Modified VSIMM Algorithm Design for Target Tracking

F3C.1

Modified VSIMM Algorithm Design for Target Tracking Huiqiang Zhuang1, Hongping Gao1, Chang Ho Yu2, Jae Weon Choi1, Tae Il Seo3, and Eui Jin Kim3 1

School of Mechanical Engineering, Pusan National University, Busan, Korea (Tel:+82-51-510-3203; E-mail: [email protected]; [email protected]; [email protected] ) 2 Department of Intelligent Mechanical Engineering, Pusan National University, Busan, Korea (Tel: +82-51-510-3203; E-mail:[email protected] ) 3 Naval Combat Systems PEO, Agency for Defense Development (ADD), Jin-Hae, Korea (Tel:+82-55-540-6704; E-mail:[email protected]; [email protected]) Abstract This paper presents a modified variable structure interacting multiple model (M-VSIMM) estimator for the complex hybrid maneuver target tracking issue with an application to the fire control system (FCS) using on warships. We designed the target model groups through the 3D dimensional dynamic target models. And we proposed optimal model group selection logic instead of the activation and termination logic in original VSIMM. The optimal model group selection logic responds the system faster. The simulation results in this paper compare with the tracking performance of the Kalman, VDIE, IMM and M-VSIMM filter in different maneuver conditions. Keywords: VSIMM, M-VSIMM, IMM, Kalman Filter, Target Model, Estimation, Target Tracking.

1. INTRODUCTION Nowadays in the VSIMM algorithm, they design the target model groups only using constant acceleration model with different initial acceleration vector in 2dimension [1]. This design method of target model group is difficult to be used in 3-dimension case because it will create a large number of target models in 3 directions and the model group design logic will not be suitable anymore. And it also has bad tracking performance when the maneuver acceleration is out of the bound. In order to solve those problems, we proposed the modified VSIMM filter to make a new algorithm – M-VSIMM filter [2]. We redesigned the target model groups using a new method in 3 dimensional case through Constant Velocity (CV) Model , Constant Acceleration (CA) Model , Abrupt Acceleration (AA) Model, 3D Constant Turn (CT3) Model and Singer Models with different maneuver times . And we propose the optimal model group selection logic instead of the activation and termination logic in the VSIMM which were shown in [3]. The new model group switching logic responds the system faster.

M 0 : [ m1 , m2 , m3 , m 4 , m5 , m6 ,m7 ] M 1 : [ m1 , m 2 , m 4 ] M 2 : [ m1 , m3 , m5 ] M 3 : [ m1 , m4 , m6 ] M 4 : [ m1 , m2 , m7 ]

Total target model group transition probability matrix is design as [2]. 3. M-VSIMM ALGORITHM M-VSIMM Algorithm Cycle: (The flowchart of M-VSIMM is shown in Fig. 1) Step 1: IMM Algorithm Cycle [4]. In this step increase the time counter k by 1, and run the IMM [ M k | Z k ] cycle. Step 2: Activation. Activate a candidate model group when both of the following two conditions are satisfied: x% > x%max (1) Tracking Error :

m2 : Constant Acceleration Model(CA)

µ kM k < tmin (2) Model Group Probability : Here x%max and tmin is design parameter. If the activation is true, go to next step. And if the activation is not true, output the estimation state xˆk and the error covariance Pk , let M k +1 = M k . Go to Step 1. Step 3: Optimal model group selection. In this step run IMM [ M 0 | Z k − a : Z k ] loop. Calculate

m3 : Constant Turn 3D(CT)

the model probabilities µ ki for total model group M 0 :

2. TARGET MODEL GROUPS DESIGN 2.1 Target Model Define We define the target models as follow: m1 : Constant Velocity Model(CV)

m4 : Abrupt Acceleration Model(AA) m5 : Singer1 τ = 60s (lazy turn) m6 : Singer2 τ = 60s (evasive maneuver) m7 : Singer3 τ = 60s (atmospheric turbulence) where τ is maneuver time. 2.2 Model groups define

µ ki =

∑

Lik µˆ ki k −1 mi ∈M 0

Lik µˆ ki k −1

, ∀ mi ∈ M 0 (i=1:7)

(3)

where the likelihoods {Lik } and predicted model probabilities

{µˆ ki |k −1}

were

obtained

in

the

IMM [ M k | Z k ] cycle at time k − 1 . Calculate the summation probability of each model group.

ICMIT 2009 2009 International Conference on Mechatronics and Information Technology

Mj

µk =

∑

mi ∈M j

µ ki

M-VSIMM model group switching times : 20 .

(4)

(Group j = 1,2,3,4 ; Model i = 1,2,3) M If µ k j = max[ µkM1 µkM 2 µkM 3 µkM 4 ] , then M j is the activated model group. Step 4: Update. Here run IMM [ M j | Z k ] cycle, and output the estimation state xˆk and the error covariance Pk . Let M k +1 = M j , then go to step 1. Initialization

Fig. 3 Tracking RMS Error k:=k+1 IMM [Mk |Z k] N

Activate a group?

Mk+1 = Mk

Output

Y

IMM [M0 | Zk-a : Z k] Calculate the model probability µiM 0 ( i = 1:7 ) Sum of each group probability Max[

µM

j

] = Mj

µM

j

( j = 1:4 )

( j = 1,2,3,4 )

IMM [ Mj | Z k ] Output Mk+1 = Mj

Fig. 1 Flowchart of M-VSIMM 4. SIMULATIONS

The simulations here show the comparisons of the tracking results between Kalman filter, VDIE filter, IMM filter and MVSIMM filter in non-maneuver, high-maneuver respectively. 4.1 Simulation Conditions
Radar error : Range error is 5m; Angle error is 0.5 × 102 rad ;
Sampling time interval : T = 0.1s
Maximum error : x%max = 5m
Limit model group probability : tmin = 0.3 Table 1. Target Maneuver Conditions. 4.2 Simulation Results Simulation 1: Non-Maneuver M-VSIMM model group switching times : 0 .

Fig. 2 RMS Error Here shows in non-maneuver target tracking case, Kalman filter tracking with the best performance. Simulation 2: High Mixed Maneuver

5. CONCLUTIONS From the simulation we can see that to track more complex mixed maneuver target will have more model group switching times in M-VSIMM filter. IMM is a little better than M-VSIMM to track the simple mixed or single type maneuver target. The reasons is MVSIMM has to make initialization when the model group switching occurred. System has to spend a short time to get into the steady state again. So, for most conditions, IMM filter is good enough to track the target. The advantage of M-VSIMM is to track the target in complex mixed maneuver with high speed and high maneuver conditions. Variable structure IMM filter is a very young theory and it still need more improvement. VSIMM estimator will have more and more applications on target tracking area in the future. ACKNOWLEDGEMENT This work was supported by a grant (UD080002KD) from basic research program of the Agency for Defense Development (ADD), Korea. REFERENCE X. R. Li, X. R. Zhi, Y. M. Zhang, “Multiple-Model Estimation with Variable Structure-Part IV: Design and Evaluating of Model-Group Switching Algorithm,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 1, January 1999. [2] H.Q. Zhuang, “VSIMM Based Target Tracking Filter Design,”, KACC Conference 2009. [3] X. R. Li, X. R. Zhi, Y. M. Zhang, “Multiple-Model Estimation with Variable Structure - Part III: ModelGroup Switching Algorithm,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 35, No. 1, January 1999. [4] E. Maxor, A. Averbuch, Y. Bar-Shalom, J. Dayan, “Interacting Multiple Model Methods in Target Tracking: A Survey,” IEEE Transactions on Aerospace and Electronic Systems, Vol. 34, No. 1, January 1998. [1]