- Email: [email protected]
UKF-based multi-sensor passive tracking with active assistance1
Journal o f Systems Engineering and Electronics, VoL. 1 7 , No, 2,2006, p p . 245
-250
UKF-based multi-sensor passive tracking with active assistance* Li Anping, Jing Zhongliang & H u Shiqiang Inst. of Aerospace Information and Control, School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong Univ. , Shanghai 200030, P. R China (Received January 18, 2005)
Abstract: A new synergy tracking method of infrared and radar is presented. To improve tracking accuracy, the unscented Kalman filter (UKF) , which has better nonlinear approximation ability, is adopted. In addition, to reduce the possibility of radar being locked-on by adverse electronic support measure (ESM) , radar is under the intermittent-working state. After radar is turned off, the possible target position is estimated by a set of time polynomials, which is constructed based on the sufficient observations done before radar is turned off, the estimated values from time polynomials are compared with the current observation values from infrared to determine the time when radar is turned on Simulation results show the method has a good tracking accuracy and effectively reduces the possibility of radar being locked-on by adverse ESM. Key words: active radar, infrared, least square, time polynomial, the unscented Kalman filter.
1. INTRODUCrION Radar can provide complete position information and/or Doppler information Of target 7 but it electromagnetic wave when it works, SO it easily suffers from electromagnetic interference and antiradiation missile’s attack. On the contrary, infrared doesn’t emit any energy, it detects and locates target by receiving thermal energy radiated from target, so it has the powerful anti-interference ability. Just because infrared doesn’ t radiate any energy, it can’ t be easily detected and located, which makes it has good covertnessL1]. But its 2-D target observations are not sufficient to locate targetsL2’. So in many cases, it has become a complementary way to combine infrared with radar. About the infrared/radar tracking, a lot of methods have been p r o p o ~ e d ~ ~ especially -~], in reducing the possibility of radar being locked-on by adverse ESML6-*’.Although these methods can effectively reduce the possibility of radar being locked-on by adverse ESM, the target range information can’t be achieved when radar is turned off, which may lead to bad tracking accuracy. To improve tracking accuracy, in this paper, the unscented Kalman filter algorithm, which has better
nonlinear approximation ability, is adopted; on the other hand, after the radar is turned off, a set of time polynomia~s are constructed to estimate
the
possible target range. Simulation results indicate that the proposed method has a good tracking accuracy and greatly decreases the possibility of radar being locked-on by adverse ESM.
2. SYNERGY TRACKING STRUCI’URE OF THE RADAR/INFRARED The tracking structures in this paper are shown in Fig. 1-Fig. 3.
The tracking system mainly in-
cludes four modules: the infrared tracking module, the radar/infrared tracking module, the maneuver detection module, and the tracking mode selection module. The whole working process is as follows.
(1) Let the infrared scan the surrounding environment alone, once a target is found or the target makes maneuver, turn on the radar.
(2) Let the radar and infrared work together for a while, then turn off the radar.
( 3 ) Construct a set of the time polynomials to estimate the target possible position after the radar is turned off.
(4) Compare the estimated values from the
* This project was jointly supported by the National Natural Science Foundation of China (60375008), the China Ph D. Discipline Special Foundation (20020248029) and the China Aviation Science Foundation (02D57003).
Li Anping, Jing Zhongliung & H u Shiqiang
246 time polynomials with the current observation values from the infrared to determine the time when the radar is turned on. (5) Select a tracking mode between the infrared tracking and the radar/infrared tracking according to whether the target makes maneuver. (6) Apply the unscented Kalman filter to the selected tracking mode. Measurement
Meas ement tracking
I
-Maneuver detection
Tracking mode selection
I
Fig. 1 Structure for the infrared tracking system with the intermittent-working radar
Target's track Fig. 3
points completely capture the true mean and covariance of the GRV, and, when propagated through the true nonlinear system, capture the posterior mean and covariance accurately to the second order for any nonlinearity. The EKF, in contrast, only achieves first-order accuracy. The unscented transformation (UT) is a method for calculating the statistics of a random vector that undergoes a nonlinear transf~rmation[~'.Let x be an n, dimensional random vector, g : Wz HWYis a nonlinear function and y = g ( x ) Assume that the mean and the covariance of x are and P,, respectively. The procedure for U T is as follows. 1 sigma Step 1 Calculate the set of 272, points and weights
.
+
I
Target's track Fig. 2
lem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample
Structure for the infrared tracking
I
Structure for the radarhnfrared synergy tracking
3. ALGORITHMDESIGN 3.1 Filtering Algorithm Design The tracking accuracy mainly relies on the filter algorithm. When the state and measurement equations are nonlinear, the most widely used method is the extended Kalman filter (EKF). But EKF only uses the first order terms of Taylor series expansion of the nonlinear functions, it often introduces large errors in the true posterior mean and covariance of the transformed Gaussian random variables (GRV) , which may lead to sub-optimal performance and sometimes divergence of the filter. In this paper, the unscented Kalman filter (UKF) is adopted. The UKF addresses this prob-
where (J(n,+A)P,); is the ith row or column of the matrix square root of (n, +A)P,, n, is state dimension, the definition of the parameters A , a and p can be found in Ref. [lo]. Step 2 Propagate each sigma points through the nonlinear transformation
Step 3 Compute y' s mean and covariance 2n-
(8) 2=0 2n-
i=O
After the unscented transformation, combining with target motion model (state equation is linear, measurement equation is nonlinear) , the
UKF-based multi-sensor passive trucking with active assistance
247 i
=
(23)
l,..-,l
where u;,d , * - * , ~ i , ~ ,--*,a;,, and ai,&,---,ai,,,,, are unknown coefficients, I is the number of target, m is the polynomial order. If the coefficients in Eq. (13) can be identified in real time, the motion model of the target will be obtained, and using this set of polynomials, the target state can be estimated after the radar is turned off. ( 1) Identification of the polynomial coeffi-
cients Assume the polynomial order is m (the order of the polynomial reflects the movement way of target, such as constant velocity movement, constant accelerate movement, etc ). To determine these coefficients, the radar and infrared must simultaneously scan the given scenario m 1 times. Suppose the radar and infrared scan target n ( n 3 m + l ) times after the kth time and the sample time is T , then the coefficients in Eq. (23) can be calculated by the following matrix equation.
+
(17) ( 3 ) Measurement update
+
variance, R is measurement noise covariance.
3.2 Parameter Identification of Target Motion Model
+ a&$+
( t ) = a;,&
yi ( t ) =
zi ( t )
=
+ t+
+ + ai,pntrn
ai,Zlt
ai,r2tZ
ui,yl
ai,y2
**.
+ ". +ai,ptm a;,&+ t +ai,,zt2 + + a;,*1
tZ
'.*
+
+
8 as
In general, the target motion trajectory can be approximated by some time polynomials. Assume the target motion trajectories in x , y and z directions are approximated by the following time polynomials. xi
yi
where & (k T ), (k T ) and Zi (k T ) are the estimated positions of the ith target in x , y and z directions at ( H T ) th time. If defining 2 , A and
Ui,Jrn
&(k+T) 2T)
$;(k+T) (k 2T)
ii(k+T)
+ Zi (k + 2T) Y;(k +nT) zi (k + n T ) i i
nT) rl R+T
(k
+ T)" 1
Li A n p i n g , Jing Zhongliang & Hu Shiqiang is the detection threshold, E E ( 0 , l ) . If any inequation in Eq. (29) is not met, it may imply that the target would have made some maneuver. The radar must be turned on in the next sample time.
8=
4. SIMULATION AND ANALYSIS
Eq. (24) can be rewritten as
Z=&
(25) 4.1
Simulation Tracks and the Initial Conditions
8 can be calculated using the least square method
e = (ATA)-’A=Z
(26)
Once these coefficients are determined, the states of target can be estimated by this set of time polynomials when the radar is turned off. (2)The polynomial order setting As a rule, the movement of target in a t h r e e dimensional space can be projected into x , y and z directions, respectively, with its constant velocity, constant acceleration, or variable acceleration. If we define 3 as the highest order of the polynomial, the target’s trajectory in x direction can be represented by Eq. (27). Equation (27) can completely describe the target movement way in x direction.
xi ( t ) = a i d
+
Ui,d
t
+
U i , d t2
i = 1,-.*,1
+
ai,z3 t3
(27)
3 . 3 Maneuver Detection Assume that the target estimated positions afe denoted by ( s ( k ) , y ( k ) ,i(k)) at the kth time after the radar is turned off, the estimated values (;(k), p(k) ,i(k)) in the spherical coordinates are calculated as
If the target makes no maneuver during the time in which the radar is turned off, the following inequationsC”’ must be met at the same time.
Suppose there is an observation station on the ground with an infrared and radar placed on the same platform. At the beginning, two targets are supposed to get close to the platform. The first one comes from an initial position 10 km in x direction, 12 km in y direction, and 10 km in z direction, with an initial velocity of -70 m/s in x direction, -100 m/s in y direction, and -90 m/s in z direction, the second one moves from an initial position 10 km in x , y , and z directions, with an initial velocity of - 80 m/s in x directions, -120 m/s and a constant acceleration of -2 m/s2 in y direction. Twenty seconds later, a third target appears in an initial position 10 km in x direction, 5 km in y direction, and 8 km in z direction. All three targets move towards the platform with a constant velocity. The velocity of the first one is -70 m/s in x direction, -100 m/s in y direction, and -90 m/s in z direction. The velocity of the second one is -80 m/s in x direction, -80 m/s in y direction, and -100 m/s in z direction. The velocity of the third one is -100 m/s in x direction, -60 m/s in y direction, and -100 m/s in z direction. The observation noises of two kinds of sensor are both Gauss white noise. The standard range and angle deviations for the radar are respectively 60 m and 5 mrad, the standard angle deviation for the infrared is 1 mrad. During the simulation, the observation values of the radar and infrared have been registered in the temporal-spatial domain. After the registration, the sample time is 1 s.
4 . 2 Simulation Results and Analysis
A simulation is performed on the above simulation are the azimuth and elevation standwhere a,, ard deviations of the infrared, ( a , (k) , & (k)) are the observation values of the infrared at kth time, E
tracks. In order to identify the coefficients of the time polynomials, radar must continuously scan the given scenario at least four times when the pol-
249
UKF-based multi-sensor passive tracking with active assistance
ynomial order is defined as 3. Assume that the simulation time is 100 s and three different detection thresholds e (0.7 , 0. 75, 0. 8) are selected, after 100-time Monte-Carlo simulations, the rootmean-square error curves of the position and velocity in y direction are shown in Fig. 4 and Fig. 5 respectively. Fig. 6 and Fig. 7 give an onetime simulation result. Given the different detection thresholds, the root-mean-square stable errors and the average cutoff time of radar are listed in Table 1. The table shows that when the detect threshold is properly selected, the working time of the radar can be greatly reduced, for example, when the detect threshold E is 0.75, there is nearly 50 s during which the radar is turned off. This will greatly decrease the possibility of the radar being locked-on by adverse ESM; on the other hand, from Fig. 4 and Fig. 5, we can see that tracking accuracy is satisfying. During the simulation, we also found a problem that the radar must be frequently turned on when the target states change quickly. The reason is that the identification accuracy of polynomials falls, the maneuver detection inequations can' t be met. One solution to this problem is to find a new algorithm for improving the infrared tracking accuracy, the other way is to improve the identification accuracy, which we are working on. E=O
&=0.8 I,I
E = 0.75
$ 8
-: -0
20
40
0
20
40
5
t/S
-:Targetl;
80
100
60
80
100
.........:Target2;
- - -:Target3
1 0 t/S
- : real tracks of the target; --
: predicted tracks produced by radar and infrared;
predicted tracks produced by polynomials and infrared
Fig. 6
20
60
Fig. 5 RMS of the velocity in the direction of y
-
8
1
The real and predicted tracks of the targets in the direction of y
-
8 .-
20
0
5
80
E = 0.75
601
- -0
.2
20
K
3
60
40
0
40
60
100
1
80
I00
&=0.7
100
h
-:Targetl; Fig. 4
ti s
......... :Target2;
- : 3-dimension real tracks; - - : 3-dimension predicted tracks
- - -:Target3
RMS of the position in the direction of y
* : predicted tracks produced by
produced by radar and infrared; polynomials and infrared
Fig. 7 T h e real and predicted tracks in 3-dimensional space
Li Anping, Jing ZhongLiang & Hu Shiqiang
250 Table 1 RMS of the position and velocity in y direction under given different detection thresholds
position in y
direction/m
0.7
Average
velocity in y direction (m/s)
1 2 6 . 1 2 1 2 6 . 9 6 1 1 6 . 8 5 1 3.02 1 3 . 4 2 1 1 . 8 7
cut-off
time/s
I
52.2
5. CONCLUSIONS A new synergy tracking method is presented in this paper. In this method, the unscented Kalman filter and the least squares identification method are used to improve tracking accuracy. Simulation results show that the method not only has a good tracking accuracy, but also can turn off the radar as much as possible for decreasing the possibility of the radar being locked-on by adverse ESM. Therefore, in practical application, this method can be applied to military defense systems.
REFERENCES [11 Wang G H, Ma0 S Y , He Y . A survey of radar and infrared data fusion Fire Control & Command Control, 2002, 27(2): 2-4. [2] Cheng Y M, Pan Q, Zhang H C. Study on infrared and radar sensor synergistic tracking algorithm Fire Control &. Command Control, 2001, 26(3) : 20-23. [3] Cui N 2 , Xie W X, Yu X N. Multi-sensor distributed Kaman filtering algorithm and its application to radar/IR target tracking. SPIE, 1997(3086) : 323-327. [4] Blackman S S, Dempster R J , Roszkowski S H. IMM/ MHT application to radar and IR multitarget tracking. S P I E , 1997(3163) : 429-439. [51 Gavish M, Weiss A J. Performance analysis of bearing-only target location algorithms. IEEE Trum . on Aerospace and
Electronic Systems, 1992, 28(5) : 817-828. [6] Simard M-A, &gin F. Central level fusion of radar and IRST contacts and the choice of coordinate system S P I E , 1993(1954) : 463-472. [7] Maltese D, Lucas A Data fusion: principles and application in defense. S P I E , 1998(3374) : 329-336. [8] Hu W L, Ma0 S Y. An approach for radiation control of tracking systems based on multisensor fusion Actu Electronicu Sinicu , 1998, 26(3) : 37-41. [9] Eric W, Rudolph V D M. The unscented Kalman filter for nonlinear estimation. IEEE Proc. Adaptive Systems f o r Signal Processing , Communications and Control Symposium, 2000: 153-158. [lo] Rudolph V D M, Arnaud D, Nando D F, et al. The unscented particle filter. CUEDIF-INFENGITR 380, 2000. [ll] Yang G S, Dou L H, Chen J, et al. Synergy decision in the multi-target tracking based on IRST and intermittent-working radar. Information Fusion, Elsevier, 2001 , 2(4) : 243-250.
Li Anping was born in 1977. He received the M. S. degree in 2003 in automation from Central South University. Currently, he is a Ph. D. candidate in Shanghai Jiaotong University. His research interests include signal processing, visual tracking and visual processing. E-mail :lapjt@sjtu. edu. cn
Jing Zhongliang was born in 1960. He received the B. S. , M. S. and Ph. D. degrees from Northwestern Polytechnical University, in 1983, 1988 and 1994, respectively, all in electronics and information technology. His research interests include intelligent information processing, information fusion, target tracking, stochastic neuro-fuzzy systems, high performance motion control, and aerospace control and information processing.
-250
UKF-based multi-sensor passive tracking with active assistance* Li Anping, Jing Zhongliang & H u Shiqiang Inst. of Aerospace Information and Control, School of Electronic, Information and Electrical Engineering, Shanghai Jiaotong Univ. , Shanghai 200030, P. R China (Received January 18, 2005)
Abstract: A new synergy tracking method of infrared and radar is presented. To improve tracking accuracy, the unscented Kalman filter (UKF) , which has better nonlinear approximation ability, is adopted. In addition, to reduce the possibility of radar being locked-on by adverse electronic support measure (ESM) , radar is under the intermittent-working state. After radar is turned off, the possible target position is estimated by a set of time polynomials, which is constructed based on the sufficient observations done before radar is turned off, the estimated values from time polynomials are compared with the current observation values from infrared to determine the time when radar is turned on Simulation results show the method has a good tracking accuracy and effectively reduces the possibility of radar being locked-on by adverse ESM. Key words: active radar, infrared, least square, time polynomial, the unscented Kalman filter.
1. INTRODUCrION Radar can provide complete position information and/or Doppler information Of target 7 but it electromagnetic wave when it works, SO it easily suffers from electromagnetic interference and antiradiation missile’s attack. On the contrary, infrared doesn’t emit any energy, it detects and locates target by receiving thermal energy radiated from target, so it has the powerful anti-interference ability. Just because infrared doesn’ t radiate any energy, it can’ t be easily detected and located, which makes it has good covertnessL1]. But its 2-D target observations are not sufficient to locate targetsL2’. So in many cases, it has become a complementary way to combine infrared with radar. About the infrared/radar tracking, a lot of methods have been p r o p o ~ e d ~ ~ especially -~], in reducing the possibility of radar being locked-on by adverse ESML6-*’.Although these methods can effectively reduce the possibility of radar being locked-on by adverse ESM, the target range information can’t be achieved when radar is turned off, which may lead to bad tracking accuracy. To improve tracking accuracy, in this paper, the unscented Kalman filter algorithm, which has better
nonlinear approximation ability, is adopted; on the other hand, after the radar is turned off, a set of time polynomia~s are constructed to estimate
the
possible target range. Simulation results indicate that the proposed method has a good tracking accuracy and greatly decreases the possibility of radar being locked-on by adverse ESM.
2. SYNERGY TRACKING STRUCI’URE OF THE RADAR/INFRARED The tracking structures in this paper are shown in Fig. 1-Fig. 3.
The tracking system mainly in-
cludes four modules: the infrared tracking module, the radar/infrared tracking module, the maneuver detection module, and the tracking mode selection module. The whole working process is as follows.
(1) Let the infrared scan the surrounding environment alone, once a target is found or the target makes maneuver, turn on the radar.
(2) Let the radar and infrared work together for a while, then turn off the radar.
( 3 ) Construct a set of the time polynomials to estimate the target possible position after the radar is turned off.
(4) Compare the estimated values from the
* This project was jointly supported by the National Natural Science Foundation of China (60375008), the China Ph D. Discipline Special Foundation (20020248029) and the China Aviation Science Foundation (02D57003).
Li Anping, Jing Zhongliung & H u Shiqiang
246 time polynomials with the current observation values from the infrared to determine the time when the radar is turned on. (5) Select a tracking mode between the infrared tracking and the radar/infrared tracking according to whether the target makes maneuver. (6) Apply the unscented Kalman filter to the selected tracking mode. Measurement
Meas ement tracking
I
-Maneuver detection
Tracking mode selection
I
Fig. 1 Structure for the infrared tracking system with the intermittent-working radar
Target's track Fig. 3
points completely capture the true mean and covariance of the GRV, and, when propagated through the true nonlinear system, capture the posterior mean and covariance accurately to the second order for any nonlinearity. The EKF, in contrast, only achieves first-order accuracy. The unscented transformation (UT) is a method for calculating the statistics of a random vector that undergoes a nonlinear transf~rmation[~'.Let x be an n, dimensional random vector, g : Wz HWYis a nonlinear function and y = g ( x ) Assume that the mean and the covariance of x are and P,, respectively. The procedure for U T is as follows. 1 sigma Step 1 Calculate the set of 272, points and weights
.
+
I
Target's track Fig. 2
lem by using a deterministic sampling approach. The state distribution is again approximated by a GRV, but is now represented using a minimal set of carefully chosen sample points. These sample
Structure for the infrared tracking
I
Structure for the radarhnfrared synergy tracking
3. ALGORITHMDESIGN 3.1 Filtering Algorithm Design The tracking accuracy mainly relies on the filter algorithm. When the state and measurement equations are nonlinear, the most widely used method is the extended Kalman filter (EKF). But EKF only uses the first order terms of Taylor series expansion of the nonlinear functions, it often introduces large errors in the true posterior mean and covariance of the transformed Gaussian random variables (GRV) , which may lead to sub-optimal performance and sometimes divergence of the filter. In this paper, the unscented Kalman filter (UKF) is adopted. The UKF addresses this prob-
where (J(n,+A)P,); is the ith row or column of the matrix square root of (n, +A)P,, n, is state dimension, the definition of the parameters A , a and p can be found in Ref. [lo]. Step 2 Propagate each sigma points through the nonlinear transformation
Step 3 Compute y' s mean and covariance 2n-
(8) 2=0 2n-
i=O
After the unscented transformation, combining with target motion model (state equation is linear, measurement equation is nonlinear) , the
UKF-based multi-sensor passive trucking with active assistance
247 i
=
(23)
l,..-,l
where u;,d , * - * , ~ i , ~ ,--*,a;,, and ai,&,---,ai,,,,, are unknown coefficients, I is the number of target, m is the polynomial order. If the coefficients in Eq. (13) can be identified in real time, the motion model of the target will be obtained, and using this set of polynomials, the target state can be estimated after the radar is turned off. ( 1) Identification of the polynomial coeffi-
cients Assume the polynomial order is m (the order of the polynomial reflects the movement way of target, such as constant velocity movement, constant accelerate movement, etc ). To determine these coefficients, the radar and infrared must simultaneously scan the given scenario m 1 times. Suppose the radar and infrared scan target n ( n 3 m + l ) times after the kth time and the sample time is T , then the coefficients in Eq. (23) can be calculated by the following matrix equation.
+
(17) ( 3 ) Measurement update
+
variance, R is measurement noise covariance.
3.2 Parameter Identification of Target Motion Model
+ a&$+
( t ) = a;,&
yi ( t ) =
zi ( t )
=
+ t+
+ + ai,pntrn
ai,Zlt
ai,r2tZ
ui,yl
ai,y2
**.
+ ". +ai,ptm a;,&+ t +ai,,zt2 + + a;,*1
tZ
'.*
+
+
8 as
In general, the target motion trajectory can be approximated by some time polynomials. Assume the target motion trajectories in x , y and z directions are approximated by the following time polynomials. xi
yi
where & (k T ), (k T ) and Zi (k T ) are the estimated positions of the ith target in x , y and z directions at ( H T ) th time. If defining 2 , A and
Ui,Jrn
&(k+T) 2T)
$;(k+T) (k 2T)
ii(k+T)
+ Zi (k + 2T) Y;(k +nT) zi (k + n T ) i i
nT) rl R+T
(k
+ T)" 1
Li A n p i n g , Jing Zhongliang & Hu Shiqiang is the detection threshold, E E ( 0 , l ) . If any inequation in Eq. (29) is not met, it may imply that the target would have made some maneuver. The radar must be turned on in the next sample time.
8=
4. SIMULATION AND ANALYSIS
Eq. (24) can be rewritten as
Z=&
(25) 4.1
Simulation Tracks and the Initial Conditions
8 can be calculated using the least square method
e = (ATA)-’A=Z
(26)
Once these coefficients are determined, the states of target can be estimated by this set of time polynomials when the radar is turned off. (2)The polynomial order setting As a rule, the movement of target in a t h r e e dimensional space can be projected into x , y and z directions, respectively, with its constant velocity, constant acceleration, or variable acceleration. If we define 3 as the highest order of the polynomial, the target’s trajectory in x direction can be represented by Eq. (27). Equation (27) can completely describe the target movement way in x direction.
xi ( t ) = a i d
+
Ui,d
t
+
U i , d t2
i = 1,-.*,1
+
ai,z3 t3
(27)
3 . 3 Maneuver Detection Assume that the target estimated positions afe denoted by ( s ( k ) , y ( k ) ,i(k)) at the kth time after the radar is turned off, the estimated values (;(k), p(k) ,i(k)) in the spherical coordinates are calculated as
If the target makes no maneuver during the time in which the radar is turned off, the following inequationsC”’ must be met at the same time.
Suppose there is an observation station on the ground with an infrared and radar placed on the same platform. At the beginning, two targets are supposed to get close to the platform. The first one comes from an initial position 10 km in x direction, 12 km in y direction, and 10 km in z direction, with an initial velocity of -70 m/s in x direction, -100 m/s in y direction, and -90 m/s in z direction, the second one moves from an initial position 10 km in x , y , and z directions, with an initial velocity of - 80 m/s in x directions, -120 m/s and a constant acceleration of -2 m/s2 in y direction. Twenty seconds later, a third target appears in an initial position 10 km in x direction, 5 km in y direction, and 8 km in z direction. All three targets move towards the platform with a constant velocity. The velocity of the first one is -70 m/s in x direction, -100 m/s in y direction, and -90 m/s in z direction. The velocity of the second one is -80 m/s in x direction, -80 m/s in y direction, and -100 m/s in z direction. The velocity of the third one is -100 m/s in x direction, -60 m/s in y direction, and -100 m/s in z direction. The observation noises of two kinds of sensor are both Gauss white noise. The standard range and angle deviations for the radar are respectively 60 m and 5 mrad, the standard angle deviation for the infrared is 1 mrad. During the simulation, the observation values of the radar and infrared have been registered in the temporal-spatial domain. After the registration, the sample time is 1 s.
4 . 2 Simulation Results and Analysis
A simulation is performed on the above simulation are the azimuth and elevation standwhere a,, ard deviations of the infrared, ( a , (k) , & (k)) are the observation values of the infrared at kth time, E
tracks. In order to identify the coefficients of the time polynomials, radar must continuously scan the given scenario at least four times when the pol-
249
UKF-based multi-sensor passive tracking with active assistance
ynomial order is defined as 3. Assume that the simulation time is 100 s and three different detection thresholds e (0.7 , 0. 75, 0. 8) are selected, after 100-time Monte-Carlo simulations, the rootmean-square error curves of the position and velocity in y direction are shown in Fig. 4 and Fig. 5 respectively. Fig. 6 and Fig. 7 give an onetime simulation result. Given the different detection thresholds, the root-mean-square stable errors and the average cutoff time of radar are listed in Table 1. The table shows that when the detect threshold is properly selected, the working time of the radar can be greatly reduced, for example, when the detect threshold E is 0.75, there is nearly 50 s during which the radar is turned off. This will greatly decrease the possibility of the radar being locked-on by adverse ESM; on the other hand, from Fig. 4 and Fig. 5, we can see that tracking accuracy is satisfying. During the simulation, we also found a problem that the radar must be frequently turned on when the target states change quickly. The reason is that the identification accuracy of polynomials falls, the maneuver detection inequations can' t be met. One solution to this problem is to find a new algorithm for improving the infrared tracking accuracy, the other way is to improve the identification accuracy, which we are working on. E=O
&=0.8 I,I
E = 0.75
$ 8
-: -0
20
40
0
20
40
5
t/S
-:Targetl;
80
100
60
80
100
.........:Target2;
- - -:Target3
1 0 t/S
- : real tracks of the target; --
: predicted tracks produced by radar and infrared;
predicted tracks produced by polynomials and infrared
Fig. 6
20
60
Fig. 5 RMS of the velocity in the direction of y
-
8
1
The real and predicted tracks of the targets in the direction of y
-
8 .-
20
0
5
80
E = 0.75
601
- -0
.2
20
K
3
60
40
0
40
60
100
1
80
I00
&=0.7
100
h
-:Targetl; Fig. 4
ti s
......... :Target2;
- : 3-dimension real tracks; - - : 3-dimension predicted tracks
- - -:Target3
RMS of the position in the direction of y
* : predicted tracks produced by
produced by radar and infrared; polynomials and infrared
Fig. 7 T h e real and predicted tracks in 3-dimensional space
Li Anping, Jing ZhongLiang & Hu Shiqiang
250 Table 1 RMS of the position and velocity in y direction under given different detection thresholds
position in y
direction/m
0.7
Average
velocity in y direction (m/s)
1 2 6 . 1 2 1 2 6 . 9 6 1 1 6 . 8 5 1 3.02 1 3 . 4 2 1 1 . 8 7
cut-off
time/s
I
52.2
5. CONCLUSIONS A new synergy tracking method is presented in this paper. In this method, the unscented Kalman filter and the least squares identification method are used to improve tracking accuracy. Simulation results show that the method not only has a good tracking accuracy, but also can turn off the radar as much as possible for decreasing the possibility of the radar being locked-on by adverse ESM. Therefore, in practical application, this method can be applied to military defense systems.
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Li Anping was born in 1977. He received the M. S. degree in 2003 in automation from Central South University. Currently, he is a Ph. D. candidate in Shanghai Jiaotong University. His research interests include signal processing, visual tracking and visual processing. E-mail :lapjt@sjtu. edu. cn
Jing Zhongliang was born in 1960. He received the B. S. , M. S. and Ph. D. degrees from Northwestern Polytechnical University, in 1983, 1988 and 1994, respectively, all in electronics and information technology. His research interests include intelligent information processing, information fusion, target tracking, stochastic neuro-fuzzy systems, high performance motion control, and aerospace control and information processing.