and which, in turn, can be related to platforms that belong to
3 classes: either Friend, Neutral, or Hostile, and to the fact that decision makers would prefer
results presented in STANAG 1241 allegiance form, which adds 2 new classes: Assumed Friend,
and Suspect, Dezert-Smarandache theory was used instead, but also compared to DempsterShafer theory. In Dezert-Smarandache theory an intersection of Friend and Neutral can lead to an
Assumed Friend, and an intersection of Hostile and Neutral can lead to a Suspect.
Results were presented showing that the theory can be successfully applied to the problem of
associating ESM reports to established tracks, confirming the work published in [14]. Results are
also compared to Dempster-Shafer theory which can only reason on the original 3 classes. Thus
decision makers are offered STANAG 1241 allegiance results in a timely manner, with quick
allegiance change when appropriate and stability in allegiance declaration otherwise.
In more details, results were presented for a typical scenario and for Monte-Carlo runs with the
same conclusions, namely that Dempster-Shafer works well over the original 3 classes, if a
minimum to the ignorance is applied. The same can be said for Dezert-Smarandache theory, and
to a lesser extent for a popular Proportional Conflict Redistribution rule, but with the added
benefit that Dezert-Smarandache theory identifies when miss-associations occur, and to what
extent.
16
References .....
[1] STANAG 1241 (2005). NATO Standard Identity Description Structure for Tactical Use,
North Atlantic Treaty Organization, April 2005.
[2] Dempster, A.P. (1967). Upper and lower probabilities induced by a multivalued mapping,
Ann. Math. Statist. 38 (1967) 325–339.
[3] Shafer G. (1976). A Mathematical Theory of Evidence, Princeton Univ. Press, Princeton, NJ,
1976.
[4] STANAG 4162 (2000). Technical Characteristics of the NATO Identification System (NIS),
March 2000.
[5] Henrich, W., Kausch, T., & Opitz, F. (2003). Data Fusion for the new German F124 Frigate
Concept and Architecture, Proceedings of the 6th International Conference on Information
Fusion, FUSION 2003, Cairns, Queensland, Australia, 8-11 July 2003, CD-ROM ISBN 09721844-3-0, and paper proceedings, pp. 1342-1349, 2003.
[6] Henrich, W., Kausch, T., & Opitz, F. (2004). Data Fusion for the Fast Attack Craft Squadron
2000: Concept and Architecture, Proceedings of the 7th International Conference on
Information Fusion, FUSION 2004, Stockholm, Sweden, 29 June to 1 July 2004, CD-ROM
ISBN 91-7170-000-00, and on the Internet at http://www.fusion2004.foi.se/papers/IF040842.pdf , 2004.
[7] Valin, P. and Boily, D. (2000). Truncated Dempster-Shafer Optimization and Benchmarking,
Sensor Fusion: Architectures, Algorithms, and Applications IV, SPIE Aerosense 2000, Vol.
4051, pp. 237-246, Orlando, April 24-28 2000.
[8] Smets Ph. (2000). Data Fusion in the Transferable Belief Model, Proceedings of the 3rd
International Conference on Information Fusion, Fusion 2000, Paris, July 10-13, 2000, pp
PS21-PS33.
[9] Multinational Maritime Tactical Instructions and Procedures (2000). MTP 1(D), Vol I,
Chapter 6, January 2000.
[10]
Smarandache, F., Dezert, J. editors (2004). Advances and Applications of DSmT for
Information Fusion, vol. 1, American Research Press, 2004.
[11]
Smarandache, F., Dezert, J. editors (2006). Advances and Applications of DSmT for
Information Fusion, vol. 2, American Research Press, 2006.
[12]
Simard M.A., Valin P. and Shahbazian E. (1993). Fusion of ESM, Radar, IFF and other
Attribute Information for Target Identity Estimation and a Potential Application to the
Canadian Patrol Frigate, AGARD 66th Symposium on Challenge of Future EW System
Design, 18-21 October 1993, Ankara (Turkey), AGARD-CP-546, pp. 14.1-14.18.
17
[13]
Djiknavorian, P. (2008). Fusion d’informations dans un cadre de raisonnement de
Dezert-Smarandache appliquée sur des rapports de capteurs ESM sous le STANAG 1241,
Mémoire de maîtrise, Université Laval, 2008.
[14]
Djiknavorian, P., Grenier, D., and Valin, P. (2007). Analysis of information fusion
combining rules under the DSm theory using ESM input, ISIF Fusion 2007 Conference,
Québec, Canada, July 2007.
18
List of symbols/abbreviations/acronyms/initialisms
CF
Canadian Forces
DS
Dempster-Shafer
DSm
Dezert-Smarandache
DSmT
DSm Theory
DST
DS Theory
ESM
Electronic Support Measures
PCR
Proportional Conflict Redistribution
STANAG
NATO Standardization Agreement
19
20
Distribution list
Document No.: DRDC Valcartier TR 2008-537
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2459 Pie-XI Blvd North
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G3J 1X5 Canada
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TITLE (The complete document title as indicated on the title page. Its classification should be indicated by the appropriate abbreviation (S, C or U)
in parentheses after the title.)
Dezert-Smarandache theory applied to highly conflictual reports for identification and recognition:
Illustrative example of ESM associations in dense environments
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Djiknavorian, P.; Valin, P., .; Grenier, D.
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DATE OF PUBLICATION
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February 2009
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13. ABSTRACT (A brief and factual summary of the document. It may also appear elsewhere in the body of the document itself. It is highly desirable
that the abstract of classified documents be unclassified. Each paragraph of the abstract shall begin with an indication of the security classification
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T
coming from a small bearing angle, which, in turn, can be related to platforms that belong to 3
classes: either Friend, Neutral, or Hostile. Decision makers prefer results presented in STANAG
1241 allegiance form, which adds 2 new classes: Assumed Friend, and Suspect. DezertSmarandache theory is particularly suited to this problem, since it allows for intersections
between the original 3 classes. In this way, an intersection of Friend and Neutral can lead to an
Assumed Friend, and an intersection of Hostile and Neutral can lead to a Suspect. Results are
presented showing that the theory can be successfully applied to the problem of associating
ESM reports to established tracks, and its results identify when miss-associations have occurred
and to what extent. Results are also compared to Dempster-Shafer theory which can only
reason on the original 3 classes. Thus decision makers are offered STANAG 1241 allegiance
results in a timely manner, with quick allegiance change when appropriate and stability in
allegiance declaration otherwise.
14. KEYWORDS, DESCRIPTORS or IDENTIFIERS (Technically meaningful terms or short phrases that characterize a document and could be
helpful in cataloguing the document. They should be selected so that no security classification is required. Identifiers, such as equipment model
designation, trade name, military project code name, geographic location may also be included. If possible keywords should be selected from a
published thesaurus, e.g. Thesaurus of Engineering and Scientific Terms (TEST) and that thesaurus identified. If it is not possible to select
indexing terms which are Unclassified, the classification of each should be indicated as with the title.)
Electronic Support Measures, Dezert-Smarandache, Dempster-Shafer; allegiance; fusion;
Defence R&D Canada
R & D pour la défense Canada
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and National Security
Science and Technology
Chef de file au Canada en matière
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Dezert-Smarandache theory applied to highly conflictual reports for

Transcription

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