Department of Electronic and Optical Engineering, Ordnance Engineering College, Shijiazhuang, , China

Transcription

1 6th International Conference on Machinery, Materials, Environent, Biotechnology and Coputer (MMEBC 06) Solving Multi-Sensor Multi-Target Assignent Proble Based on Copositive Cobat Efficiency and QPSO Algorith Gongguo Xu,a, Xiusheng Duan,b, Wenhua Hu,c, Hailong Zhang,d Departent of Electronic and Optical Engineering, Ordnance Engineering College, Shijiazhuang, , China China Xi an Satellite Control Center, Xi an, 70043, China a eail: xugguo@yeah.net, beail: sjzdxsh@63.co, ceail: hwhgaq@sina.co, deail: woishailong@sina.co Keywords: Multi-Sensor Multi-Target Assignent; Quantu Particle Swar Optiization; Air Defense Syste Abstract. Aiing at the ulti-sensor ulti-target assignent (MSMTA) proble under coplex air defense cobat environent, a new MSMTA odel is proposed with the copositive cobat efficiency of the identification, tracking and positioning stage. And then, the quantu particle swar optiization (QPSQ) algorith is iported in order to solve the MSMTA proble. Finally, the experients show that the new MSMTA odel is effective and copare the perforances between the QPSO and particle swar optiization (PSO) algoriths. Introduction With the developent of the odern warfare, air defense cobat environent is becoing ore and ore diversified and coplicated with characteristics of whole-airspace, all-weather, ulti-sensor, and ulti-target. Therefore, the role of sensor anageent is becoing ore and ore proinent, especially in the C3I air defense syste. The ulti-sensor ulti-target assignent (MSMTA) proble is the key proble in sensor anageent. In order to achieve axiu cobat effectiveness and eet the real-tie requireent in the battlefield, that the sensor resources are allocated to ultiple targets quickly and rationally has becae the research focus in the odern air defense, cobat and coand syste. MSMTA proble is a classic NP-hard coplete proble belonging to the ilitary operation research, which actually is the nonlinear and ultiple constraints integer prograing proble. The ain difficulty is to solve the coplex proble accurately and rapidly. There are lots of traditional solving ethods, such as prograing theory[], covariance control theory[], inforation theory[3], gae theory[4], etc. Each ethod has its strengths and applicable situations. On the basis of the above researches, this paper analyses the influence of each cobat stage perforance to the copositive cobat efficiency based on the actual process of the air defense operation, and a new STA odel is proposed with the copositive cobat efficiency of the identification, tracking and positioning stage. The proposed odel is ore close to the actual battlefield environent. And then, the quantu particle swar optiization (QPSQ) algorith is iported to solve the MSMTA proble. Finally, the experients show that the new MSMTA odel and QPSQ algorith are effective. MSMTA Proble Objective Function The traditional ulti-sensor ulti -target assignent ethods generally regard a single ai as the objective principle of distribution, such as the axiu probability of detection, the optial accuracy of the positioning[] or the axiu inforation gain[4]. However, in the actual air defense cobat operation, a single ai does not describe the operational process, which has its liitations. Besides, the task of the sensor anageent becoes ore and ore coplex. In the air defense cobat, sensor tasks include search, interception, identification, tracking, and positioning. 06. The authors - Published by Atlantis Press 089

2 The perforance of different sensor in different stage is different. Therefore, cobined with the practical battlefield environent, a new allocation odel is built based on the ultistage copositive cobat efficiency including identification, tracking, positioning stage. Furtherore, coputing ethods of cobat efficiency fusion are also proposed. The calculation ethod is proposed as follows: Gain = c Reco + c Trac + c3 Loca. () where, the Gain is the copositive cobat efficiency, the Reco is identification cobat ability, the Trac is tracking cobat ability, the Loca is positioning cobat ability; ccc 3 are the weights, and c + c + c =, ccc 3 [0,], which can change according to the actual environent. 3 MSMTA Proble Model Assuing in an air defense operation, the target nuber is n represented ast, T,... T; n the sensor nuber is represented as S, S,... S, and each sensor tracking ability is C, C,... C ; therefore, the tracking ability of the syste is C = C + C C. When a target is tracked by two sensors siultaneously, the concept of virtual sensors is introduced in, which constitutes the new sensor. At the sae tie, the nuber of the sensor should be ( + )/; the copositive cobat efficiency can be calculated by the forula() shown in the atrix Gain[ n,( + ) / ] : G G... G ( + )/ Gain = Gij... () Gn Gn... G n ( + )/ n ( + )/ where, Gij is the copositive cobat efficiency when the sensor i is assigned to the target j. Furtherore, the assignent atrix is defined as R = [ r ij ] n,when the sensor i is assigned to the target j, r ij =; otherwise, r ij =0 Through the above analysis, the STA proble in air defense operation can be converted to the following odel: n Maxiize P( Ti ) Gain( i, R). (3) i= i= and the constraint conditions are as follows: rij j= n r ij n C j rij C j= i= t Tax where, C j is the tracking ability of sensor j, C is the tracking ability of the syste, T ax is tie liit. PT ( j ) is target priority deterination of sensor j. Quantu Behaved Particle Swar Optiization Algorith After the establishent of the MSMTA odel, the proble has been transfored into a cobinatorial optiization proble. Especially when the nubers of sensors and targets are large, the coplexity of this proble is relatively high. In view of the traditional PSO algorith easily falls into the local optiization and has slow convergence speed, the QPSO algorith is iported to solve the proble in this paper. In order to avoid disadvantages of the general particle swar optiization (PSO) algorith. On the basis of quantu theory, the quantu behaved particle swar optiization algorith is (4) 090

3 proposed by Sun Jun [5]. This ethod gives the quantu behaved particle, that is, the position of the particle is described by the wave function, and the particle state is decided by the Schrodinger Equation. The specific particle position equation is as following: xt ( ) = Q± L / ln( / µ ) (5) where, the µ is the rando nuber on the [0,], L Q can be calculated by the forula(6) and forula(7). L( t + ) = b () t best() t x() t (6) Qt () = ϕpib () t + ( ϕ) pgb () t (7) where, β = 0.5( iter / iter), iter is the iterations, iter is the axiu nuber of iterations, best is the average value of particles, ϕ is the rando nuber on the [0,], pib () t is the best value of particle i, pgb () t is the best value of all particles. And then, the particle position equation is shown below. x() t = ϕpib () t + ( ϕ) pgb () t + rand() t b() t best() t x()ln(/ t ) (8) where, if ( ψ 0.5) rand() t = (9) if ( ψ 0.5) and ψ is also the rando nuber on the [0,] Copared with the general PSO algorith, QPSO algorith, because of the introduction of the characteristic of quantu particle, the whole searching ability of QPSO algorith is iproved greatly. Siulation Results Assuing in an air defense operation, the target nuber is 6 represented ast, T, T 3, T 4, T 5, T 6 ; the sensor nuber is also 6 represented as S, S, S 3, S 4, S 5, S 6, in which the tracking ability of S5 S6 is 3 and the tracking ability of S S S 3 S 4 is only ; and the copositive cobat efficiency is shown in Table ; every target is allocated up to sensors; the particle nubers is 50 and the axiu nuber of the iteration is 00. Table The total cobat effectiveness of sensor-target assignent T T T3 T4 T5 T6 S S S S S S S &S S &S S &S S &S S &S S &S S &S S &S S &S S3 &S S3 &S S3 &S S4 &S S4 &S S5 &S

4 Fig The optial allocation schee T T T3 T4 T5 T6 (S S6) (S4 S6)(S5 S6)(S3) (S) (S5) The optial allocation schee of the Siulation Results is shown in Fig 8. The best copositive cobat efficiency is ,and the consuption tie is 0.47s, which eets the real-tie requireent. Besides, the results are also eet other conditions. Every target is allocated up to sensors. Every target allocated to one sensor is not ore than the tracking ability of the sensor. In suary, the experient shows that the iproved algorith is effective. For the further analysis of the perforance of QPSO algorith, through the experient, the QPSO and PSO algoriths were copared. Selecting the top 00 iteration steps in a process of optiization, the global best values are shown in Figure. Fro the figure, the QPSO algorith has a better searching ability than the PSO algorith and QPSO, which has better global optiization ability and consues less tie. Fig The coparison of convergence curves of the three algoriths On the basis of the above experients, repetitive operation of 00 ties, the experiental results are shown in Table. Obviously, the average optiization value and the success rate through the QPSO algorith are both better than the PSO algorith. The variety of 00 experiental results are respectively shown in the Figure 3 and Figure 4, it is obvious to see, the QPSO algorith searching is ore stable and has better optiization results. Table The coparison of algorith perforances PSO QPSO Average Optiization Value Success Rat Average Steps Consued

5 Fig 3 The optiization results of PSO algorith Fig 4 The optiization results of QPSO algorith Conclusions This paper has focused on the proble of the ulti-sensor ulti-target assignent (MSMTA) under coplex aerial defense cobat environent. The study can effectively solve the MSMTA proble, and has a great effect to iprove the ability of the ground air defense cobat. Moreover, the QPSQ algorith also has great application value for other ulti-attribute decision aking probles. In the future, the research effort should be focused on the iproveent of the QPSQ algorith. References [] Chhetri A S, Morrell D, Papandreou- Suppappola A. Sensor resource allocation for tracking using outer approxiation[j]. IEEE Signal Processing Letters, 007, 4(3): 3-6. [] Zhou Wenhui, Hu Weidong, Yu Wenxian. An Adaptive Sensor Allocation Algorith with Covariance Control[J]. Signal Processing, 005, ():57-6.( In Chinese) [3] Fowler M L, Chen M, Binghaton S. Fisher inforation based data copression for estiation using two sensors[j]. IEEE Transactions on Aerospace and Electronic Systes, 005, 4(3):3-37. [4] MA Fei, CAO Ze-yang, LIU Hui. Construction and search of strategy space of target assignent based on gae theory[j]. Systes Engineering and Electronics, 00, (9): (In Chinese) [5] Sun J. A global search strategy of quantu-behaved particle swar optiization[c]//proceedings o f IEEE conference on Cybernetics and Intelligent Systes, 004: