Target tracking based on frequency spectrum amplitude1

Journal of Systems Engineering and Electronics , Vol, 17 , No. 3 , 2006 , p p . 4 73

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4 76

Target tracking based on frequency spectrum amplitude* G o Huidong, B a n g Xinhwz & X i a Zhijun Research Center on Signal and Information, Dalian Navy Academy, Dalian 116018, P. R China (Received January 6, 2005) Abstract: The amplitude of frequency spectnm~can be integrated with probbilistic data Bssociation (PDN to distinguish the target with clutter echoes, espeually in low SNR underwater e n v i m m t A new target-trackmg algorithm is presented which adopts the amplitude of frequency spectrum to improve target trackmg in clutter. The probbilistic density distribution of frequency spectrum amplitude is analyzed, By simulation, the results show that the algorithm is superior to PDA This approach enhances stability for the association probbiity and incrrases the performme of target traclang.

Keywords: target tracking, amplitude, frequency spectrum, probabilistic data association.

1. INTRODUCTION

by using frequency spectrum amplitude of target. The frequency spectrum amplitude combined with

In target tracking, attribute parameters can be used to improve the performance of data association. The probabilistic data association ( PDA ) which employ the attribute enhance the capability of data association and improve the performance for target tracking. The method of PDA is performed in the environment of high signal to noise (SNR) generally and the SNR is in excess of 10 dB.But the SNR in the actual environment is lower than 10 dl3 commonly. When SNR is below 0 dB, the target is always inundated in the clutter, high probability of mis-association and high false alarm happen. Both state parameters and attribute parameters can be used to calculate the association probability. How to utilize the attribute paramters besides signal return to enhance the precision of data processing in the circumstance of lower SNR is the issue we should resolve imminently. The PDA method is analyzed in Ref. [11, D. Lerro and Slocumb. B. Jc2-‘’ use the strength of target echoes to incorporate attribute parameters in estimation process, attribute parameter and state parameter can be estimated separately. As mentioned above, the target echoes cannot be distinguished in low SNR, especially in underwater conditions. New method should be adopted to improve the performance of target tracking. As well known, the frequency spectrum information can be extracted from target in the clutter environment, target can be separated from the clutter effectively

PDA (acronym FSPDA) is proposed based on PDA. According to Refs. [5, 61, frequency line tracing model is introduced, the probability association can be calculated exactly. The simulation of FSPDA and PDA is processed on different condition of SNR. Subsequently, the relationship between SNR with FSPDA is analyzed. Simulation results show that FSPDA performs stably.

2. AMPLITUDE OF FREQUENCY SPECTRUM When tracking target frequency line in underwater, the signal measurement of multi-frequency can be denoted as

where no(

)

is the Guassian noise which has zero

mean, and

As all known, the narrow band frequency which is filtered out Guassian noise can be denoted by r(t>cas (2xfJ +8(t>>

(3)

fc is the center frequency of narrow band In low SNR environment, frequency spectrum can reflect whether the signal comes from the target or the clutter affmtively. By extracting this underlying and useful target infomtion, the state of target can be esti-

* This project was supported by the Defense PreResearch Pmject of the ‘TenthFiveyearplan’

of China (40105010101).

474

G o Huidong, Zhang Xinhua

mated accurately, the amplide of target freqspec aumcanbe used to beina3prated to probabiIityassociation Refenx~[5] gives the protatdity distribution of amplitde and the probability of two sindar f r e q d e s Firstly the spectrum of the data series over finite time interval (windows) is analyzed with length T, = NT,. By applying FFT techniques, the equivalent envelopes of each frequency cell can be denoted by 4

Ti

=

[C7q1''

(4)

,=1

where rij,i=1,2,.*.,n,j=1,2,...,nc are the amplitudes of the frequency bins contained in the ith cell and n, is the number of frequency bins contained in each cell. The maximum likelihood estimate of A,,[5*61is

& Xia Zhijun

ments, not associated in the partition with any of the tracks O j ( k ) . And

B(k)

= P(Oi(k)

I

Zk>

(9)

Eq. (9) is the probability which expresses the events that the ith measurement comes from target, and towards {Oo (k) (k) , ,&,
,el

(10) is0

For tracking target in clutter, Eq. (10) is the a x e partion of PDA, and how to assign the probability of every returnin*und is the emphasis of the new&

4. DATAASSOCIATION BASEDON ATTRISUTE We k n ~ w C ~ . ~ ] PD1

= soapi(r)dr

(11)

denotes the probability of a frequency lines which can scan in the narrow bin NT

03

Pm

(5)

(12)

p2(r)dr

=

denotes the probability of two frequency lines which can scan in the narrow bin When one frequency line is in the range of frequency variation, the probability density function of the envelope r ( t ) is

(7)

If there is no frequency line in the range of variation,

Pb

(13)

= [mpo(r)dr

denotes the false alarm pmbability of scan, r denotes the threshold of amplitude in the former formula. The validation region of target tracking is (zk - 2 k j b i >S;' (

~ - Z k l k i )

<7

(14)

The pdf of true measurement in the validation can be shown asC1"31

P[zi

I e m ,?nk

,Zk] = pT (ai>ei

(15)

The pdf of false measurement in the validation can be shown asc1-31 The set of measurements obtained at time k is Z ( k > = { z, yL:), and the set of measurements up to time k is denoted as Zk= { Z ( n >};5=1, measurements not having originated from a target are assumed to be independent identically distributed m ( k ) is the quantity of measurements in the time k,Oj (k) is the event of which means z j ( k ) is the true measurement comes from target. e0 (k) is unfeasible track, which consists of the measure-

p c d I 8i(k),mk,Zk] v b

= p/2cn= I

= s k

&(a:)V;'

I 'I2

(16)

(17)

The ratio of target's amplitude to clutter's amplitude idz1

The probability of data association of all validate measurement in the time k[2*33

Target tracking based on frequency sfiectrum amplitude

475

Z(k) i=l

b m'

=

(19)

+C e d i

,i=o To permit comparison of the different tracking algorithm, the following Figs. 1-6 RMSE are introduced

i=l

In Eq. (19), there are

Pc is the probability of gate, cn, is the volume of n, dimension unit super spherical, y is the value of thrmld When annputing the probability of data association f i , the parameter d e l is adopted; the false measwement M subject to a Poisson model is p r o p a d

Figure 1 depicts the curve of the probabilistic function to target frequency spectrum amplitude. Figure 2 depicts the curve of the probability p1 ( r ) of frequency spectrum amplitude for target and clutter and Fig. 3 is corresponding to po ( r ) .

m = O,l,***,N--1

Where V ( k ) = 7 ( y I S ( k ) I " ' , the parameter d e l PDAF is obeyed to lonow the density of clutter space pnor. The covariance of state in the s t a t m t is as follows

0.4 0.35 Q- 0.3 0.25 0.2

03

02

0.15 0.1

0.1

100 200 300 400 500

FIHz

Amplitude

P ( k , k ) = P(K,k - 1) (1 - - p o ) K ( k ) S ( k ) K T ( k ) + R k

Fig. 1

)

m

F(k)= K(k)[ 2flui(k)zfT(k) -v(k)vT(K) i=l

(22)

1

(23)

9

v ( k )=C@' (k) is the "association infomtion", and i=l

v ' ( k ) = z i ( k ) -&,k-

1)

(24)

5. SIMULATION Parameters setting for underwater targets are as follows: the initial position and velocity to target is [ X , Y,V,,V,]= [15 km, 15 km, 12 m/s, 12 d s ] ; 8 = 50m,&=3 mrad,T=2 s,y=16,A=3. 2X10-5 m h a d >, referring to 3rd paragraph, we adopt parameter model in simulation; the clutter is subject to aver age distribution in gate In PDA simulation, we suppose the probability of target detection P D = l . rl

0

pdf

Fig. 2 (50Hz/120Hz) spectrum amplitude pdf (pi (r))

In Fig. 4,the dot line denotes the curve of maximum likelihood h of frequency spectrum line in 0 dB, the s l i d line is corresponding to 10 dEi The association pmbability /3 is deducted by the maximum likelihood of frequency spectrum h, despite SNR vary, the maximum likelihood ratio of target sgnal is always higher than 1. Evidently, the maximum likelihood ratio of frequency indicates the information "entropy" of target As the probability of data association to target increases, the target statement approach to the truth nearly, the probability of misassociation decreases accordingly.

T 01 Fig. 3

10 0

of merit to

0

11

l T 1

(50Hd120Hz) spectrum amplitude pdf ( p o ( r ) )

Fig.4 0 &/lo & PI (r)/po (r)

476

Guo Huidong

Figure 5 shows the curve of probability in data association to the method of FSPDA in different SNR Fig. 6 shows the curve of probability of data association to the method in PDA. We suppose the probability of detection is 1 and the gate probability is 0. 997 in simulation of PDA. In Fig. 5,the association probability increases when SNR increases. Especially, the association probability p approaches to 1 in 10 dB. By comparing Fig. 5 with Fig. 6 , the amplitude information of target conduce substantial increase of maximum likelihood ratio, weighted probability of target is increased consequently, statement estimation approach to target measurement, not clutter measurements. As a result, the method of FSPDA enhances the value of p to diminish the disturbing effect of clutter. 0.8 0.7

1:

s

b 0.4

Q.

-03

02

......:6 &; -:

0&

Sample number

Fig. 5 The association probability of an FSPDA

0.1 0 102030405060708)90100

sample number Fig, 6 The association probability of PDA

In Fig. 5, the probability of data association to FSPDA in -6 dB/O dB, the value of 10 d 3 is little higher than the value in 0 dB, which denotes the enhancement of SNR don' t improve FSPDA evidently, Accordinally, FSPDA is applicable to the circumstance in low SNR, the method of FSPDA improves the performance of target tracking. The RMSE errors of range to FSPDA and PDA are shown in Table 1. Table1 ' I b e R M S E a m ~ o f ~ n g e t o F s P D A s n d P D A

RMSE of range error FSPDA

SNR to signal 10 dB OdE3 3.018 6 e--2 3.210 5 e-2

, Zhang Xinhua & X i a

Zhijun

6. CONCLUSION By simulation, FSPDA and PDA are computed in difference SNR, the performance of FSPDA is better than that of PDA. The algorithm enhances the true probability in data association to target and the robustness in target tracking. How to extract the frequency line quickly and apply to the field of multitarget tracking are our future works. Moreover, FSPDA is adapted to not only underwater target tracking but also radar target tracking,

REFERENCES [l] &shalom Y, Fortman T E Tracking and data association. Boston: Academic Press, 1988. [2] Lerro D, Barshalom Y. Interacting multiple model tracking with target amplitude feature IEEE Trans on AES,1993,29(2): 494-509. [3] Kirubarajan T, Bat-shalom Y. Low observable target motion analysis using amplitude information. IEEE T r a n s . a A E S , 1996,32 (4): 1367-1384. [4] Slocumb B J. A comparison of tweaugmented PDA filters. American control conference, Albuquerque, New Mexico, 1997: 3688-3692. [5] Xie Xianya, R J. Multiple target tracking and multiple frequency line tracking using hidden Markov models. IEEE Tramon S P , 1991,39(2): 2659-2676. [6] Xie Xianya, R J. Multiple frequency line tracking with hidden markov models -further results. IEEE Trans. on SP 1993,41( 1) : 334-343. [7] Barret R F, Holdsworth D. A frequency line tracking using HMMs with amplitude and phase information. IEEE Trans. a S P , 1993,41(10): 2965-2975. [8] Roy L Streit, Ross F I3 Frequency line tracking using hidden markov models. IEEE Trans. m S P , 1990,38 (11: 586-598. [9] Kershaw David J, Robin J evans. Waveform selective probabilistic data association. IEEE Trans. on A E S , 1997,33(4): 1180-1188.

-6 dB 5.021 8 e--2

From simulation results, the algorithm of FSPDA is more applicable to clutter tracking than PDG Results reveal the superiority of FSPDA in target tracking.

Guo Huidong was born in Zhejiang Province on December, 1976. Now undertake a Ph. D. degree in electrical engineering at Dalian Navy Academy. His main area of expertise is multisensor data fusion, with recent work including: multistatic sonar, passive sonobuoy, and sensor management.