Multitarget Tracking Performance based on the Quality Assessment of Data Association

2016·0.8 MB·

by  Jean Dezert

19th International Conference on Information Fusion
Heidelberg, Germany - July 5-8, 2016
Multitarget Tracking Performance based on the
Quality Assessment of Data Association
Jean Dezert Albena Tchamova Pavlina Konstantinova
The French Aerospace Lab (ONERA) Institute of I&C Tech. European Polytechnical University
BP80100, FR-91123, Palaiseau, France.Bulgarian Acad. of Sci., Sofia, Bulgaria. Pernik, Bulgaria.
E-mail: [email protected] E-mail: [email protected] E-mail: [email protected]
Abstract—The main objective of this paper is to present, to aspect - all of them solve the optimal DA problem and use
apply, and to test the effectiveness of the new method, based on alloptimalobservations-to-trackspairings,selectedinthefirst
belief functions, proposed by Dezert et al. in order to evaluate
best DA solution to update tracks, even if some of them have
the quality of the individual association pairings provided in
poor quality. In consequence the overall tracking performance
the classical optimal data association solution for improving
the performances of multitarget tracking systems in clutter, couldbedegradedsubstantially.Inordertodealwiththiscase
when some of the association decisions given in the optimal the most recent method to evaluate the Quality Assessment
assignment solution are unreliable and doubtful and lead to of Data Association (QADA) encountered in multiple target
potentially critical mistake. This evaluation is based on a Monte
tracking applications in a mono-criterion context is proposed
Carlo simulation for particular difficult maneuvering and non-
by Dezert and Benameur [10]. It is extended in [11] for
maneuvering MTT problems in clutter. A comparison with the
results obtained on the base of Kinematic only Data Association the multi-criteria context. This novel method assumes the
and Generalized Data Association is made. reward matrix is known, regardless of the manner in which
Keywords: Data association, Belief Functions, PCR6 fusion it is obtained by the user. It is based on BF for achieving
rule, multitarget tracking. the quality of pairings (interpreted as a confidence score)
belonging to the optimal data assignment solution based on
I. INTRODUCTION its consistency (stability) with respect to all the second best
Dataassociation(DA)isafundamentalandcentralproblem solutions, provided by a chosen algorithm.
in up-to-date multitarget tracking (MTT) systems ( [1] and This paper is an extension of our preliminary study on the
[2]).Itentailsselectingthemosttrustableassociationsbetween effect of applying QADA method in MTT presented in [17].
uncertainsensor’smeasurementsandexistingtargetsatagiven The main purpose of our paper is to assess the efficiency of
time. In the presence of dense MTT environment, with false QADA method in a critical, conflicting MTT situation. The
alarms and sensors detection probability less than unity, the evaluationisbasedonaMonteCarlosimulationforparticular
problem of DA becomes more complex, because it should difficult maneuvering and non-maneuvering MTT problems
contendwithmanypossibilitiesofpairings,someofwhichare in clutter. The QADA based MTT performance is compared
in practice very doubtful, unreliable, and could lead to critical with the results, obtained for KDA and GDA based MTT,
associationmistakesinoveralltrackingprocess.Toavoidsuch concerning the same scenarios. The paper is organised as
cases, sometimes it is better to wait for a new measurements follows. In order to achieve a good readability of the paper,
during the next scan, instead of taking a hard DA decision, we recall in section II the data association problem within
which actually is not always unique. the MTT context, and in a section III the details of the new
Several methods have been devised over the years, in method, proposed by Dezert et al. [10] for quality assessment
order to resolve properly DA problem. They are originating of pairings, chosen in the optimal DA solution. In section IV
from different models. Some rely on the established reward we discuss and propose the way in which Kalman filtering
matrix based on Kinematic only Data Association (KDA) and could be affected in order to reflect the knowledge we have
on a probabilistic framework [3], [4]. Some other studies obtained on the base of QADA method. Two simulation MTT
are based on Belief Functions (BF) ([5]- [9]), motivating scenarios(withnon-maneuveringandmaneuveringtargets)are
the incorporation of the advanced concepts for Generalized presented and the results, obtained on the base of QADA-,
Data Association (GDA) ([6]- [8]), where a particular target’s KDA-, and GDA based MTT are discussed. Conclusions are
attribute is introduced into the association logic in order to made in Section VI.
compensate the complicated cluttered cases, when kinematics
data are insufficient for adequate decision making. Dezert-
II. DATAASSOCIATIONPROBLEMINMTTCONTEXT
Smarandache Theory (DSmT) of plausible and paradoxical
reasoning [8] is used to model and to process the utilized The DA problem consists in finding the global optimal
attribute data. Although interesting and approved, all these assignments of targets Ti,i=1,...,m to some measurements
methods currently developed are limited to the following zj,j = 1,...,n at a given time k by maximizing the overall
978-0-9964527-4-8©2016 ISIF
gain in such a way, that no more than one target is assigned to utilize both, first and second assignment solutions A1 and
to a measurement, and reciprocally. A2. For a self-containing purpose, this section recalls briefly
The m×n reward (gain/painoff) matrix Ω = [ω(i,j)] is the principle of QADA that has been already detailed in [10],
defined by its elements ω(i,j) > 0, representing the gain of [11] with a tracking application in [17].
the association of target Ti with the measurement zj. These The main idea behind it is to compare the values a1(i,j)
valuesareusuallyhomogeneoustothelikelihoodratios.Inour in A1 with the corresponding values a2(i,j) in A2, and to
case ω(i,j) represents the normalized distances between the identify if there is a change of the optimal pairing (i,j). In
measurement Zj and target Ti : d2(i,j)(cid:2)(zj(k)−zˆi(k|k− our MTT context (i,j) means an association between mea-
1))(cid:2)S−1(k)(zj(k) − zˆi(k|k − 1)) ≤ γ computed from the surement zj and target Ti. One establishes a quality indicator
measurementzj(k)anditspredictionzˆi(k|k−1)computedby associated with this pairing, depending on the stability of
the tracker of target i (see [2] for details), and the inverse of the pairing and also, on its relative impact in the global
thecovariancematrixS(k)oftheinnovationcomputedbythe reward. The proposed method works also when the 1st and
tracking filter. In this case the DA problem consists in finding 2nd optimalassignmentsA1 andA2 arenotunique,i.e.,there
the best assignment, minimizing the overall cost. are multiplicities available. The construction of the quality
The optimal DA problem consists in finding the m × n indicator is based on BF theory and Proportional Conflict
binary association matrix A = [a(i,j)] with a(i,j) ∈ {0,1}, RedistributionRuleno.6(PCR6),definedwithinDSmT[8].It
maximizing the global reward R(Ω,A), given by: dependsonthetypeofthepairingmatching,asitisdescribed
(cid:2)m (cid:2)n below:
R(Ω,A)(cid:2) ω(i,j)a(i,j). (1) • Ifa1(i,j)=a2(i,j)=0,onehasafullagreementonthe
i=1j=1 hypothesis ’non-association’ of the given pairing (Ti,zj)
If a(i,j) = 1, it means that one has an association between in A1 and A2. This ’non-association’ has no impact
targetTi andmeasurementzj.Theassociationindicatorvalue on the global reward values R1(Ω,A1) and R2(Ω,A2),
a(i,j)=0 means that they are not associated. therefore it will be useless to utilize it in DA. Hence,
(cid:3)
in this case, the quality indicator will be set to zero,
a(i,j)= 1, if zj is associated to track Ti (2) q(i,j)=0.
0 otherwise • If a1(i,j) = a2(i,j) = 1, one has a full agreement on
The importance of the assignment problem is quite clear the hypothesis ’association’ of the pairing (Ti,zj) in A1
and various successful solutions to its solving already exist. and A2. This ’association’ (Ti,zj) has different impacts
Among the well known are Kuhn-Munkres algorithm (known on the global reward values R1(Ω,A1) and R2(Ω,A2).
as Hungarian) [12], [13], and its extension proposed by In order to estimate the quality of this matching pairing,
Bourgeois and Lassalle in [14] to rectangular matrices. More one establishes two Basic Belief Assignments (BBAs),
sophisticated Murty’s method [15] provides not only the first ms(.),s=1,2, according to both sources of information
best assignment, but also the m-best assignments in order of (1st and 2nd optimal assignments matrices A1 and A2).
increasing cost, as it was shown in the examples in [10], [11]. The frame of discernment consists of a single hypothesis
Thebestoptimalassignmentsolutionisnotnecessarilyunique, X = (Ti,zj) : measurement zj belongs to the track Ti.
aswellasthesecondbestone.UsuallyinMTTalgorithmsthe The ignorance is modelled by the proposition X ∪ X¯,
¯
first best assignment solution is taken as a hard decision for where X is the negation of hypothesis X:
(cid:3)
association. But in some real practical cases of dense multi-
tsaorlgveet, abnedcaculsuettseoremdeeonfvitrhoenmasesnotc,iaDtiAonpsrodbelceimsionissdai(fifi,cju)ltatroe mmss((XX)∪=X¯a)1=(i,1j)−.ωm(is,(jX)/)R1(Ω,A1) (3)
unreliable, so they could lead to potential mistakes.
Applying the conjunctive rule of combination [8] (Vol.
For example, in case of incorrect determination of the
1), one gets:
incomingmeasurementsfortwotracksinsuchaway,thatthey
⎧
are too close, the solution of the assignment problem, that is ⎪⎨m12(X)=m1(X)m2(X)+m1(X)m2(X ∪X¯)
tibhseeimmcpooorreesscoibafluetthitoeousGbenloosbutaftlfiocNrieeenlaytrleyosntexNaplelliigcthihteb.oIpnuarisrui(nGcghNsaNcoc)anasfiper,pmritoedawciihlnl, ⎪⎩m12(X∪X¯+)=m1m(X1(X∪X∪¯)X¯m)2m(X2()X ∪X¯)
(4)
the first best solution, no matter than only some of them are
The pignistic transformation [16] is applied in order
trustable enough. Utilizing the already obtained and available
to obtain pignistic probabilities, built on the base of
m-bestassignmentssolutions,Dezertetal.[10],[11]provided
combined belief assignments, such as: BetP(X) =
an appealing method for taking into account this knowledge. m12(X)+ 12.m12(X∪X¯) and BetP(X¯)= 12.m12(X∪
III. QUALITYASSESSMENTOFPAIRINGSINDA X¯). Then one chooses the quality indicator, associated
In order to establish the quality of particular associations, with the pairing (i,j), as q(i,j)=BetP(X).
associated with the optimal assignment matrix A1, and sat- • If a1(i,j) = 1 and a2(i,j) = 0, then a conflict is
isfying the condition a1(i,j) = 1, QADA method proposes encountered on the association (Ti,zj) in A1 and A2.
Thenonecouldfindtheassociation(Ti,zj2)inA2,where The difference z˜(k+1)(cid:2)z(k+1)−Hxˆ(k+1|k), called a
j2 istheindex,suchthata2(i,j2)=1.Inordertodefine measurement innovation (or residual), reflects the discrepancy
thequalityofsuchconflictingassociation,oneestablishes between the predicted measurement zˆ(k + 1|k) =H(k +
two BBAs, ms(.),s = 1,2 according to both sources 1)xˆ(k+1|k) and the true one z(k+1), where H(k+1) is
of information (A1 and A2). The frame of discernment the so-called observation matrix. If z˜(k+1) is equal to zero,
consists of two propositions: Θ = {X = (Ti,zj),Y = it means, that both, the true measurement and predicted one
(Ti,zj2)}, and the BBAs are defined by [10]. are in full agreement, which is the perfect case. The matrix
(cid:3) W(k+1) is the filter’s gain matrix obtained by minimizing
m1(X)=a1(i,j)· R1ω((Ωi,,jA)1) (5) the a posteriori estimate error covariance. It is given by
m1(X ∪Y)=1−m1(X) the following formulae, where R is the measurement error
(cid:3) covariance, and P(k+1|k) is the predicted covariance matrix
m2(Y)=a2(i,j2)· Rω2((Ωi,,jA2)2) (6) of the state estimate error:
m2(X ∪Y)=1−m2(Y)
W(k+1)=P(k+1|k)HT(k+1)S−1(k+1) (9)
Applying PCR6 fusion rule [8] (Vol. 3), one gets:
⎧ =P(k+1|k)HT(k+1)
⎪⎨m(X)=m1(X).m2(X∪Y)+m1(X)· mm11((XX))+mm22((YY)) ·[H(k+1)P(k+1|k)HT(k+1)+R]−1 (10)
⎪⎩m(Y)=m1(X ∪Y).m2(Y)+m2(Y)· mm11((XX))+mm22((YY))
m(X ∪Y)=m1(X∪Y)m2(X ∪Y) From Eqs. (8) and (10) one could conclude, that the value
(7) ofmeasurementerrorcovarianceRinfluencesthegain’svalue
Applying again the pignistic transformation, one gets W(k+1),andrespectivelythestateestimateinthewaybelow:
BetP(X) = m(X) + 1.m(X ∪ Y) and BetP(Y) =
2
m(Y) + 1.m(X ∪ Y). Hence, the quality indica- • If the measurement error covariance R → 0, the true
2
tors here are chosen as: q(i,j) = BetP(X) and measurement z(k+1) is trusted more, and in the same
q(i,j2) =BetP (Y). T(cid:8)he ab(cid:8)solute quality factor be- time predicted measurement Hxˆ(k+1|k) is trusted less.
comes: Qabs(A,A2)= mi=1 nj=1.a(i,j).q(i,j). • IfthemeasurementerrorcovarianceRincreases,thetrue
Once obtained, this quality matrix Q = [q(i,j)], i = measurementz(k+1)istrustedless,andinthesametime
1,...,m; j = 1,...,n, where the elements q(i,j) ∈ predicted measurement Hxˆ(k+1|k) is trusted more.
[0,1] define the quality of particular associations, chosen
Let’s now recall again what kind of information one obtains,
in the optimal assignment matrix A1. It will be utilized having in hand the quality matrix, derived by QADA method
inthenextstepoftheclassicalMTTalgorithm-Kalman [10]. It gives us a knowledge about the confidence q(i,j) in
filtering (KF). all pairings (Ti,zj),i = 1,..,m;j = 1,..,n, chosen in the
firstbestassignmentsolution.Thesmallerquality(confidence)
IV. KALMANFILTERINGINFLUENCEDBY QADAMETHOD
of hypothesis “zj belongstoTi” means, that the particular
The classical target tracking algorithm was run, consisting measurementerrorcovarianceRwasincreasedandoneshould
of two basic steps: (i) data association to associate the proper not trust fully in the actual (true) measurement z(k+1).
measurements (distance, angle) with correct targets and (ii)
Having this conclusion in mind, in this work we propose,
track filtering to update the targets state vectors, once the
such a behaviour of the measurement error covariance to be
optimal assignment is found. In our simulation the Global modelled by R = R , for every pairing, chosen in the
Nearest Neighbour (GNN) [1] approach is applied in order q(Ti,zj)
first best assignment and on the base of corresponding quality
to make a decision for data associations. GNN approach is
value obtained. Then, Kalman filter gain decreases, and as a
a DA method that provides an assignment matrix for quality result, the true measurement zj(k+1) is trusted less in the
assessment of data association. updated state estimate xˆ(k+1|k+1).
TheConvertedMeasurementKalmanFilter(CMKF)isused
The MTT algorithm tested in this paper is based on the
for track filtering. We will not recall it in details, which can
classical one (using Kalman Filters based on kinematics mea-
be found in many standard textbooks ( [1], [2]), but will
surements)becauseweareonlyconcernedwithimpactQADA
make an impact on the manner, in which the obtained quality
on the performances of such type of tracking filters for now.
assessment of pairings in the optimal assignment solution
Our aim is not to compare this QADA-MTT to other more
influences the target’s state updating.
sophisticate MTT algorithms1, but we believe that QADA
In order to derive KF equations, the goal is to find an
equationcomputinganaposterioristateestimatexˆ(k+1|k+1) approach could also be useful for improving performances of
more sophisticate MTT algorithms as well. This is left for
at time (k+1) as a linear combination of an a priori estimate
xˆ(k + 1|k), and a weighted difference between the true future research works.
measurement z(k+1) and a measurement prediction:
1Infact,wewilljustcompareQADA-MTTtoKDA-MTTandGDA-MTT
xˆ(k+1|k+1)=xˆ(k+1|k)+W(k+1)z˜(k+1) (8) basedonCMKFinSectionV.
V. SIMULATIONSCENARIOSANDRESULTS 1x 104 Noised Scenario
Two simulation MTT scenarios - non-maneuvering and 0.8
maneuvering are presented and the results, obtained on the 0.6 1 C
0.4
base of QADA-, KDA-, and GDA based MTT are discussed. 2 F
0.2
A. Maneuvering targets simulation scenario Y[m] 0 3 C
−0.2
Thesimulationscenario(Fig.1)consistsofthreeairtargets −0.4
withtwoclasses.Thestationarysensorislocatedattheorigin. −0.6
The sampling period is Tscan = 5sec and the measurement −0−.18
standard deviations are 0.4 deg and 25m for azimuth and −1 −0.8 −0.6 −0.4 −0.2 X[0m] 0.2 0.4 0.6 0.8 x 1041
range respectively. The targets go from West to East with the
Figure2. NoisedmaneuveringMTTScenario.
followingtypeorderCFC(C=Cargo,F=Fighter)withconstant
velocity 100m/sec. At the beginning the targets move from
different directions. The first target moves from North-West Monte Carlo (MC) simulations for the considered MTT
with heading 120 degrees from North. At scanno. = 8 scenario are made for 200 MC runs, applying KDA, QADA,
the target performs a maneuver until scanno. = 15 with and GDA. Our goal is to evaluate, show, and to discuss
transversalacceleration+1.495m/s2 andsettlestowardsEast, the effect of Quality Assessment of Optimal Assignment for
moving in parallel according to X axis. The second target Data Association on the overall target tracking performance
moves during the whole scenario in parallel according to in comparison to results, obtained for the same scenario,
X from West to East without maneuvering. The third target by Kinematic only Data Association, and Generalized Data
at the beginning moves from South-West with heading 60 Association based MTT. We use an idealized track initiation
degrees from North. At scanno. = 8 the target performs a in order to prevent uncontrolled impact of this stage on the
maneuver until scanno. = 15 with transversal acceleration statistical parameters of the tracking process during Monte
−1.495m/s2 and settles towards East, moving in parallel Carlo tests of the new developed algorithm. The true targets
according to X axis. The inter-distance between the targets positions (known in our simulations) for the first two scans
during scans 15th - 18th (the parallel segment) is approxi- are used for tracks initiation.
mately 150m. At scanno. = 18 to scanno. = 25 the first TheevaluationofMTTperformanceisbasedonthecriteria
and the third targets make new maneuvers. The first one is oftracks’purity,tracks’life,andpercentageofmiscorrelation.
directed to North-East and the second - to South-East. The Track’s purity criteria examines the ratio between the number
process noise standard deviations for the two nested models of particular performed (jth observation - ith track) associ-
forconstantvelocityIMM(InteractingMultipleModels)filter ations (in case of detected target) over the total number of
[1], [3] are 0.1m/s2 and 7m/s2 respectively. The number of all possible associations during the tracking scenario. Track’s
false alarms (FA) follows a Poisson distribution and FA are life is evaluated as an average number of scans before track’s
uniformly distributed in the surveillance region. deletion. In our simulations, a track is cancelled and deleted
from the list of tracked tracks, when during 3 consecutive
x 104 Noise−free Scenario scans it cannot be updated with some measurement because
1
there is no validated measurement in the validation gate. We
C call this, the “cancelling/deletion condition”. The status of the
0.5
F tracked tracks is denoted “alive”.
Y[m]0 C nuTmhbeerpoefrcinecnotarrgeecto(fobmseirsvcaotriroenl-attoio-tnracekx)amasisnoecsiattihoensredluartiinvge
−0.5 the scans.
The results for less noised case (with 0.2 FA in average in
−1 the filter validation gate) are given in Table 1.
−1 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1
X[m] x 104
TableI
Figure1. Noise-freemaneuveringMTTScenario.
MANEUVERINGSCENARIO:COMPARISONBETWEENKDA,QADA,GDA
Fig. 2 shows the respective noised scenario. BASEDMTTPERFORMANCESFORFA=0.2.
GDA-MTT [6], [7] improves DA process by utilizing KDA-MTT QADA-MTT GDA-MTT
target’stypedecisionbasedontheconfusionmatrixC=[Cij] AverageTrackLife[%] 86.65 92.82 91.06
coupled with the classical kinematic measurements, where AverageMiscorrelation[%] 7.27 3.69 3.06
Cij = P(Td = Tj/TrueTargetType = Ti) represents the TrackPurity[%] 77.44 88.20 85.74
probability of decisions Td = (T1 (cid:2) Fighter,T2 (cid:2) Cargo), QADA-MTTexceedsKDA-MTTaccordingtoaveragetrack
that the target t(cid:9)ype is j w(cid:10)hen its real type is i. In our
lifeandtrackpurity,andshowsbetterperformanceconcerning
0.95 0.05
simulation C= . the encountered average track life in comparison to GDA-
0.05 0.95
MTT. Figure 3 shows the most informative knowledge - a
percentage of miscorrelations, encountered during the consec- The figures 5 and 6 show typical performances of QADA-
utive scans. One could see, that QADA-MTT shows almost MTT and KDA-MTT systems.
two times better performance in comparison to KDA-MTT,
and is close to GDA-MTT performance.
Average Miscorrelations in KDA−MTT, QADA−MTT, GDA−MTT
30
KDA
QADA
25 GDA
FA=0.2
20
%
15
10
5
Figure5. Maneuveringscenario:TypicalperformanceofQADAbasedMTT.
0
0 5 10 15 20 25 30
scans
Figure 3. Maneuvering scenario: Average miscorrelations in KDA-MTT,
QADA-MTT,GDA-MTTfornoisedcaseFA=0.2
The respective results for the most noised case (with 0.4
FA in average in the filter validation gate) are given in Table
2 below.
TableII
MANEUVERINGSCENARIO:COMPARISONBETWEENKDA,QADA,GDA
BASEDMTTPERFORMANCESFORFA=0.4
KDA-MTT QADA-MTT GDA-MTT
AverageTrackLife[%] 74.27 86.61 86.52 Figure6. Maneuveringscenario:TypicalperformanceofKDAbasedMTT.
AverageMiscorrelation[%] 10.58 7.05 4.68
TrackPurity[%] 60.42 77.96 79.35 The figures 7 and 8 show the averaged filtered errors along
X (designated by asterisk) and Y (designated by circles) axes,
As a whole, the results for FA = 0.4 are deteriorated and the distance error associated with the maneuvering track
in comparison to the less noised case, but still QADA-MTT 1 in the considered scenario.
shows stably better performance with respect to KDA-MTT
performance. The average track life keeps a little bit higher Maneuvering Scenario:Filtered Errors along X,Y−track 1: KDA−MTT, QADA−MTT, GDA−MTT
160
than in GDA-MTT case. 140 XX−−eerrrroorr QKADDA−AM−MTTTT
The Fig.4, showing the percentage of miscorrelations in X−error GDA−MTT
120 Y−error KDA−MTT
more difficult noised case, confirms that QADA-MTT over- 100 YY−−eerrrroorr QGADDAA−M−MTTTT
comes KDA-MTT performance. m]80 FA=0.2
[
60
Average Miscorrelations in KDA−MTT, QADA−MTT, GDA−MTT 40
40 KDA 20
QADA
35 GDA 00 5 10 15 20 25 30
FA=0.4 scans
30
Figure 7. Filtered errors along X,Y for maneuvering track 1 - KDA-MTT,
25
QADA-MTT,GDA-MTT.
%20
15 For the maneuvering target 1, the errors, along X axis,
obtained by using QADA-MTT, are definitely smaller than
10
those, encountered with KDA-MTT. The errors along Y are
5
a little bit bigger than respective errors along X, but as a
00 5 10 15 20 25 30 whole the distance error, encountered by using QADA-MTT
scans
aresmallerthaninKDA-MTT.MCerrorsareevaluatedonthe
base of the averaged errors associated with all “alive” tracks.
Figure 4. Maneuvering scenario: Average miscorrelations in KDA-MTT,
QADA-MTT,GDA-MTTfornoisedcaseFA=0.4 Some of the errors occurred (for example in Fig.7 and Fig.8)
Distance Errors − maneuvering track 1 for KDA−MTT, QADA−MTT, GDA−MTT B. Non-maneuvering targets simulation scenario
180
KDA−MTT
160 QADA−MTT Thenoise-freenon-maneuveringtargetssimulationscenario
GDA−MTT
140 FA=0.2 (see Fig.11) consists of three air targets moving in parallel
120
from West to East with the type order CFC (C=Cargo,
m]100 F=Fighter) with constant velocity of 100m/sec and a
[ 80
60 distancebetweenthem150m.Thestationarysensorislocated
40 at the origin. The sampling period is Tscan = 5sec, and the
20 measurement standard deviations are 0.5 deg and 65m for
00 5 10 15 20 25 30 azimuth and range respectively. The surveillance of moving
scans
targets is performed during(cid:9)15 scans. T(cid:10)he confusion matrix,
Figure 8. Maneuvering scenario: Distance errors for maneuvering track 1 - utilized by GDA is C = 0.95 0.05 . Fig. 12 shows the
KDA-MTT,QADA-MTT,GDA-MTT. 0.05 0.95
respective noised scenario.
couldbeexplainedbytheunrealizedcancelingoftracksatthe
endofthescenario,whensometracksgotowardcanceling,but
Noise−free nonmaneuvering scenario
cannotsatisfythecancelingconditionbecauseoflackoftime.
4000
As a result they are not cancelled (and not deleted) leading
that way to the increasing error.
2000
Figures 9 and 10 show the behaviour of the same errors, C
but now associated with the near-by non-maneuvering target m] F
0
2. Y[ C
−2000
Maneuvering Scenario:Filtered Errors along X,Y−track 1: KDA−MTT, QADA−MTT, GDA−MTT
70
X−error KDA−MTT
60 X−error QADA−MTT −4000
X−error GDA−MTT −5000 −4000 −3000 −2000 −1000 0 1000 2000 3000 4000
50 YY−−eerrrroorr QKADDA−AM−MTTTT X[m]
Y−error GDA−MTT
m]40 FA=0.2 Figure11. Noise-freenon-maneuveringMTTScenario.
[30
20
10
Noised nonmaneuvering targets scenario
0 4000
0 5 10 15 20 25 30
scans
3000
Figure 9. Maneuvering scenario: Filtered errors along X,Y for non- 2000
maneuveringtrack2-KDA-MTT,QADA-MTT,GDA-MTT. 1000 C
m] F
Y[ 0 C
−1000
Distance Errors − non−maneuvering track 2 for KDA−MTT, QADA−MTT, GDA−MTT
50 KDA−MTT −2000
45 QADA−MTT
GDA−MTT −3000
40
FA=0.2
35 −4000
−4000 −3000 −2000 −1000 0 1000 2000 3000 4000
30 X[m]
m]
[25
20 Figure12. Noisednon-maneuveringMTTScenario.
15
10
As reported in Table 3, QADA-MTT shows again almost
5
0 2 times better performance, in comparison to KDA-MTT,
0 5 10 15 20 25 30
scans
according to the average miscorrelations, and also better
Figure10. Maneuveringscenario:Distanceerrorsfornon-maneuveringtrack performance regarding the average track life and track purity.
2-KDA-MTT,QADA-MTT,GDA-MTT.
For the non maneuvering target 2, the filtered errors
TableIII
along X and Y axes, obtained by using QADA-MTT, are NON-MANEUVERINGSCENARIO:COMPARISONBETWEENKDA,QADA,
smooth and definitely smaller then those, encountered with GDABASEDMTTPERFORMANCESFORFA=0.2.
KDA-MTT. As a consequence, the associated with QADA-
KDA-MTT QADA-MTT GDA-MTT
MTT distance error is smaller than in KDA- and GDA-MTT. AverageTrackLife[%] 89.79 94.21 97.59
Theerrorsarecalculatedonthebaseonlyofthe“alive”tracks. AverageMiscorrelation[%] 21.36 10.77 5.82
TrackPurity[%] 64.46 81.72 90.15
Fig.13 shows the percentage of miscorrelations in less
noised case (with 0.2 FA in average per gate).
Average Miscorrelation in KDA−MTT, QADA−MTT, GDA−MTT
35
KDA
30 QADA
GDA
25
FA=02
20
%
15
10
5 Figure15. Non-maneuveringscenario:TypicalperformanceofQADAbased
MTT.
0
0 5 10 15
scans
Figure 13. Non-maneuvering scenario: Average miscorrelations in KDA-
MTT,QADA-MTT,GDA-MTT.
ThesameQADA-MTTbehaviourisvalidinthemoredense
cluttered environment with 0.4 FA in average per gate (see
table 4 and fig. 14).
TableIV
NON-MANEUVERINGSCENARIO:COMPARISONBETWEENKDA,QADA,
GDABASEDMTTPERFORMANCESFORFA=0.4.
KDA-MTT QADA-MTT GDA-MTT
Figure 16. Non-maneuvering scenario: Typical performance of KDA based
AverageTrackLife[%] 90.72 92.18 96.77
AverageMiscorrelation[%] 20.69 12.15 6.26 MTT.
TrackPurity[%] 65.46 77.38 88.82
Nonmaneuvering scenario: Filtered Errors along X,Y−track 2: KDA−MTT, QADA−MTT, GDA−MTT
140
X−error KDA−MTT
120 X−error QADA−MTT
Average Miscorrelation in KDA−MTT, QADA−MTT, GDA−MTT X−error GDA−MTT
35 KDA 100 YY−−eerrrroorr QKADDA−AM−MTTTT
QADA Y−error GDA−MTT
2350 FA=0G.D4A [m]6800 FA=0.2
20 40
%
15 20
10 00 5 scans 10 15
5
Figure17. Non-maneuveringscenario:FilterederrorsalongX,Yfortrack2
0
0 5 scans 10 15 -KDA-MTT,QADA-MTT,GDA-MTT.
Figure 14. Non-maneuvering scenario: Average miscorrelations in KDA- Nonmaneuvering scenario: Filtered Errors along X, Y − track 2: KDA−MTT, QADA−MTT, GDA−MTT
90
MTT,QADA-MTT,GDA-MTT. X−error KDA−MTT
80 X−error QADA−MTT
X−error GDA−MTT
Thefigures15and16showtypicalperformancesofQADA- 70 Y−error KDA−MTT
Y−error QADA−MTT
MTT and KDA-MTT systems. 60 Y−error GDA−MTT
Thefigures17–20showtheencounteredfilterederrorsalong m]50 FA=0.4
[40
X and Y axes and the distance errors, associated with the
30
intermediate track 2 for both noised cases (when the number 20
of FA per gate is 0.2 and 0.4). 10
0
0 5 10 15
scans
One observes (for example in Fig.9 and Fig.17) that er-
rors associated with this simpler (non-maneuvering) scenario Figure18. Non-maneuveringscenario:FilterederrorsalongX,Yfortrack2
-KDA-MTT,QADA-MTT,GDA-MTT.
sometimes appear to be greater than in the previous more
complicated (maneuvering) one. It is because the sensor’s
errors are defined deliberately greater in the non-maneuvering VI. CONCLUSIONS
scenario. It provokes a complex situations, where the impact This work assesses the efficiency of MTT performance in
of QADA method is better demonstrated. cluttered conflicting situations, based on the recent QADA
Nonmaneuvering scenario: Distance Errors − track 2 for KDA−MTT, QADA−MTT, GDA−MTT Hence, it could be applied successfully in all cases when
140
KDA−MTT attribute or/and kinematic data are available.
QADA−MTT
120 GDA−MTT
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only). Therefore, the ability of GDA-MTT to provide better
tracking performances is what we naturally expect. However,
we must emphasize that QADA method could also be used to
improveGDA-MTTaswellinasimilarmannerasithasbeen
usedtoimprovetheperformancesofKDA-MTT.Thispossible
improvementofGDA-MTTwithQADAisunderinvestigation
and will be reported in a forthcoming publication.
Taking in mind, that MTT problems as a general do not
abletoutilizeadditionaltargetattributeinformation,(i.e.when
only kinematic measurements are available), applying QADA
instead of KDA leads to better MTT performance, because
of its ability to estimate the quality of the individual pairings
given in the optimal assignment solution. QADA is totally
independentoftheappliedlogictoobtainthebestDAsolution.