511
1 INTRODUCTION
The need for an accurate and resilient situational
awareness has been increasingly growing in the
maritimedomainduetoavarietyofreasons:theever
increasing global trade constantly calls for ships
larger in size and numbers, which still need to
navigatetheinternationalwaterwaysandharborsina
secure and efficient manner. In addition, it is a
stringentnecessitytot
rafficmanagementandsecurity
authorities to detect abnormal vessel behavior, to
prevent harm to marine infrastructure, humans and
nature. Apart from that, the trend towards
autonomous navigation is clearly entering the
maritime world calling for advanced solutions as
enabling technologies. From our perspective two
conclusionscanbedrawnfromtheseconsiderat
ions:
firstly,maritimesituationawarenessiscrucialtoallof
these applications and secondly, the described
challenges call for a refined and more reliable
situation picture. The dominating source for traffic
situationassessmentinthemaritimedomainhasbeen
and will be the ma
rine radar, which is still the
primary sensor for collision avoidance. Various
approaches have been published in the literature to
augmentmaritimesurveillanceorcollisionavoidance
systems,mostlybasedonradarfusionwithadditional
sensors such as laser in Perera, Ferrari, Santos,
Hinostroza,and Soares (2015) or mult
iple stationary
radarsystemsforexploitingaspectanglediversityas
inBraca,Vespe,Maresca,andHorstmann(2012).The
matterofAISandradarfusionwasmainlyaddressed
foranomalydetection,e.g.,basedonmultihypothesis
tests in Guerriero, Willett, Coraluppi, and Carthel
(2008) or by exploiting historical traffic route
knowledge for SAR/AIS fusion in Mazzarella and
Vespe(2015).InKazim
ierskiandStateczny(2015)an
overview was given for different AIS/radar fusion
techniques incorporating online covariance
estimation. In Siegert, Banyś, and Heymann (2016)
and Siegert, Banyś, Hoth, and Heymann (2017),
implementations of IMM‐MSPDA and IMM‐JPDA
Validation of Radar Image Tracking Algorithms with
Simulated Data
F.Heymann,J.Hoth,P.Banyś&G.Siegert
GermanAerospaceCenter(DLR),Neustrelitz,Germany
ABSTRACT:Collisionavoidanceisoneofthehigh‐levelsafetyobjectivesandrequiresacompleteandreliable
description of the maritime traffic situation. The radar is specified by the IMO as the primary sensor for
collisionavoidance.Inthispaperwestudytheperformanceofmulti‐ta
rgettrackingbasedonradarimageryto
refinethemaritimetrafficsituationawareness.Inordertoachievethiswesimulatesyntheticradarimagesand
evaluatethetrackingperformanceofdifferentBayesianmulti‐targettrackers(MTTs),suchasparticleandJPDA
filters.Forthesimulatedtracks,thetargetstateestimatesinposition,speedandcourse overgroundwill be
compared to the reference data. The performa
nce of the MTTs will be assessed via the OSPA metric by
comparing the estimated multi‐object state vector to the reference. Thisapproach allows a fair performance
analysisofdifferenttrackingalgorithmsbasedonradarimagesforasimulatedma
ritimescenario.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 11
Number 3
September 2017
DOI:10.12716/1001.11.03.18
512
filters were applied to on‐board maritime traffic
situationassessmentconsideringsingle andmultiple
targets in a clutter environment, respectively. These
approaches all follow the basic assumptions of
classical Kalman filtering concerning Gaussian
processandmeasurementnoiseandthattheproblem
formulation is only mildly nonlinear. In cases, in
which
these assumptions do not hold, particle
filteringhasbecomeapopularalternative.Introduced
by different authors, such as Gordon,Salmond, and
Smith (1993), Kitagawa (1996) and Isard and Blake
(1998), a particle filter implements the formal
recursiveBayesianfilterusingsequentialMonteCarlo
methods. The sought for posterior probability
distribution
function (pdf) of the state vector is not
described in a functional form, but is instead
approximated by a set of random samples. The
applicationof particlefiltersto marine radar images
for fusing radar data with AIS was introduced in
Heymann, Banyś, and Saez (2015) arguing that the
Gaussian
noise assumption might be violated when
using radar images as measurement input. In this
study,we wantto comparethe performance ofboth
classes of recursive Bayesian filters in a maritime
multi‐target scenario. For this reason, an Interacting
Multiple Model (IMM)‐Joint Probabilistic Data
Association (JPDA) filter was designed
based on
UnscentedKalmanfiltering(UKF)thatisconditioned
on measurement data from radar images. In fact a
blob detector is applied to extract target candidates
from one radar image. This filter will be compared
against a newly proposed Repulsive Multi Particle
Filter (RMPF) that is conditioned directly on the
current
radarimage.
The remainder of this document is organized as
follows. The simulated reference scenario will be
described in Section 2. This is followed by the
proposal of two methods for multi‐target tracking
based on radar image processing in Section 3. Both
frameworkswillbeevaluatedandcomparedin
their
performanceinSection4.Aconclusionandoutlookis
giveninSection5.
2 SIMULATIONOFMARITIMESCENARIO
For evaluation of both multi‐target trackers a
maritime scenario was simulated with a commercial
ship navigation simulator (ANS6000 by Rheinmetall
AG). Two tugs were set up to maneuver in the
vicinity
of a third ship, which was anchored. The
simulated radar response of this quasistatic vessel
was used as input to both multi‐target trackers.
Figure1showstheconfiguredtracks,whileFigure2
depicts one radar scan during the simulation time.
The multi‐target reference data was obtained from
interfacing
totheNMEAoutputontheserialportof
the simulator, which contained the encoded AIS
messages.
3 MULTI‐TARGETTRACKERS
Ingeneral,thefieldofmulti‐targettracking(MTT)in
presenceofmultipleandingeneralimperfectsensors
has been widely explored, ranging from classical
enumerative to non‐enumerative schemes.
Algorithmsrepresentingtheformercategory,suchas
Global Nearest Neighbor (GNN) and Joint
Probabilistic Data Association (JPDA) filtering,
integer programming or Multi Hypothesis Tracking
(MHT)arewell‐describedinBar‐Shalom,Daum,and
Huang (2009), Kim, Li, Ciptadi, and Rehg (2015),
Pulford (2005) and Khaleghi, Khamis, Karray, and
Razavi (2013).
More recent work has also applied
RandomFiniteSet(RFS)theorytoMTTyieldingthe
Probability Hypothesis Density (PHD) or
Cardinalized PHD (CPHD) filters Mahler (2015). In
specific situations where the assumption of linear
state equation under Gaussian noise is violated,
sequential Monte Carlo methods Doucet, Smith, de
Freitas, and Gordon
(2001) can be considered as an
alternativesolutionHue,LeCadre,andPérez(2002).
Thanks to the ever increasing availability of
computingpowerthecomputationalneeds,oneofthe
drawbacks of particle filter algorithms, become less
constraining forrealtime applications. In this work,
wewanttocomparetheperformance
oftwodifferent
multi‐targettrackersin amaritimescenariointerms
oftheirestimatedmulti‐targetstate.Atfirst,anIMM‐
JPDAfilterwas implementedascurrent state‐of‐the‐
art approach for MTT. Secondly, a novel Repulsive
MultiParticleFilter(RMPF)willbeintroducedwhich
isnotsubjectto
theGaussianerrorstateassumption.
Figure1. Simulated multi‐target scenario in theBaltic Sea.
Two tugs were steered to circle around an anchored
(quasistatic) vessel, which monitors the situation by her
radar.
Figure2. Snapshot of radar response to simulated multi‐
targetscenario,showingbothtugvesselsclearlyonscreen.
513
The range was set to 6 NM at head‐up display. Some sea
clutterduetothesimulatedwavesisvisible.
3.1 Targetdynamicsandmeasurementmodel
In general, for tracking vessels of various types, we
assumetopropagatethestatevector
1
t
k
x
of the
th
t
targettothenexttimeframekthroughanon‐linear
motionmodelfollowingthenotationof
|1 1
,
titq
kk k k
f
xxε (1)
where
~,
qi
kk
N
ε0Q and no further control
input given. To distinguish between different
dynamic models in the upcoming section, we
introducethesuperscriptitothenon‐linearfunction
i
f . The predicted state estimate
|1
t
kk
x will be
corrected by evaluating the residual between the
actual radar measurement
k
z associated to the
th
t
target and the predicted measurement following the
generalformulationof
|1 |1
ˆ
,
tr
kk kk k
h
zxε
, (2)
where
r
k
ε is drawn from the assumed sensor noise
distribution (e.g.,
~,
r
kk
N
ε0R for the
Gaussianassumption).
3.2 TheIMM‐JPDAfilter
Considering the inherent trade‐off between
complexity and tracking performance the JPDA
frameworkwaschosen,beingcombinedwithanIMM
filter to capture different target dynamics. In the
remainder of this section, we will define the set of
dynamicandmeasurement
modelsthatconstitutethe
IMM‐JPDA framework for multi‐sensor, multi‐target
tracking. Being first introduced in Fortmann, Bar‐
Shalom, and Scheffe (1983), the key feature of the
JPDAisthe computation ofconditionalprobabilities
ofjointassociationevents
1
M
jt
j
A
kAk
, (3)
with respect to the current time k, in which A
jt(k)
represents the event of the j
th
measurement
originatingfromtargett,with1≤j≤Mand0≤t≤N.
In this context, M refers to the number of
measurementsattime k, N to the number of known
targets and t
j is the target index the
th
j
measurementisassociatedto.Witht=0thespecific
caseofameasurementoriginatingfromclutterisalso
beingconsidered.Thismeans,incontrasttoaNearest
Neighbor (NN) association rule, the JPDA also
accountsforsituationsinwhichasinglemeasurement
canbeassigned,withacertainlikelihood,
tomultiple
targets at the same time. Details can be found in
Fortmann Bar‐Shalom, and Scheffe (1983) and Bar‐
Shalom,Daum,andHuang(2009).
Inthiswork,weuseanextensiontoclassicalJPDA
filtering known as IMM‐JPDA filter. The IMM was
introducedby Blom andBar‐Shalom (1988)
toadapt
toquicklychangingtargetdynamicsbyconsideringa
finitesetofkinematicmodelsthatruninparallel.In
contrasttohardswitchingschemes,theIMMweighs
the different target state estimates based on the
likelihood of each model to explain the current
measurement data. The mode transition is
thereby
governed by an underlying Markov chain. In our
case, we consider a set of two dynamic models to
capture either straight path or turning maneuver
based motion. For the former a Constant Velocity
(CV)modelwasdesigned,whereastheConstantTurn
RateVelocity(CTRV)modelissupposedtofitbest
to
thelatter.Thecorresponding target state vectors are
definedas
,,
,,,
T
CV
keknkkk
p
pv
x , (4)
,,
,,,,
T
CTRV
k eknkkkk
pp v
x
, (5)
with
,,
,
ek nk
pp the 2D position coordinates in the
local ENU frame,
k
the course over ground,
k
v
thespeedovergroundand
k
theturnrateattime
k.Theuncertaintywithinthemodelsisexpressedin
2
2
2
2
0
0
,.
0
0
v
CV CTRV
kk
v
QQ
(6)
The detailed definitions of the process models
i
f
for CV and CTRV can be found in Siegert,
Banyś, Martínez, and Heymann (2016). Careful
attention needs to be paid to the augmentation of
statevectorsofdifferentdimensions.Inthispaperwe
follow a strategy described in Glass, Blair, and Bar‐
Shalom (2013) for unbiased mixing of different
process models. In contrast to the common
formulationof either IMMorJPDA, which both use
Extended Kalman Filtering (EKF) to adapt to non‐
linearities in the dynamic models, we deploy the
Unscented Kalman Filter (UKF) instead (see Julier
and Uhlmann, 1997). It turns out that due to the
sigma point
sampling approach the UKF is more
robust against non‐linearities induced by the radar
measurement update equation, whereas the
approximationtoafirst‐orderTaylorseriesexpansion
within the EKF was found to diminish its
performance (see Braca, Vespe, Maresca, and
Hoffmann(2012)fordiscussion).Thecombinationof
IMM and
JPDA filtering schemes to a well‐defined
frameworkwas initiallyproposed by Blom andBar‐
Shalom(1988)andextendedtothemulti‐sensorcase
inTugnait(2003).Intheend,arecursivestep‐by‐step
algorithm was derived fusing the asynchronous
measurements from different sensors sequentially.
514
The final state update equation for the t
th
target
trackedinmodei∈{CV,CTRV}becomes
,
,, ,
|0|1 |
1
tk
M
ti i ti ti i
kk t kk kk jt
j
j
xx x , (7)
withM
t,kthe number of validated measurements for
target t and
,
|
ti
kk
j
x the UKF target estimate
conditioned on the j
th
measurement at time k. The
weights
i
j
t
are interpreted as association
probabilities following the convention in Braca,
Vespe,Maresca,andHoffmann(2012),with
0
i
t
ith
jt
P none of the measurements origins from target t
P the j measurements origins from target t
(8)
3.2.1 Trackmanagement
In general, the JPDA filter is subject to several
assumptions. Most importantly for our application,
thefinitesetoftargetstobetrackedisassumedtobe
known, i.e., neither track initialization nor track
pruning is covered by the standard formulation of
JPDA. Toovercomethese
restrictions itissuggested
inBar‐ShalomandLi(1995)toapplyanM‐of‐Nrule,
which is implemented according to Braca, Vespe,
Maresca,andHoffmann(2012)asfollows:
1 Trackinitialization:
For each radar scan, every unassigned target
candidate measurement becomes a tentative
track.The gate assignedto
thistrack accounts
for the (assumed) maximum velocity and
sensor uncertainty, i.e., this bound is rather
conservative.
If a targetcandidate from the next radar scan
falls within the gate of a tentative track, it
becomesapreliminarytrack.Incaseatentative
trackis not supported byany
detectionin the
nexttimeframeitisdroppedagain.
ForeachpreliminarytrackaUKFisinitialized
propagating the target state through a CV
dynamicmodel.
IfapreliminarytrackisconfirmedforMoutof
thenextNradarscans,itbecomesaconfirmed
track.Ifnot,
itisdropped.
Each confirmed track will be tracked in the
IMM‐JPDAfilter.
2 Tracktermination:
Incaseaconfirmedtrackwasnotupdatedfor
Mt out of Nt consecutive radar scans it is
terminated,whereindextdenotesadifference
between M and N from the
initialization
process.
A confirmed track will also be terminated, in
case the corresponding error state covariance
exceedsthresholdsinpositionand/orvelocity.
3.2.2 Targetcandidateextractionfromradarimages
In order to update the IMM‐JPDA filter with
measurements,targetcandidatesneedtobedetected
andextractedfromradarfirst.
Theutilizedapproach
toextractradartargetinformationisbasedonimage
processing instead of directly working on the radar
signal level. To extract target candidates from the
current radar image at time k, the following
procedureisapplied:
1 Masking the image to eliminate features of the
userinterface,
e.g., colored heading lines, blob in
center,radarinformationtables.
2 Conversion of the image from RGB to gray‐scale
(weightedaveragefromcolorchannels).
3 Blob detection with fixed range settings for
convexity,circularity,inertia,sizeandintensityof
expectedtargets.
4 Each detected target candidate per frame is
expressed in range and bearing, relative to the
positionofthevesselcarryingtheradar.
Thekeyaspectinthisprocessingchainiscertainly
thescale‐invariantblobdetectiontoeventuallydetect
targetcandidates.Thisalgorithmiswell‐describedin
the literature and finds many applications in image
basedtargetdetection
andtrackingsuchasdescribed
in Isard and MacCormick (2001). For this work the
implementationprovidedbytheOpenCVframework
was used (OpenCV 3.1.0:
https://github.com/Itseez/opencv.git). Figure 3 shows
the final outcome of the different radar processing
stages. The set of extracted radar measurements is
defined as
1
,,
M
kk k
zz with the
th
j
measurement vector
,
T
jrb
kkk
zz
z comprising
range and bearing of the target candidate. The state
update of
|1
i
kk
x
conditioned on the associated radar
target measurements is based on the definition of
,
|1
,
irs
kk k
h
xε fromEquation2givenas
22
,| 1 ,| 1
,
|1
,| 1
,| 1
,
arctan
ekk e nkk n
irs r
kk k
k
nkk n
ekk e
pppp
h
pp
pp
xε ε, (9)
with
{, }
en
p
p the 2D reference coordinates of the
radarsystemintheENUframeofthetrackedvessel.
515
Figure3. Extracted target candidates (redcircles)at time k
afterblobdetectioninpre‐processedradarimage.
3.3 TheRepulsiveMultiParticleFilter
The use of particle filters in marine radar image
processing(Heymann,Banyś,andSaez,2015)showed
the potential to overcome the assumption of non‐
Gaussian noise when using radar images as
measurement input. However, this study uses a
classical particle filter algorithm without any
comparison of the results to existing fusion
technologies. In this study, we compare the
performance of both classes of recursive Bayesian
filters,namelytheparticlefilter(RMPF)andKalman
filter based (IMM‐JPDA) approaches, in a maritime
multi‐targetscenario.
Following the description of the target dynamics
and measurement model
in Section 3.1 the
implementationoftheparticlefilterusedinthisstudy
uses the dynamic model of constant velocity and
thereforethedefinitionoftheparticlestatespaceasin
Equation4isused.Undertheassumptionofahidden
Markov process and conditional independent
observations
,,
y
n
kk
k yy the
formulationsofDoucet,Godsill,and Andrieu (2000)
are used. The RMPF implements the Sequential
ImportanceResampling(SIR) approach inwhichthe
particlesresamplingisdoneaftereverymeasurement
step. In the SIR each new particle state
k
x is
sampledfromthedistribution
|
i
kk
p xx.
TheRMPFwasmotivatedbytheclassicalbehavior
of sequential Monte Carlo trackers, which tend to
convergetoasingletargetsolution.Byexploitingthis
phenomenon together with the physical principle of
repelling charged particles the main parts of the
RMPF are described. As soon as the particle filter
picks
up the track of a single target, a new filter is
initializedtostarttrackingadifferenttarget.Thetime
to acquisition of a target is determined by a fixed
threshold, which specifies a maximum uncertainty
bound during target tracking. This particle filter
generatesarepellentforcereducingtheweight
ofthe
samples from other particle filters which are
generated whenever a new target is detected. The
down‐weightingisdefinedbythefollowingequation:
2
max
exp 3
i
j
wi
, (10)
where
()wi
is the weightof particle i in filter k ,
j
istheloopvariableoverallotherfiltersexcept
k
and
max
i
is the largest standard deviation in the
positiondomain.
(a)Acquisitionphaseofthe2ndtarget.
(b)BothtargetsaretrackedbytheRMPF.
Figure4. Different stages of target acquisition for the
RepulsiveMultiParticleFilter.
The process of acquisition of the targets is
illustratedinFigures4aand4b.Theredpointsshow
the first particle filter which is fully converged in
Figure 4a and the second filter is initialized and
drawntothetargetintheleftpartoftheradarscreen.
This can be
seen by the purple circle whose center
positionisatthemeanoftheparticledistributionof
thesecondfilterandradiusofthecircleisdetermined
by the largest standard deviation of the position
domain.InFigure4bthesecondfilterhasconverged
aswellandbothtargetsare
finallytracked.
516
3.4 MTTperformanceassessment
InSchuhmacher,Vo,andVo(2008)theOptimalSub‐
pattern Assignment (OSPA) metric was introduced
andisconsideredasstate‐of‐the‐artmethodforMTT
performance assessment. The OSPA metric yields
severalcharacteristicsthatmakeitattractiveforMTT
performanceassessment:
Ithasa
physicalinterpretation.
Itcapturesmulti‐targetstateerrorsandcardinality
errorsmeaningfully.
TheOSPAmetricdependsononlytwotuning
parameters (the order
p
and cut‐off
parameter
c
).
Itisrelativelyeasytocompute.
Consider two finite subsets
1
,,
m
X
xx and
1
,,
n
yYy within W , where
0
,mn , and
denote by
k
the set of permutations on
{1, 2 , , }k forany k .TheOSPAmetricisthen
definedasthefunction
1
()
1
1
,: min , ,
n
p
m
p
c
cp
pi
i
i
dXY dxy cnm
n
(11)
with
()
()
(, ) min(,(,))
c
ii
dxy cdxy
denoting the
distancebetweenxandybeingcutoffat
0c .This
definition holds for
mn
, in case of mn we
substitute
()
,
c
p
dXY
with
()
,
c
p
dYX
.According
to Schuhmacher, Vo, and Vo (2008), the impact of
localizationandcardinalityerrorstotheoverallmetric
canbeexpressedas
1
()
,
1
1
,: min ,
n
m
p
p
c
c
i
i
ploc
i
eXY dxy
n
(12)
and
1
()
,
,:
p
p
c
pcard
cnm
eXY
n
. (13)
4 RESULTS
Wewillevaluatebothproposedmulti‐targettrackers
based on simulated radar images in the following
section.InFigure 5 the resulting tracks of the IMM‐
JPDAareplottedontopoftheextractedradartarget
candidates obtained from the blob detector. The
correspondingoutputofRMPF
isplottedinFigure6.
Inthiscaseonlytheestimatedtracksareshown,since
thefilterisconditionedontheradarimagenoton a
finitesetoftargetcandidates.
Figure5. Resultingtracks (in blue and green) by applying
theIMM‐JPDAfiltertothesimulatedmulti‐targetscenario.
The accumulated radar target candidates are plotted as
blackdots.
Figure6.Resultingtracks(inblueandgreen)fromapplying
the RMPF to the simulated multi‐target scenario. Track 1
getslostwhilethetargetmovesinablindspotoftheradar.
Thefilterconvergesbacktothecenteroftheimage,asthe
clutterresponseisstrongestcloseto
theradar’sposition.
It can be observed that both filters pick up two
tracksfromtheradarimagedata.TheIMM‐JPDAand
RMPFarecontinuouslytrackingbothvesselsoverthe
time of the simulation. The RMPF shortly loses one
targetatthepointintimewhenthevesseliscovered
by the second
ship in the radar. While IMM‐JPDA
filtering overpasses this outage of measurement
updatesbyinflatingtheerrorstatecovariancedueto
continuouspredictionstheparticlesoftheRMPFstart
tospreadandacquiretheremainingclutterresponse
in the vicinity of the hidden target. At the time the
vessel
appears again in the radar image the filter
convergesquicklybacktothecorrectposition.
The OSPA metric to compare the two filters is
shown in Figure 7. The overall OSPA metrics
computed from Eq. 11 are plotted against time for
both filters. In this analysis the cut‐off parameter
(penalizing
cardinality errors) was set to c = 250 m;
theorderpto2.Infacttheshortlossofonetargetin
case of the RMPF is reflected only by small peaks
comparedtotheperformanceoftheIMM‐JPDA.This
is due to the chosen cut‐off parameter
c. If this
parameteris setto500 mthemismatchbetweenthe
numberofreferencetargetstothenumberoftracked
objectsgetsa higherimpactin the multi‐targetstate
error
()
,
c
p
dXY.Figure8showstheresultinggraphs
and the peak at around 2700s shows the higher
impact of the multi target state error. However, in
terms of the overall multi‐target tracking accuracy
517
bothfiltersshowsimilarperformance,withtheRMPF
outperformingtheIMM‐JPDAatcertaintimes.
Figure7.PerformancecomparisonbetweentheIMM‐JPDA
(dotted blue curve) and the Particle Filter (dashed red
curve)onbehalfoftheOSPAmetric,withc=250mandp=
2. The plot depicts the overall multi‐target state errors
()
,
c
p
dXY.
Other parameters of interest for performance
comparison are the time‐to‐acquisition and
completeness. While the former describes the elapsed
timeuntilalltracksarepickedupandconfirmed,the
latterdenotestheratiobetweentheamountofcorrect
multi‐target states against the overall number of
multi‐target states.
In Table 1 the corresponding
valuesforeach ofthe filtersarelisted.The numbers
show that the IMM‐JPDAframework is much faster
in target acquisition, while the RMPF shows similar
performanceintermsofcompleteness.
Figure8. Performance comparison between the IMMJPDA
(dotted blue curve) and the Particle Filter (dashed red
curve)forc=500mandp=2.
Table1. Comparison betweenboth multi‐targettrackers in
terms of time‐to‐acquisition and completeness of multi‐
targetstate.
_______________________________________________
Time‐to‐AcquisitionCompleteness
_______________________________________________
IMM‐JPDA12s99.7%
RMPF31.6s97.4%
_______________________________________________
5 CONCLUSION
In this paper we have compared two methods for
maritime trafficsituation assessment basedon radar
image processing. At first, an IMM‐JPDA filter was
designed that is conditioned on radar target
candidates, which are extracted via blob detection
fromthecurrent radarimage.Secondly,a Repulsive
Multi
ParticleFilterwasproposedthatusestheradar
image directly as measurement input to update the
particle distribution. In both cases, the track
management, e.g., the target initialization, was done
fully automatic. For performance evaluation we
considered the multi‐target state errors as well as
time‐to‐acquisition and track
completeness. It was
shownthattheRMPFandtheIMM‐JPDAareonpar
in all of those aspects. The accuracy of the multi‐
target state estimation is degraded in case of the
RMPF after the loss of one target during times of
coverage.Thisalsoaffectstheperformanceinterms
of
track completeness of the RMPF, which is slightly
worsecomparedtotheIMM‐JPDA.Additionally,the
RMPFtakesmoretimetoconvergetoasingletarget
state, degrading its score on track completeness.
However, in times of correct target acquisition the
RMPF performs as good as the IMM‐JPDA
if not
better.
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