Track-to-track Fusion using Multiple Detection Linear Multitarget

Integrated Probabilistic Data Association

Yuan Huang, Sa Yong Chong and Taek Lyul Song

Department of Electronic Systems Engineering, Hanyang University, Ansan, Republic of Korea

Keywords:

Track-to-track Fusion, Centralized Fusion, Multiple Detection, LM-IPDA.

Abstract:

The multi-sensor multiple detection target tracking problem is considered in this paper. The probability of

target existence is used as the track quality measure and plays an important part in the fusion paradigm. The

multiple detection linear multi-target integrated probabilistic data association (MD-LM-IPDA) is utilized and

extended to the multi-sensor structure. Both centralized fusion MD-LM-IPDA and distributed track-to-track

fusion MD-LM-IPDA are proposed. The centralized fusion method utilizes the information from all local

sensors’ measurements to get the best tracking performance but suffers from the high communication load.

The distributed fusion method can control the communication load by adjusting the threshold for transmitting

local tracks to the fusion center. One can make a choice between these two structures based on the tracking

performance requirement and the computation resources.

1 INTRODUCTION

The multiple detection problem gained a substantial

amount of attention in recent years due to that many

kinds of high resolution sensors and radars are rou-

tinely used in many surveillance and tracking scenar-

ios (Vivone et al., 1999; Baum and Hanebeck, 2014;

Chen et al., 2014). In these multiple detection tar-

get tracking applications, the point target assumption,

which allows each target generate at most one detec-

tion at each scan, cannot remain valid (Bar-Shalom

et al., 2011). Instead, there can be more than one mea-

surements come from the same object, the data as-

sociation process need to enumerate the one-to-many

track-to-measurements assignments and evaluate the

corresponding posteriori data association probabili-

ties. Both random matrix (Lan and Li, 2016) and

measurement partition method (Mahler, 2009) are in-

troduced to cover this multiple detection problem.

In target tracking applications, the real targets ex-

istence information is not known prior. The tracks can

be initialized by both target measurements and clut-

ter measurements which leads to the existence of both

true tracks (tracking targets) and false tracks (tracking

clutter) in the surveillance area (Musicki et al., 1994).

The true track and false track states can be inter-

changed during tracking period based on the informa-

tion extracted from the measurements. The probabil-

ity of target existence is introduced as a judging stan-

dard of the existence of a target in order to solve the

false track discrimination (FTD) problem, which in-

volves true tracks conﬁrmation and false track termi-

nation (Musicki and Evans, 2004; Musicki and Scala,

2008).

The multiple detection linear multitarget in-

tegrated probabilistic data association (MD-LM-

IPDA), which embedded the measurement partition

method into the LM-IPDA algorithm (Musicki and

Scala, 2008), is an efﬁcient method designed for

multitarget multiple detection applications. In tra-

ditional MD structures (Habtemariam et al., 2013;

Habtemariam et al., 2011), the selected measure-

ments are partitioned into measurement cells, where

each cell contains one or some of the selected mea-

surements, and then these measurement cells are uti-

lized in the joint track-to-measurement cell assign-

ments. The MD-LM-IPDA bypass the joint track-

to-measurement cell assignments process by treating

the possible measurement cells of targets followed

by other tracks as additional clutter measurements to

modulate the clutter spatial density. This mechanism

makes MD-LM-IPDA work efﬁciently in the closely

spaced multitarget tracking applications but lose part

of the optimality.

In the centralized fusion structure, the local sen-

sors transmit measurements to the fusion center for

global tracks update. This approach is optimal but

usually not feasible due to the high communication

Huang, Y., Chong, S. and Song, T.

Track-to-track Fusion using Multiple Detection Linear Multitarget Integrated Probabilistic Data Association.

DOI: 10.5220/0006410104310439

In Proceedings of the 14th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2017) - Volume 1, pages 431-439

ISBN: 978-989-758-263-9

431

load or for the reason that the local sensors only out-

put the track information. The distributed track-to-

track fusion approach focus on fusing the local sensor

tracks with the global tracks at the fusion center. The

performance of this approach is usually worse com-

pared to centralized fusion method. However, the dis-

tributed track-to-track fusion approach requires only

a fraction of the computation time needed for the cen-

tralized fusion since the number of local tracks trans-

mitted to the fusion center is much less compared to

the number of local sensor measurements (Musicki

et al., 2015; Lee et al., 2014).

In this paper, both track-to-track fusion and cen-

tralized fusion are considered under the multiple de-

tection situation. The MD-LM-IPDA is implemented

in these two fusion structures. The probability of tar-

get existence is used as the track quality measure for

local tracks and global tracks and only the conﬁrmed

local sensor tracks are sent to the fusion center for

track-to-track fusion. In both these two fusion struc-

tures, the fusion center generates global tracks and

uses local sensor output, tracks for track-to-track fu-

sion and measurements for centralized fusion, to up-

date global track states and probabilities of target ex-

istence.

In the track-to-track fusion structure, local sen-

sors use the original measurements to update the local

track states and the conﬁrmed tracks (both true tracks

or false tracks) are transmitted to the fusion center.

Then, these conﬁrmed tracks come form the local sen-

sors assume the role of measurements to update the

global track states at the fusion center. The probabil-

ity of target existence of the local tracks are used in

calculating the fusion probabilities. The fusion pro-

cess improves both FTD and tracking accuracy com-

pared to local sensor performance.

In the centralized fusion structure, all local sen-

sors send the measurements to the fusion center and

the global tracks are updated using these measure-

ments. Usually the measurements used by the global

tracks in centralized fusion is different from that of

the distributed fusion. This different is due to that

in the distributed fusion structure, each local sensor

processes the tracking algorithm to generate tracks

and conﬁrmed local tracks are considered as measure-

ments at the fusion center. Usually the centralized fu-

sion obtains better performances than distributed fu-

sion but plagued by the high communication burden.

Section 2 depicts the target and measurement

models. Section 3 demonstrates the centralized fu-

sion structure. The distributed fusion process is given

in Section 4. In Section 5, the performances of the

two fusion structures are compared followed by the

conclusion in Section 6.

2 PROBLEM STATEMENT

The dynamic state for target τ propagates according

to a constant velocity model, given by

k+1

= Fx

+ v

(1)

where x

stands for the target state at scan k, F is the

state propagation matrix. v

is the zero-mean Gaus-

sian process noise with covariance Q.

The target measurement detected by sensor “s” is

generated by

= H

+ w

(2)

where H

is the measurement matrix and w

is the

zero-mean Gaussian measurement noise with covari-

ance R

. The process noise and measurement noise

are assumed independent. Since the multiple detec-

tion problem is considered, each target can generate

more than one measurements.

The clutter measurement follows the Pois-

son/uniform distribution which means that the num-

ber of clutter measurements at each scan followsPois-

son distribution and the spatial distribution of a clutter

measurement follows the uniform distribution in the

surveillance area.

Let Z

stand for the measurements obtained by

sensor “s” and z

k, j

is the j-th measurement of Z

. The

measurements gathered by sensor “s” from initial to

scan k is denoted by

k,s

= {Z

,.. . ,Z

} (3)

so that all the measurement obtained by all the sensors

from initial to current scan k is given as

k,1

k,2

,.. . ,Z

k,L

(4)

where L is the number of sensors.

The probability of target existence event χ

and

not exist event

satisﬁes





+ P





= 1 (5)

For reasons of clarity, here we deﬁne that

= P



k,s



;

= P



k−1,s



(6)

and the prediction relation between these two param-

eters is given by

= p

k−1

(7)

where p

is the propagation probability that a target

exists at scan k− 1 and keeps existence at scan k.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

432

Signal

processing

Signal

processing

Fusion

center

Association

Filter

update

Global

tracks

Figure 1: The structure of centralized fusion.

The number of measurements selected

by sensor “s” at scan k

τ,max

The predetermined maximum number

of target τ detections

τ,max

The maximum number of tar-

get originated measurements in

the m

selected measurements,

τ,max

= min(φ

τ,max

)

(k) One measurement cell of track τ at

time k

The number of measurements origi-

nated from target τ such that 1 ≤ ϕ

≤

τ,max

An index that indicates if the measure-

ment cell z

(k) is one of the possi-

ble c

combinations, where there are

measurements originating from tar-

get τ; n

∈



1,2,.. .,c



and c

!(m

−ϕ

k,0

The event that none of the selected

measurementsoriginated from target τ

k,z

The event that measurement cell

originated from target τ

3 CENTRALIZED FUSION

STRUCTURE

In the multiple detection centralized fusion structure,

each local sensor gathers measurements and sends

these measurements to the fusion center. Some no-

tations for algorithms derivation are given above and

the structure of centralized fusion is shown in Figure

Here, we use a simple example to show the mea-

surement cells generated by the measurement parti-

tion method. Assuming that at scan k track τ se-

lects two measurements

k,1

k,4

out of the total

k,1

k,2

k,3

k,4

and the corresponding partition

events are:

• Only one of these two selected measurements is

target detection (ϕ

= 1), the number of possi-

ble combinations c

= C

= 2 and the n

varies

from 1 to 2. The measurement cells are:

1,1

(k) = z

k,1

1,2

(k) = z

k,4

• Both these two selected measurements are target

detections (ϕ

= 2), the number of possible com-

binations c

= C

= 1 and the n

is 1. The mea-

surement cell is:

2,1

(k) =



k,1

k,4



At the fusion center, the MD-LM-IPDA algorithm

is used to update the global tracks using the local sen-

sors measurements sequentially. For the brevity of

notations, the time index k of the measurement cells

are omitted and a brief description of this algorithm is

given as follows:

k,z

is deﬁned as the a priori probability that

target τ exists and measurement cell z

is gener-

ated by target τ. This probability is given by

k,z

∆



k,z

,χ

k−1



≈

k,z

τ,max

∑

k,z

· P

Dϕ

)

(8)

where p

k,z

is the measurement cell likelihood

calculated by the same method as given in [10]. P

Dϕ

is the probability that detected a target ϕ

times. P

the gating probability (Challa et al., 2011).

In (8), ρ

is calculated by

∏

∈z



k, j

∑

σ=1

σ6=τ

)

k, j

(9)

where p

k, j

is the measurement likelihood function of

k, j

for track σ and ρ

k, j

stands for the clutter measure-

ment density at point z

k, j

Track-to-track Fusion using Multiple Detection Linear Multitarget Integrated Probabilistic Data Association

433

Here, deﬁne

k,z

as the modulated clutter

measurement density, satisﬁes

k,z

∆

= ρ

k,z

∑

σ=1

σ6=τ

k,z

1− P

k,z

(10)

where ρ

k,z

∏

k, j

∈z

k, j

The measurement likelihood ratio Λ

is deﬁned by

∆



|χ

k−1





k−1



≈1− P

Dec

τ,max

∑

k,z

Dϕ

)

(11)

The a posteriori probability that target τ exists and

there is no measurement generated by target τ is



k,0

,χ

k,s



(1− P

Dec

)

1− P

Dec



k,0

k,s



(12)

The a posteriori probability that target τ exists and

measurement cell z

is the set of target τ detec-

tions satisﬁes



k,z

,χ

k,s



≈

Dϕ





1−



1− Λ



k,z

(13)

The probability of target existence of track τ is up-

dated by



k,s





k,0

,χ

k,s



τ,max

∑



k,z

,χ

k,s



≈

1− P



1− Λ



(14)

The data association probabilities are given by

k,0



k,0

,χ

k,s





k,s



≈

1− P

Dec

(15)

and

k,z



k,z

,χ

k,s





k,s



≈

Dϕ





k,z

(ϕ

(16)

Each measurement cell updates the track state us-

ing a modiﬁed Kalman ﬁlter [10] and together with

the predicted state are used to generate the ﬁnal track

state by a Gaussian Mixture.

4 DISTRIBUTED

TRACK-TO-TRACK FUSION

STRUCTURE

The LM-IPDA algorithm is a suboptimal method

for multitarget tracking/fusion problem in which the

computational load is linear with the number of

tracks. The conﬁrmed local sensor tracks are used

to update the global track states at the fusion cen-

ter sequentially. Here we consider the situation that

updating track τ using tracks {ζ} comes from sensor

“s”. In the track-to-track fusion structure, the tracks

in {ζ} that follow other potential targets are treated as

‘clutter’ tracks with respect to τ. Then these ‘clutter’

tracks are used to modulate the clutter track density

and by doing so the single target tracking approach is

enabled to cover the multitarget tracking problem.

In the fusion center, the local tracks are treated as

measurements and the a priori probability that mea-

surement ζ comes from target τ is

= P

∑

l∈{ζ}



(17)

where P

is the track detection probability and the

measurement likelihood p

is given by

= N



ˆx

; ˆx



(18)

and the parameters used in (18) will be given latter.

The ρ

used in (17) is the clutter track density and

a simple way to calculate this value is

(19)

where b is the number of conﬁrmed tracks transmitted

to the fusion center by sensor “s” andV is the volume

of the surveillance area.

The modulated clutter track density is deﬁned as

∆

= ρ

∑

σ6=τ

1− P

(20)

where in this modulated clutter density, the possibil-

ity that track ζ is tracking another target is taken into

consideration. This clutter track density expression is

the core of the LM track-to-track fusion approach.

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

434

Signal

processing

Signal

processing

Association

Filter

update

Tracks

Association

Filter

update

Tracks

Fusion center:

track

to track

association and

fusion

Global

tracks

Figure 2: The structure of distributed fusion.

Then, the measurement likelihood ratio is ex-

pressed by

= 1− P

+ P

∑

(21)

The a posteriori probability of target existence of

track τ is updated by

1− (1− Λ

)

(22)

where

is the predicted target existence probability

given in (7).

The track fusion probabilities, where the modu-

lated clutter track density is used, can be obtained by

(

1− P

ζ = 0

ζ > 0

(23)

In the track-to-track fusion structure, even through

the measurement noises of different sensors can be

assumed independent there is still estimation errors

correlate between two track if these two tracks are

tracking the same targets (Bar-Shalom et al., 2011;

Bar-Shalom, 1981; Bar-Shalom and Campo, 1986;

Chen et al., 2003). So that the correlated Kalman ﬁlter

(CKF) is employed for track state update.

The innovation covariance is generated by

= P

+ P

− P

−





(24)

where the cross covarianceP

considers the correlated

trajectory estimation errors between target ζ and τ,

calculated by

= E

h

ˆx

− x



( ˆx

− x

)

(25)

The Kalman gain is calculated by



− P





−1

(26)

The track state and corresponding covariance are

updated by

ˆx

= ˆx

+ K



ˆx

− ˆx



(27)

and



I − K





I − K



+ K







I − K







+ K







I − K



(28)

In the distributed track-to-track fusion structure,

the global tracks in the fusion center are updated by

the local sensor tracks sequentially. In all above equa-

tions, the state and state covariance for target τ are not

speciﬁed by a time index k. When track τ is fused

with the ﬁrst sensor’s local tracks, the predicted infor-

mation ˆx

k|k−1

and P

k|k−1

are used as ˆx

and P

. Then,

in order to fuse with the second sensor’s local tracks,

the updated state ˆx

and state covariance P

are used

as ˆx

and P

. In the probability of target existence

update recursion, the predicted existence probability

is updated using the ﬁrst sensor’s conﬁrmed tracks

information. When this parameter is updated by the

second sensor, the updated existence probability

used as the predicted information for the second sen-

sor.

5 SIMULATION STUDIES

Two simulations are considered in this part, one is

used for comparing different fusion structures and the

other is used for comparing multiple detection struc-

ture with single detection structure.

Track-to-track Fusion using Multiple Detection Linear Multitarget Integrated Probabilistic Data Association

435

Table 1: Simulation parameters.

Centralized T2TF T2TF-2 Sensor1 Sensor2 Sensor3

Initial PTE 0.0001 0.0001 0.0001 0.0001 0.0001 0.0001

Conﬁrmed threshold (local) – 0.001 0.1 0.999 0.999 0.999

Conﬁrmed threshold (fusion center) 0.99 0.95 0.97 – – –

[0.4,0.3] – – [0.4,0.3] [0.4,0.3] [0.4,0.3]

– 0.7 0.7 – – –

Number of conﬁrmed false tracks 1 1 1 1 2 2

Simulation time (per each run) 13.27s 0.31s 0.26s 0.27s 0.28s 0.28s

0 100 200 300 400 500

100

150

200

250

300

350

400

450

500

X (m)

Y (m)

Target 1

Target 1 Start Point

Target 2

Target 2 Start Point

Target 3

Target 3 Start Point

Figure 3: Simulation scenario.

5 10 15 20 25 30 35 40

100

200

300

400

500

600

700

800

900

scan

number of confirmed true tracks

Centralized

T2TF

T2TF−2

Sensor1

Sensor2

Sensor3

Figure 4: Conﬁrmed true tracks for all the targets.

5.1 Simulation One

In this simulation scenario, three targets move in a

500m × 500m Cartesian coordinates with the con-

stant velocities. All of them reach the same location

[250m, 250m] at scan 20. Totally 300 Monte Carlo

simulation runs where each run contains 40 scans

with the scan interval equal to 1s. Three sensors are

used to detect targets, all these sensors are located at

the origin of the coordinates and each detects targets

independent from the others. In this simulation, the

multiple detection problem is considered where the

detection probability of the local sensors and central-

ized fusion structure is set as [0.4,0.3] which denotes

5 10 15 20 25 30 35 40

scan

root mean square position error (m)

Centralized

T2TF

T2TF−2

Sensor1

Sensor2

Sensor3

Figure 5: Root mean square position error of target 2.

that each sensor obtains one detection from a target

with probability 0.4 and two detections from a target

with probability 0.3. In the distributed fusion struc-

ture, the track detection probability P

at the fusion

center is set as 0.7. The average number of clutter

measurements occurs at each scan for each sensor is

25.

The target state propagation matrix and the pro-

cess noise covariance are given as

F =







1 0 T 0

0 1 0 T

0 0 1 0

0 0 0 1







(29)

and

Q = 0.75m

−3









3 0 T



2 0

0 T



3 0 T



2 0 T 0

0 T



2 0 T







(30)

The process noise covariance is given by

R =



25 0

0 25



(31)

The initial states of these three targets are

target 1 :



50m 250m 10m/ s 0m/s



target 2 :



90m 350m 8m/s −5m/s



target 3 :



170m 430m 4m/s −9m/s



(32)

ICINCO 2017 - 14th International Conference on Informatics in Control, Automation and Robotics

436

Each local sensor utilizes the MD-LM-IPDA al-

gorithm for tracking targets. The probability of target

existence is used to solve the FTD problem. Once the

probability of a track exceeds the conﬁrmed thresh-

old, it remains conﬁrmed state. All the local sen-

sors’ performances are shown and compared with dis-

tributed and centralized fusion structures.

In the track-to-track fusion (T2TF) structure, af-

ter each sensor utilizes the MD-LM-IPDA algorithm,

the conﬁrmed local tracks of each sensor are trans-

mitted to the fusion center and then the global tracks

are fused with local conﬁrmed tracks sequentially us-

ing the method proposed in Section IV. The track

conﬁrmed threshold used for selecting local tracks to

transmit to the fusion center can be adjusted to con-

trol the number of tracks transmitted. The inﬂuence of

this parameter can be seen from Figure 4 and Figure 5

where two different performances obtained by using

different values for the local track conﬁrmed thresh-

old are demonstrated (T2TF and T2TF-2).

The centralized fusion implements tracking pro-

cess using each sensor’s measurements sequentially.

This optimal fusion framework immediately extracts

targets information from local sensor measurements,

which obtains the best performancecompared to other

fusion structures but not always feasible due to both

communication load and computational burden.

The simulation parameters for different algo-

rithms are shown in Table I. The initial probabilities

of target existence (PTE) for different algorithms are

set the same and the conﬁrmed thresholds are adjusted

in order to obtain almost same number of conﬁrmed

false tracks. The method for adjusting whether a track

is a conﬁrmed true track or a conﬁrmed false track is

the same as given in (Musicki et al., 2013).

The number of conﬁrmed true tracks of different

algorithms are shown in Figure 4. The tracking per-

formance after using fusion paradigm is much better

compared to that of the single sensor. The fusion

process enhances the target existence information,

the centralized fusion method obtains the best per-

formance as expected. The performance of track-to-

track fusion process is worse than centralized method

but much more efﬁcient in the sense of computational

expense. And the performance of track-to-track fu-

sion using a lower local track conﬁrmed threshold is

better compared to the one uses higher value because

more information is transmitted to the fusion center.

In Figure 5, the root mean square position er-

rors are shown. The position estimates after fusion

are more accurate compared to single sensor perfor-

mances. Since both centralized and distributed fusion

take advantage of the information from all the sen-

sors, they obtain similar performances.

Here the average number of measurements ob-

tained by each sensor at each scan over 300 runs and

the average number of conﬁrmed tracks (treated as

measurements at the fusion center) transmitted to the

fusion center of each sensor at each scan over 300

runs are shown in Figure 6. This ﬁgure indicates that

in the distributed fusion structure, local sensor trans-

mits much less information to the fusion center which

makes this structure more efﬁcient compared to cen-

tralized fusion especially in high clutter environment.

When adjusting the conﬁrmed threshold, the number

of tracks transmitter to the fusion center changed a lit-

tle bit, this is due to the fact that the tracks excluding

conﬁrmed true tracks cannot survive for a long period

(they are merged or terminated).

0 5 10 15 20 25 30 35 40

scan

number of measurements at each scan

Local sensor

T2TF

T2TF−2

Figure 6: Number of measurements at each scan.

5.2 Simulation Two

The simulation scenario demonstrated in Figure 3 is

applied. Only distributed fusion structure is consid-

ered to compare MD-LM-IPDA and LM-IPDA in or-

der to show the difference between multiple detection

structure and single detection structure. The simu-

lation parameters used by these two algorithms are

shown in Table 2 and the other parameters about tar-

gets and environment background are the same as

those given in subsection 5.1.

Figure 7 demonstrates the number of conﬁrmed

true tracks for all these three targets. It is obvious that

MD-LM-IPDA has a bitter performance compared to

LM-IPDA in the sense of true track conﬁrmation. The

root mean square position errors for each of these

three targets are similar so that only the performance

for target 2 is shown in Figure 8. From this ﬁgure, we

can see that the target state estimation error of MD-

LM-IPDA is lower than that of LM-IPDA.

Track-to-track Fusion using Multiple Detection Linear Multitarget Integrated Probabilistic Data Association

437

Table 2: Simulation parameters.

LM-IPDA MD-LM-IPDA

Initial PTE 0.0001 0.0001

Conﬁrmed threshold (local) 0.1 0.1

Conﬁrmed threshold (fusion center) 0.97 0.97

0.7 [0.4,0.3]

0.7 0.7

Number of conﬁrmed false tracks 1 1

Simulation time (per each run) 0.24s 0.26s

5 10 15 20 25 30 35 40

100

200

300

400

500

600

700

800

900

scan

number of confirmed true tracks

number of CTTs at Each Scan for All Targets

LM−IPDA

MD−LM−IPDA

Figure 7: Conﬁrmed true tracks for all the targets.

5 10 15 20 25 30 35 40

scan

root mean square position error (m)

RMSE for target2

LM−IPDA

MD−LM−IPDA

Figure 8: Root mean square position error of target 2.

6 CONCLUSIONS

In this paper, we propose both centralized and dis-

tributed fusion structures based on a suboptimal mul-

tiple detection multitarget tracking algorithm called

MD-LM-IPDA. These two structures utilize the prob-

ability of target existence to cover the true track con-

ﬁrmation and false track discrimination problem.

In the distributed fusion paradigm, local sen-

sor uses the target existence information to conﬁrm

tracks. Only conﬁrmed tracks are transmitted to the

fusion center and used as measurements to update

global tracks. By adjusting the local track conﬁrmed

threshold, the amount of information (track states and

target existence probabilities) transmitted to the fu-

sion center can be controlled.

Since centralized fusion utilizes the information

from all the measurements, it obtains the best per-

formance with a high communication burden between

local sensors and fusion center. In distributed fusion

structure, local sensors process tracking algorithm to

generate tracks and send high quality tracks (with

high probability of target existence) to the fusion cen-

ter which makes this structure more feasible in many

practical applications.

When distributed fusion structure is considered,

MD-LM-IPDAoutperforms LM-IPDA in the sense of

true track conﬁrmation and state estimation accuracy.

This performancesuperiority of MD-LM-IPDA is due

to that multiple detection structure helps to extract tar-

get state information contained in measurements by

considering more possible target oriented measure-

ment combinations.

ACKNOWLEDGEMENTS

This work was supported by LIGNEX1 under the con-

tract LIGNEX1-2017-0201(00).

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