Application of Multi-sensor Track Fusion Technology in Fire Control Radar Network

Wang Fujun1 , Ding Xiaoyan2 , Kong Min1

1.Beijing Satellite Navigation Center 2.Geographical Science Research Institute, Hebei Academy of Science

Beijing 100094, China Phone: +86-15201138929, Email: fujunwang@163.com

Abstract – This paper presents a fire control radar networking solution to improve the probability of intercepting the cruise missile. It is the basic idea that fire control radars working alone are linked to the central computer to form a distributed fire control radar network system. Every fire control radar is a node in the network, it can scan and track independent target. At the same time, it sends state information (target state information of node) to central computer. The central computer uses fusion algorithm to produce fused target state information (target state information of system), and then which is returned to node. It has the potential to improve target tracking accuracy and aerial defense domain. Firstly, the functional architecture of the fire control radars network is proposed. Secondly, some robust, practical track fusion algorithms, such as track-to-track association, track fusion and track management etc., are introduced. Finally, track fusion algorithms are tested with different scenario (parallel, cross, bifurcation, maneuvering trajectory). The test result shows that through constructing a fire radar network under low cost, the target track accuracy and the scope of tracking target can be improved largely.

Keywords –data fusion, track-to-track association, track fusion.

I. INTRODUCTION

Cruise missile is a kind of important, high precision attack weapon in modern war. Because of its characteristics of high accuracy, low altitude flight, small reflecting area, it poses a deadly threat to aerial defense system. The research on how to effectively fight against cruise missile technology and tactics has become an extremely important task for homeland defense. Aerial defense missile is used usually to intercept cruise missile. But the practice proved that only aerial defense missile system is unable to finish the interception task completely. The aerial defense group must be formed by a variety of aerial defense system. They are overlap in the distance and firepower, the continued firepower attacking is done in the cruise missile flight process in order to improve the probability of interception. For example, the United States often utilizes the composition of aerial defense system which is composed of "Patriot", "Hawke" and antiaircraft gun to protect important military targets. Through the analysis of performance parameters of cruise missile

and antiaircraft gun system, antiaircraft gun system can be incorporated into the cruise missile defense system. Antiaircraft gun with the rapid maneuvering, continuous shooting and low cost characteristics and missile with precise attack, large shooting range advantages can both be given full play. In order to further enhance the role of the existing antiaircraft gun in cruise missile defense, improve tracking accuracy and the probability of intercepting cruise missile, we can adopt multi-sensor information fusion technology to reform the existing fire-control radar of antiaircraft gun system and linked them to central computer, construct a fire-control radar network system[7].

This paper will be organized as follows. Section II describes fire control radar network structure based on data fusion technology; Section III presents the track fusion algorithms operating at central station computer, including track-to-track association, track fusion and track management. Etc. In section 4 we will show the result of simulation in different scenarios and finally Section 5 summarizes the main results.

II. FIRE CONTROL RADAR NETWORK STRUCTURE

Fig. 1. Schematic diagram of the structure of fire control radar network based on information fusion technology

Every fire control radar system in fire control radar network searches and tracks independently target, estimate target state (target position and kinematical information), calibrate time and space position coordinate, and sent those target information (target track of node) to the central station computer. At first, central station computer processes the association of tracks from different nodes. If the central station computer receives only the target track of one node, directly use it as the target track of fusion center (target

sensor

sensor

sensor

Pre-process

Pre-process

Pre-process

Target tracking

Target tracking

Target tracking

Trackassociatio

n

Trackfusio

n

Fire-control radar node Fusion center

System

track

The 11th IEEE International Conference on Electronic Measurement & Instruments ICEMI’2013

____________________________________978-1-4799-0759-5 /13/$31.00 ©2013 IEEE

�

track of system). Otherwise, tracks from the same target are associated using track-to-track association algorithms. Secondly, then track fusion is performed and target track of system is obtained. Finally the threat estimation and firepower distribution are done. All the information about certain node is distributed to that node in the network. Fire-control radar node computes the firing data and control antiaircraft gun to attack target according to those information. System structure of fire control radar network based on track fusion technology is shown in Fig. 1 [1, 4].

III. DATA FUSION ALGORITHM

It can be seen from structure of Fig. 1 above that fire control radar track fusion system includes mainly two parts: track association and track fusion. Before we built fire radar network, two problems must be considered: one is that the fusion accuracy is not less than the lowest accuracy of every fire control radar node; the other is that the fusion algorithm must meet the real-time requirements. We study next the track association and track fusion algorithm operating in the central computer according to the real-time and accuracy requirements of fire control radar system.

A. Track association algorithm

Track association is also called validation of measurements (gating), which is a technique for eliminating unlikely measurement-to-track pairs. A validation region (gate), corresponding to the predicted positional uncertainty, is formed around the predicted track position. If it is decided that two tracks from different nodes represent the same target, then track fusion is performed to combine their corresponding state estimate. If two tracks of different target are represented into track fusion algorithm, track accuracy of system is even lower than track accuracy of node. This is the ambiguity of the association. It is the main problem of data fusion to overcome. Therefore, track association must be performed before track fusion. The central computer receives the node track data coming from radar node (time and space alignment are performed), distinguish which come from the same target, and which come from different target. The track to track association (normalization) are performed.

Track association problem was presented at first by singer, Etc. At present the main algorithms include weighted test statistics approach, modified weighted test statistics approach, independent sequential approach, relative sequential approach, limited memory and attenuation memory association approach. Article [1-3] introduced those algorithms, presented a comparison of track performance for those algorithms. The last three algorithms are better than the front two algorithms. Considering number of attacking cruise

missile is small and manoeuvring ability is poor, we choose limited memory algorithm. At first we introduce weighted test statistics approach below, and then derive limited memory sequential approach.

1. Weighted test statistics algorithm Given two target state estimate i and j from two

nodes at time k ,ˆ ( ) [ , , ]i i i iX k x y z� ; ˆ ( ) [ , , ]j j j jX k x y z�

Given the two error covariance matrixes,

1 2 3( ) ( , , )i i i iP k diag p p p�

1 2 3( ) ( , , )j j j jP k diag p p p� ;Define two hypotheses:

0H )(ˆ kX i and )(ˆ kX j are the node state estimate from the same target;

1H )(ˆ kX i and )(ˆ kX j are the node state estimate from the different targets;

Then test statistical is given by 1ˆ ˆ( ) ( ( ) ( )) ( ( ) ( ))ij i j T i jD k X k X k P k P k �� � �

ˆ ˆ( ( ) ( ))i jX k X k� �2 2

1 1 2 2

( ) ( )i j i j

i j i j

x x y yp p p p� �

� �� �

2

3 3

( )i j

i j

z zp p�

��

Assuming that estimate error of two nodes to the same target is statistical independence in above formula.

Assuming zero-mean white noise processes in the hypotheses 0H . Thus test statistical D ij )( k have an

approximate )(2 n� distribution. Let 3�n , and probability level is given by

05.095.011 ����� CAP� , Where CAP is the probability of correct association rate. We can obtain a gate )3(95.0

2� =7.815. If test statistical

D ij 815.7)( �k , the hypotheses become 0H .That is to say, state estimate i and j are association. Otherwise, the hypotheses becomes 1H , they are not association.

2. Limited memory sequential algorithm Weighted test statistics approach computers test

statistics base on a target sample, then selects hypotheses. Under probability level is determined, the probability of correct association and false association are respectively ��� 1CAP and ��MAP . We know

the probability of false association FAP is related to probability level and sample rate. When the probability level is determined, in order to low the probability of false association FAP , we can increase the length of the target samples. The longer the target has been tracked, the more accurate the estimates. But the longer the

The 11th IEEE International Conference on Electronic Measurement & Instruments ICEMI’2013

�

target has been tracked, the longer initial decision time. Two factors must be considered comprehensively. According to the result of the simulation, we select sample rate 5m � . The formula is

1

1

ˆ ˆ( ) ( ( ) ( ))

ˆ ˆ ( ( ) ( )) ( ( ) ( )) ( 1) ( ) ( )

kij i j T

l k m

i j i j

ij ij ij

CS k X l X l

P l P l X l X lCS k D k D k m

� � �

�

� � �

� �

� � � � �

Because test statistics )(kCS ij has an approximate

)(2 mn� distribution. Where 155*3 ��mn . If probability level is

05.095.011 ����� CAP�Where CAP is the probability of correct association.

Then We can obtain a gate )15(95.02� =24.996. if

)(kCS ij � 24.996, track i and track j are association, otherwise, they are not association.

Considering that test statistics is calculated based on multi-samples, limited memory sequential algorithm ignores the influence of common noise of node track. This algorithm is simple and needs smaller computational burden and less filter parameter.

B. Track fusion algorithm

For intercepting attacking cruise missile in real time, beside track fusion algorithm has the high probability of correct association, and it must meet real time requirement. Then algorithm must be simple. Cross-covariance weighted fusion algorithm, which ignores the influence of the common noise, is suboptimal algorithm in the maximum likelihood estimation. But it is simple, and need less filter parameters; we select it as track fusion algorithm. The node track is:

ˆ ( ) , , 1 2Ti i i iX k x y z i N �� �� �

Where N ( 8N � ) is node track number coming from the same target in time k .

The prediction error covariance matrix is

1 2 3( ) ( )i i iiP k diag P P P� 1 2i N� �

Then fusion solution is:

�

��

�

��

���

�

N

i

iiN

i

iF kXkPkPkX1

11

1

1 )(ˆ)()()(ˆ

��

�

���

�

�

�

�

�

�

�

N

i iP

N

i iP

iz

N

i iP

N

i iP

iy

N

i iP

N

i iP

ix

1 3

1

1 3

1 2

1

1 2

1 1

1

1 1 ,,

Considering that the measurement model of fire-control radar is similar, and track prediction error covariance matrix is similar. Then equal weighted fusion is used. The fusion solution which is simplified is:

1

1

1 1 1

1 1 1

ˆ ˆ( ) ( )N

F iN

i

N N Ni i i

N N Ni i i

X k X k

x y z

�

� � �

�

��� ��

C. Track management

Track management mainly finishes management of target track number and another some event. Main content include:

1. Number initial target track. 2. Relay target track number. 3. process the false association problem of target track. 4. shift fire-power of fire-control system. 5. Process intermittent track of fire-control system 6. Export target track.

IV. FUSION ALGORITHM SIMULATION

To confirm the validity of the track association and fusion algorithm, we developed a simulation platform. Fire-control node configuration ( 1 8FC FC� ) is shown in Fig. 2:

Fig. 2. The configuration of fire-control radar node

The simulation system can generate target trajectory which are added motion noise, measurement noise, and Kalman filter process. by setting parameters. It can generate parallel, cross, bifurcation and manoeuvring target trajectory at the same time. At first, eight fire control radar nodes track targets (Kalman filter) and then send estimated state of target to fusion center. Fusion center performs track-to-track association and

The 11th IEEE International Conference on Electronic Measurement & Instruments ICEMI’2013

�

fusion algorithm, finally obtain the system track and return it to eight fire control radar nodes.

A. The simulation example 1:

The performance of the fusion algorithm in this section is evaluated with constant trajectory shown in Fig. 3. Target is moved at constant speed all the time. A comparison of the root mean square error (RMSE) of target position coordination in the X direction for a node, fusion system consisting of three nodes and fusion system consisting of eight nodes is presented respectively in Fig. 4, Fig. 5 and Fig. 6. It can be seen from the result of simulation that the track performance of fusion system is better than that of Kalman filter of one node, and the more nodes, higher track accuracy of fusion system is.

Fig. 3. The motion trajectory of target 1

Fig. 4. The errors in the x position estimates for kalman filter of one node (unit: m)

Fig. 5. The errors in the x position estimates for fusion algorithm of three nodes (unit: m)

Fig. 6. The errors in the x position estimates for fusion algorithm of eight nodes (unit: m)

B. A simulation example 2:

The performance of the fusion algorithm in this section is evaluated with the highly manoeuvringtrajectory shown in Fig. 7. Target starts to move at constant velocity, then a 2g turn is made, after which the

target returns to constant velocity motion. A comparison of the root mean square error (RMSE) of target position coordination in the X direction for a node, fusion system consisting of three nodes and fusion system consisting of eight nodes is presented respectively in Fig. 8, Fig. 9 and Fig. 10. It can be seen from the result of simulation that track performance of fusion system, whether three nodes or eight nodes, is not very obvious in the target manoeuvring period. But track performance of the entire track is much better than that of Kalman filter of one node, and the more nodes, higher track accuracy of fusion system is.

Fig. 7. The motion trajectory of target 2

Fig. 8. The errors in the x position estimates for kalman filter of one node (unit: m)

Fig. 9. The errors in the x position estimates for fusion algorithm of three nodes (unit: m)

Fig. 10. The errors in the x position estimates for fusion algorithm of eight nodes (unit: m)

V. CONCLUSION

This paper has presented a solution based on the existing aerial defense weapon system to improve the cruise missile interception probability, where

The 11th IEEE International Conference on Electronic Measurement & Instruments ICEMI’2013

�

fire-control radars are connected together to the central computer through the network. According to this solution, we need only to change existing weapon system very small, and add a central computer. But the result of simulation shows that this fire-control radar network can not only expand the target range, but also improve target track accuracy. Thus it greatly improves cruise missile defence capability of aerial defence troop.

ACKNOWLEDGMENT

The author wishes to thank all colleagues who previously provided technical support.

REFERENCES

[1] HE Y, WAN G H, LU D X,et al. Multisensor Information fusion with Application[M]. Publishing House of Eletronics Industry, Dec. 2007.

[2] LIU T M, XIA Z X,XIE H CH. Data Fusion Technology and Application[M]. National Defense Industry Press, Oct. 2009.

[3] HE Y, LU D X,PENG Y N. Survey of Multisensor Data Fusion Algorithm[J]. Fire Control and Command Control, 1996,21(1): 14-22.

[4] HE Y, LU D X ,PENG Y N. Survey of Multisensor Data Fusion Model[J]. Journal of Tsinghua University, 1996,36(9):58-63.

[5] SINGER R A, KANYUCK A T. Computer Control of Multiple Site Track Data Automation. 1971,7(3): 455-463.

[6] DITZLER W R. A Demonstration of Multisensor Tracking[C]. In Proceeding of the 1987 Tri-Service Data Fusion Susposium, 1987:303-311.

[7] ZHU Y CH,ZHAO F H. Principle and Application of Fire Control System [M]. National Defense Industry Press, Oct. 1994.

AUTHOR BIOGRAPHY

Wang Fujun was born in Tangshan, China, in 1972. He received BS from Kunming Engineering College, China, in 1997. He received MS and PhD from Shijiazhang Machanical Engineering College, China, in 2005 and 2008, respectively. Now he is an engineer in Beijing Satellite Navigation Center, China. His research interests include information fusion, satellite navigation.

Ding Xiaoyan was born in Shijiazhuang, China, in 1972. He received BS from Hebei Economy and Trade University, China, in 1996. Now he is an engineer in Geographical Science Research Institute, China. His research interests include computer, and mathematical statistics.

The 11th IEEE International Conference on Electronic Measurement & Instruments ICEMI’2013

�