J. Marine Sci. Appl. (2013) 12: 240-244

DOI: 10.1007/s11804-013-1191-0

Linear Track Estimation Using Double Pulse Sources for Near-field Underwater Moving Target

Zhifei Chen1*, Hong Hou2, Jianhua Yang1, Jincai Sun2 and Qian Wang2,3

1. School of Automation, Northwestern Polytechnical University, 710072,China 2. School of Marine, Northwestern Polytechnical University, 710072,China 3. The 705th institute of China Shipbuilding Industry Corporation, 710075,China

Abstract: The double pulse sources method (DPS) is presented for linear track estimation in this work. In the field of noise identification of underwater moving target, the Doppler will distort the frequency and amplitude of the radiated noise. To eliminate this, the track estimation is necessary. In the DPS method, the bearings of two sinusoidal pulse sources installed in the moving target are estimated through baseline positioning method in the first step. Meanwhile, the emitted and recorded time of each pulse are also acquired. Then the linear track parameters will be achieved based on the geometry pattern with the help of double sources spacing. The simulated results confirm that the DPS improves the performance of the previously presented double source spacing method. The simulated experiments were carried out using a moving battery car to further evaluate its performance. When the target is 40~60m away, the experiment results show that biases of track azimuth and abeam distance of DPS are under 0.6o and 3.4m, respectively. And the average deviation of estimated velocity is around 0.25m/s. Keywords: linear track estimation; double pulse sources; baseline positioning method; time-of-arrival difference Article ID: 1671-9433(2013)02-0240-05

1 Introduction1

In the field of noise identification, the Doppler of underwater high-speed moving target has great effect. To obtain correct noise identification results, we have to resolve Doppler in received signals with the help of track information (Jidan et al., 2010, Tegborg et al., 2011). Roughly, the existing underwater acoustic positioning system could be divided into two groups. One is based on array signal processing, especially for adaptive beamforming with passive acoustic array (Gershman et al., 1995, Ruiz et al., 2004). The other is baseline positioning system, such as ultra-short baseline acoustic positioning system (Hattori et al., 2010). Nowadays, the cost of underwater Global positioning system (GPS) is still too high to be used in this field. In this work, a cooperative underwater moving target with linear track is considered. And two reference sources are installed to aid track estimation.

Received date: 2013-03-11. Revised date: 2013-04-22. Foundation item: Supported by China Postdoctoral Science Foundation (No. 2012M512027) *Corresponding author Email: chenzhifei@gmail.com

© Harbin Engineering University and Springer-Verlag Berlin Heidelberg 2013

In reference (Yan et al., 2009), a double sources spacing method (DSS) is proposed to estimate the velocity of a moving target with linear track. Two sinusoidal sources with different frequencies are utilized in DSS. After bearing estimation of two sources in two time points, the velocity is obtained based on the geometry pattern. In the DSS method, the accuracy of bearing estimation is disturbed by Doppler. Therefore, the sinusoidal sources are replaced with sinusoidal pulse sources in this work. And the bearing estimation will be achieved without Doppler through baseline positioning method in the first step. In addition, DPS makes use of the time-of-arrival difference to further improve the performance of DSS.

In the fowling section, the DPS method was proposed. Then simulations were presented to investigate influencing factors of DPS with Monte Carlo experiments. Next, simulated experiments were carried out with a battery car in Section 4. At last, conclusions were drawn in Section 5.

2 Double pulse sources method

For convenient, the linear track and array are constrained in x-y plane as shown in Fig. 1. Then the track azimuth θ (visible region (−π/2, π/2)) and abeam distance R0 (R0>0) will determine the linear track. Two sinusoidal pulse sources with distance r0 are installed in the moving target. Based on the bearing estimation of double sources in different time, the DPS method will provide us the track parameter θ and R0, and velocity v at different time.

Fig. 1 linear motion target with two reference sources

The baseline positioning method has a better performance in bearing estimation compared with that of range estimation

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(Cheng et al., 2011). Because its bearing estimation is based on the time delay estimation of each pulse, it is not affected by Doppler. And the array number is also reduced compared with that of DSS. Consider two sinusoidal pulses are radiated at the same time with same cycle Tc and different frequencies. After filtering, two pulse sources are separated. For each pulse cycle, it has

2 2 2 2 2( ) ( ) ( ) ( )m s m s m s m sx x y y z z c t t (1)

where c denotes sound velocity. Sm=(xm, ym, zm) and tm are the coordinate of the mth array element and its record time of pulse leading edge, respectively. On the other hand, (xs, ys, zs) and ts indicate the coordinate of the source and the corresponding radiated time, respectively. In the above equation, tm could be got with time delay estimation in time domain and Sm is known a priori. And (xs, ys, zs) and ts are variables we are desired. When the number of equation is more than four, it will be overdetermined equations. After resolving it, the source coordinate (xs, ys, zs) and ts are obtained. In this paper, an uniform linear array (ULA) with 7 elements is applied to estimate the DOA α and β in Fig. 1, also ts and tm.

For double pulses with k=1 in Fig. 1, the linear track and line OAk could be denoted as

0tan

tan k

y x R

y x

(2)

It follows that

0 0 tan, ,0

tan tan tan tank

kk k

R RA

(3)

where k . It is easy to be satisfied. Replace αk with βk in

above, the coordinate of Bk is obtained. It results in

0 k kr A B (4)

where AkBk denotes the distance between Ak and Bk. The above equation in the case of different groups of double pulses will constitute equations of θ and R0. The reciprocal of its sum of absolute residual is taken as the estimator of linear track estimation method based on double source spacing (DSS).

DSS 0

01

1, K

k kk

f Rr A B

(5)

where K is the number of double pulses group. DSS has similar idea with that of reference (Yan, 2009). Here, it is expanded to the field of track estimation with multiple time points. Furthermore, the velocity in the time interval of adjacent pulses becomes

1

( 1) ( )k k

ks s

A Av

t k t k

(6)

where AkAk+1 indicates the distance between Ak and Ak+1. On the other hand, the adjacent pulse cycles have the

geometry relationship as shown in Fig. 2. For the first reference source, the time difference between

adjacent pulses in the received signal of the mth sensor is defined as Tm=tm2-tm1. It could be estimated from tm in Eq. (1). Then the path difference becomes

2 1 2 1= = ( )m m m cR r r S A S A c T T (7)

Fig. 2 Path difference of adjacent pulse cycles

where SmA1 and SmA2 denote the distance from Sm to A1 and A2, respectively. Both of them are functions of θ and R0. There are similar equations for different sensor and different adjacent pulses. They will constitute equations of track parameters. And the reciprocal of the sum of the absolute residual is also taken as an estimator named as linear track estimation based on path difference (PD).

PD 0 1

11 1

1,

( )M K

m k m k mk cm k

f RS A S A c T T

(8)

where M and K are the number of sensor and pulse cycle, respectively. Here, K is identical with that of Eq. (5). Tmk indicates the time-of-arrival difference between the kth and (k+1)th pulse in the record signal of the mth channel, i.e. Tmk= tm (k+1)-tm (k).

In essence, DSS makes use of double source spacing and DOA estimation in different time to estimate track parameters, while PD takes advantage of path difference caused by Doppler. It results in a new estimator by combining two methods (Wei et al., 2010). It is denoted as linear track estimation based on double pulse sources (DPS).

DPS 0 DSS PD1 PD2,f R f f f (9)

where fPD1 and fPD2 are the PD estimator of each reference source.

3 Simulations

The DPS estimator is composed of DSS and PD. The performance of DSS is determined with the bearing error Δφ, i.e. the bias of α and β. And the performance of PD estimator is affected with the bias of path difference ∆R which is denoted as Δr. And it is transformed to time-of-arrival difference error Δτ=Δr/c. To review the effect of Δφ and Δτ, the simulation results are presented in the following paragraphs.

As shown in Fig. 1, consider an ULA with M=7 and sensor spacing d=0.3m as the baseline array. The double pulse sources have center frequencies f0=[6000, 9000]Hz with same cycle Tc=200ms and spacing r0=0.64m. The sound speed in water is set to c=1500m/s. The moving target has a linear track with a constant speed v=20m/s, and track parameters θ=10o, R0=41.8m. Here, the pulse group number K is set to 6 to implement the DSS, PD and DPS methods.

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(a) average bias of track azimuth of DSS

(b) average bias of abeam distance of DSS

(c) average bias of track azimuth of PD

(d) average bias of abeam distance of PD

(e) average bias of track azimuth of DPS

(f) average bias of abeam distance of DPS

Fig. 3 The effect of bearing bias and time-of-arrival difference error to DSS, PD and DPS

After Monte Carlo simulation with 100 trials, Fig. 3 presents the average deviation of θ and R0 under different Δφ and Δτ. Note that the added errors are random numbers with uniform distribution in [−Δφ, Δφ] or [−Δτ, Δτ]. In Fig. 3, the performance of DSS is determined with Δφ. When Δφ=0.1°, the average deviation of θ and R0 of DSS are 7.4o and 3.3m, respectively. In contrast, the performance of PD is constrained with Δτ. When Δτ=0.1ms, the average biases of θ and R0 of PD are 2.2o and 3.6m, respectively. However, the DPS estimator combined the constraints of double sources spacing and path difference. It has a better performance, which will be further illustrated with experimental results. When Δφ=0.1° and Δτ=0.1ms, the average biases of θ and R0 of DPS are 1.8o and 1.6m, respectively. Both of them are smaller than those of DSS or PD.

In the case of above trace with θ=10o and R0=41.8m, the estimated trace using DPS is presented in Fig. 4 when signal to noise ratio (SNR) is 0dB. Here, SNR is defined as the power ratio between the pulse sources and background noise. Compared with the real trace, the result of baseline positioning method fluctuates around 10m in range estimation. While the estimated track parameters of DPS are θ=9.9o and R0=41.4m. Clearly, the DPS method has a better performance.

Fig. 4 Estimated trace using DPS when SNR=0dB

After Monte Carlo simulation with 100 trials in the same conditions, Fig. 5 provides the average deviation of track parameters of three methods in different SNR. Obviously, DPS deserves the best performance. And DSS has the largest track azimuth deviation. In the aspect of abeam distance, PD

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possesses the worst performance.

(a) average deviation of track azimuth

(b) average deviation of abeam distance

Fig. 5 Average deviation of track parameters estimation of DSS, PD and DPS in different SNR

4 Experiments

The cost of experiments for underwater moving target is high. Thus, a battery car with linear track is applied to verify the performance of DSS, PD and DPS. As shown in Fig. 6, four acceleration sensors were stuck on T-squares and they were put on the linear track with same distance of 4 meters. The acquisition system recorded signals of acceleration sensors and microphone sensors simultaneously. Then the time that the car ran over T-squares will be recorded. Combined with the measured geometry, the real track can be obtained. The estimated track will be compared with it to evaluate the performance of DSS, PD and DPS.

Fig. 6 Experiment illustration of linear motion targets

Consider an ULA with M=7 and sensor spacing d=0.3m as the baseline array. Two sinusoidal sources have same pulse cycle Tc=200ms and different carrier frequencies f0=[2400,

1800]Hz. Their amplitude ratio is 1:2 in time domain and double sources spacing r0=0.64m. The linear track parameters are set to θ=0o and R0=40.6m. The battery car follows accelerated linear track with speed v=[4.25, 4.83, 5.13, 5.32]m/s at T-square positions x=[−8,−4,0,4]m. Here, the Doppler effect of 5m/s in air is equivalent to that of 22m/s in water.

The spectra of DSS, PD and DPS are shown in Fig. 7 with pulse number K=6. The normalized spectra of DSS and PD are illustrated in Fig. 7(a). Fig. 7(b) gives the spectrum of DPS. Obviously, the peak shapes of DSS and PD like mountain ridges. Their peak points will move in these ridges along with SNR descending. It deteriorates the performance of DSS and PD. The spectrum of DPS is a product of that of DSS and PD. Its cone peak just locates at the intersection area of the mountain ridge of DSS and PD. Clearly, the performance of DPS is more robust. On the other hand, the estimated x coordinates of these 6 pulses are [−9.8, −9.1, −8.2, −7.3, −6.4, −5.5]m. The corresponding estimated velocities are [3.97, 4.13, 4.50, 4.47, 4.59]m/s. It means the bias of estimated velocity is around 0.25m/s.

(a) DSS and PD

(b) DPS

Fig. 7 Spectra of DSS, PD and DPS

The experimental results are listed in Table 1. Here, there are two linear tracks. And two trials are conducted in each track. The track 1 is illustrated in Fig. 6. And the parameters of track 2 are θ=−45o and R0=57.4m through a counterclockwise rotation of the array. In Table 1, the results of all trials are listed. Thus, two bias results are obtained for each track in different methods. In addition, PD1 and PD2 denote the PD method for each pulse source. Obviously, the performance of DSS, PD and DPS improve in sequence.

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Specially, in the case of DPS the biases of θ and R0 are under 0.6o and 3.4m, respectively.

Table 1 The track parameter biases (|Δθ|, |ΔR0|) of a moving

car with linear track / ( o, m)

Methods Tracks

DSS PD1 PD2 DPS

Track 1 (11.0, 6.8) (4.0, 12.6) (2.4, 7.2) (0.6, 3.4) (16.6, 7.6) (2.6, 9.4) (1.0, 4.2) (0.4, 1.6)

Track 2 (20.0, 17.2) (1.6, 9.0) (1.8, 16.0) (0.2, 2.8) (19.8, 13.8) (2.4, 10.0) (0.2, 2.0) (0.6, 2.2)

5 Conclusions

The DPS method was presented to improve the performance of DSS. The estimated track parameters will be applied to resolve Doppler of the emitted sound of the underwater moving target. Then the processed data could be used to noise identification with correct frequency and amplitude. The DPS method makes use of the pulse source for DOA estimation through baseline positioning method. Compared with DSS, it requires less array number and its bearing estimation is not affected by Doppler. The DPS estimator takes advantage of the cross part of DSS and PD estimator, which makes DPS be more robust.

References

Cheng Y, Wang X, Caelli T, Moran B (2011). Tracking and localizing moving targets in the presence of phase measurement ambiguities. IEEE Transactions on Signal Processing, 59(8), 3514-3525.

Gershman AB, Turchin VI, Zverev VA (1995). Experimental results of localization of moving underwater signal by adaptive beamforming. IEEE Transactions on Signal Processing, 43(10), 2249-2257.

Hattori T, Watanabe Y, Ochi H, Shimura T (2010). A calibration of SSBL acoustic positioning system in the ocean. OCEANS '10 IEEE Sydney, Sydney, Australia, 1-6.

Jidan M, Xueli S, Longxiang G, Jingwei Y (2010). Sea trial research on multi-source underwater acoustic image measurement technology based on the sparse array. OCEANS'10 MTS/IEEE Seattle, Seattle, Washington, USA, 1-5.

Ruiz IT, de Raucourt S, Petillot Y, Lane DM (2004). Concurrent mapping and localization using sidescan sonar. IEEE Journal of Oceanic Engineering, 29(2), 442-456.

Tegborg V, Pettersson MI, Claesson I (2011). Experimental results of passive imaging of moving continuous broadband sound sources within a sensor field. IEEE Journal of Oceanic Engineering, 36(1), 25-36.

Wei HW, Peng R, Wan Q, Chen ZX, Ye SF (2010). Multidimensional scaling analysis for passive moving target

localization with TDOA and FDOA measurements. IEEE Transactions on Signal Processing, 58(3), 1677-1688.

Yan G, Chen Z, Sun J (2009). Using a linear array to estimate the velocity of underwater moving targets. Journal of Marine Science and Application, 8(4), 343-347.

Author biographies Zhifei Chen was born in 1982. He is a postdoctor at School of Automation, Northwestern Polytechnical University. His research interests are array signal processing and noise source identification.

Hong Hou was born in 1966. He is a professor at School of Marine, Northwestern Polytechnical University. His research interests are acoustics, noise and vibration control.

Jianhua Yang was born in 1967. She is a professor at School of Automation, Northwestern Polytechnical University. Her research fields include integrated test facility, noise and vibration measurement.

Jincai Sun was born in 1938. He is a professor at School of Marine, Northwestern Polytechnical University. His research interests include sound signal processing and acoustics.

Qian Wang was born in 1982. He is an engineer at the 705th Institute of China Shipbuilding Industry Corporation. And he is pursuing his PhD degree in Northwestern Polytechnical University. His research field is noise and vibration control.