Self-localization of autonomous underwater vehicles with accurate sound travel time solution

Computers and Electrical Engineering 50 (2016) 26–38

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Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng

Self-localization of autonomous underwater vehicles with accurate sound travel time solutionR Jing Li a, Han Gao a, Shujing Zhang b, Shuai Chang a, Jiaxing Chen b, Zhihua Liu c,∗ a

College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, Hebei, China College of Vocational Technology, Hebei Normal University, Shijiazhuang 050024, Hebei, China c College of Information Technology, Hebei Normal University, Shijiazhuang 050024, Hebei, China b

a r t i c l e

i n f o

Article history: Received 4 February 2015 Revised 18 November 2015 Accepted 18 November 2015

Keywords: Underwater acoustic sensor networks Autonomous underwater vehicles Self-localization Sound travel time Ranging optimization

a b s t r a c t In underwater acoustic sensor networks, long baseline localization for autonomous underwater vehicles (AUVs) requires distance estimation that always encounters severe problems: (a) Time-synchronization is hard to achieve in underwater environment, which baffles ranging methods based on the synchronized time. (b) Long propagation delay of acoustic signals and the impact of AUVs’ mobility make it rash to use the round trip ranging (RTR) technology. (c) Sound speed uncertainty enlarges the inaccuracy of distance estimation. This work addresses those problems above and proposes an AUVs self-localization algorithm with accurate sound travel time solution (SL-STTS), which is time-synchronization free and ranging optimization based. Simulation results show that under the measurement noise of time and angles, the root mean square error of SL-STTS is decreased by about 8–79% compared with the counterparts. In addition the average distance estimation error of SL-STTS is declined by 42% compared with RTR. © 2015 Elsevier Ltd. All rights reserved.

1. Introduction In underwater acoustic sensor networks (UASNs), autonomous underwater vehicles (AUVs) have been increasingly gaining concerns, as they make it accessible to those untouchable areas for human beings and assist with complex and arduous ocean tasks. AUVs are untethered and intelligent mobile platforms [1]. In many scenarios like target tracking [2], AUV-aid localization [3], and demining etc., AUVs need accurate localization for the accuracy of the gathered data [4]. And due to tough underwater conditions and technical restrictions, to localize a moving AUV is still challenging and needs more complementary researches. Since the global position system (GPS) cannot work underwater because of bad attenuation of radio frequency (RF) signals, the inertial navigation system (INS) is mostly applied on AUVs. INS suffers from error accumulation. High-quality INS is however greatly expensive and can only provide relative locations. Overall, it is a better and available scheme to take advantage of acoustic communication for AUVs self-localization [5]. Acoustic localization system for AUVs includes long baseline (LBL), short baseline (SBL) and ultra-short baseline (USBL). Compared with SBL and USBL, LBL is more cost-effective [4]. In LBL, AUVs communicates with one or more transponders fixed on the seabed to measure range information and achieve self-localization. One-way ranging is mostly based on time of arrival (ToA) and time difference of arrival (TDoA). ToA needs strict time-synchronization, which is energy-intensive and hard to achieve. Multiplenode cooperation in TDoA [6,7] increases cost and is computationally complex. The round-trip ranging (RTR) technology [8] is R ∗

Reviews processed and approved for publication by the Editor-in-Chief. Corresponding author. Tel.:+86 13930194955, +86 15227865118. E-mail addresses: [email protected] (J. Li), [email protected] (J. Chen), [email protected], [email protected] (Z. Liu).

http://dx.doi.org/10.1016/j.compeleceng.2015.11.018 0045-7906/© 2015 Elsevier Ltd. All rights reserved.

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

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frustrated by the long propagation delay and AUVs’ mobility. In RTR, the two-way travel time (TWTT) between the AUV and a transponder is halved as the one-way travel time (OWTT), which is the propagation delay of acoustic signals traveling from the AUV to a transponder or the opposite case. Consequently the ranging error is increased since the AUV has sailed away from where it signals. But many approaches ignored this e.g. [6,7,9]. Moreover, the underwater sound speed is no constant but varies with salinity, temperature and depth [10], which adds uncertainty of location estimates. To solve these problems stated above, we propose a self-localization algorithm with accurate sound travel time solution (SLSTTS) for AUVs in shallow water (depth < 500 m). SL-STTS is time-synchronization free. The ranging accuracy relies on precise time measurement. It is accessible in microsecond resolution with seabed transponders [11] whose locations are known in advance with some technologies e.g. [12]. Orientation for the AUV and angle of arrival (AoA) for acoustic signals from transponders are analyzed to calculate the OWTT. As we know, the error of OWTT estimation in milliseconds may cause error of distance estimation in meters, which weakens localization accuracy. So it’s indispensable to work out a high performance sound travel time solution. We model the function relating the distance estimates to the location vector of AUV. The Levenberg–Marquardt algorithm (LMA) [13] is utilized to optimize the distance estimates. Our main contribution is as follows. First, the time-synchronization free scheme is presented which saves energy used for frequent two-way packet exchange in the time-synchronization ones. Second, the accurate sound travel time solution is proposed which improves ranging and localization accuracy. Third, we analyze the mathematical expectation of underwater sound speed, employ it for distance estimation and further analyze the rationality in theory. Fourth, we employ the LMA in solving the nonlinear least squares optimization problem and localizing the AUV. SL-STTS can also be used in recalibrating the INS without resurfacing. A reminder of this paper presents as follows: the related work are reviewed in Section 2. Section 3 gives an overview of the proposed algorithm and expatiates on how an AUV localizes itself. The performance of our algorithm is discussed in Section 4. Next a conclusion and the future efforts are summarized in Section 5. 2. Related work Recent years, problems of AUVs localization have been studied extensively. In this section algorithms concerning AUVs localization presented in recent works are briefly reviewed. In underwater area, acoustic signal is an ideal information carrier for it is less attenuated and can travel longer distances [14]. All underwater acoustic localization systems suffer most from sound speed uncertainty. In [10] the relation between OWTT and AUV location was modeled on the isogradient sound speed profile and Snell’s law. Based on this model, the extend Kalman filter (EKF) was used to localize the AUV. Kussat et al. [11] conducted a series of sea trails in shallow water. They investigated the sources (salinity, temperature and depth) leading to sound speed uncertainty. Sound propagation ray trace was studied in [15] to model depth-dependent sound speed profile. Based on unknown-but-bounded uncertainty and distance estimates, Caiti et al. [16] calculated out the region where the AUV resides. Then the sound propagation ray path was analyzed to obtain how the varying sound speed affected such region. Liu et al. [5] studied coordinated localization for multiple AUVs based on TDoA technology. In [15] a non-linear least squares estimator using the Newton’s method was performed to give location estimates based on the ToA measurements. Meanwhile a gradient descent algorithm was adopted to improve the estimates. Karimi et al. [17] adopted a two-loop decentralized data fusion method. EKF worked in both loops to estimate locations of the AUV with its information of velocity, orientation and depth. A decentralized information filter did the final fusion of the estimates produced in both loops. Eustice et al. [18] proposed a max likelihood sensor fusion method based on the OWTT information, but it needs synchronous clock and surface ships as GPS to assist underwater localization, which is not economical. Those algorithms listed above well disposes the localization uncertainties caused by measurement noise by means of denoising. The ranging optimization in this work is motivated by this point, for the main challenge that confronts LBL is the ranging uncertainty. However, the above methods solve the OWTT through mathematically analyzing RTR, ToA or TDoA, which meets limitations stated in Section 1. Especially the RTR technology may trigger large ranging error. One major difference between this work and the above methods is that this problem has been considered and addressed well by the proposed sound travel time solution. And in the above approaches, the sound speed uncertainty is either processed with complicated computation or not given enough consideration. However, this work proposes a more simple way to estimate the sound speed. 3. Algorithm design In this work we focus on AUVs self-localization in shallow water (depth < 500 m). The orientation of an AUV includes yaw angle, pitch angle and roll angle [17]. In this work we only need the information of yaw angle and pitch angle. All the locations and angles are computed in the global Cartesian coordinates. The AUV is equipped with sensors measuring its forward velocity, zaxis gyro and inclinometer measuring its yaw angle and pitch angle [2,17], and AoA antennas measuring AoA of received acoustic signals. Conductivity–temperature–depth (CTD) instruments [11] are preloaded onto the AUV and transponders to help estimate sound speed by measuring salinity, temperature and depth. We first take an overview on SL-STTS and afterwards demonstrate how SL-STTS works in detail.

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J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

Fig. 1. Network model of SL-STTS.

3.1. Overview of SL-STTS The AUV localizes itself through acoustic communication with seabed transponders. The network model is given in Fig. 1. Consider the case that an AUV travels with velocity V in a three-dimensional (3D) underwater environment. At time instant t, the AUV locates at Mt : (xMt , yMt , zMt ) undetermined. It broadcasts a localization request, meanwhile starts a timer and measures the sound speed c(TAUV , sAUV , zAUV ). Assume that there are w (w ≥ 3) transponders receiving this request and define the set as A = {ai }, i = 1, 2, . . . , w, where i is the identifier (ID) of transponder ai with known location Ai : (xai , yai , zai ). For transponder ai as an example. After ai receives the request at its local time t1i , it puts its ID, the sound speed measured by CTD and its location into a localization packet i . At its local time t2i , it adds the leaving time t2i into i as soon as it responds to the AUV with i . The AUV receives i at its local time t3i . When the timer is out, the AUV stops receiving replies from transponders and processes the received localization packets. Assume the communication range of AUV to be R. The maximum TWTT of an acoustic signal between the AUV and transponder ai is 2R/c (TAUV , sAUV , zAUV ) + α , where α is the max time needed for transponders to process acoustic signals and prestored by the AUV. Thus the timer period can be defined as

timer period = 2R/c (TAUV , sAUV , zAUV ) + α

(1)

From Fig. 1 we can observe that due to the AUV’s motion, when the AUV receives i at t3i , it may have moved to the next location. Thus the OWTT of an acoustic signal traveling from the AUV to a transponder may not equal the opposite case. And since the time is not synchronized between transponders and the AUV, the OWTT cannot be calculated with single t1i − t or t3i − t2i . Generally, SL-STTS performs in two steps, (a) ranging and (b) optimization and iterative localization. Next we will give the detail process. 3.2. Ranging for SL-STTS The AUV first broadcasts a localization request to estimate distances relative to transponders. The ranging step includes three stages: OWTT estimation, sound speed estimation and distance estimation. 3.2.1. OWTT estimation The AUV measures the TWTT ti based on transponder ai with

    ti = t3i − t − t2i − t1i

In the RTR technology usually used in other algorithms, ti /2 is taken as the OWTT, which may cause large ranging error.

(2)

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

29

Fig. 2. Model of TWTT between the AUV and transponder ai .

When the AUV receives i , it has moved from Mt to Mt i : (xM i , yM i , zM i ) as shown in Fig. 2. For simplicity we assume V to 3

be a constant. Thus the traveling distance of AUV is



t

t

3

3

t

3



Di = t3i − t · V

(3)

Define the OWTT of a signal traveling from the AUV (at Mt ) to transponder ai as tiPDt , from transponder ai to the AUV (at Mt i ) PD f

as ti

PD f

. Obviously tiPDt and ti

3

may not be equal. Redefined the TWTT model as

ti = tiPDt + tiPD f = 2tiPDt + εi It’s clear that εi = ti

PD f

(4)

− tiPDt .

−−−→ −−−−→ In Fig. 2, let β i denote the angle between vectors Ai Mt i and Mt Mt i . Define the elevation AoA and azimuth AoA of the received 3

3

acoustic signal from transponder ai be φ i and ϕ i , which are measured from the positive Z-axis and X-axis by AoA antennas, respectively. Since in shallow water the ray trace of sound can be treated as straight line [15], the values of direction cosine for −−−→ Ai Mt i along X-axis, Y-axis and Z-axis are sin φ i cos ϕ i , sin φ i sin ϕ i and cos φ i , respectively [19]. 3

The pitch angle θ i and yaw angle ψ i of an AUV can be measured by inclinometer and z-axis gyro [2,17]. As illustrated in Fig. 3, θ i and ψ i are the rotation about the Yl -axis and Zl -axis in the AUV’s local coordinates, respectively. The only difference between the AUV’s local coordinates and the global Cartesian coordinates is that Zl -axis is in the opposite direction of Z-axis. Thus in the global Cartesian coordinates, the pitch angle of AUV is π − θi and the yaw angle is still ψ i . In the ideal case, the AUV doesn’t change its orientation (next we will analyze the case where the AUV changes its orientation). −−−→ −−−−→ Similar to Ai Mt i , the values of direction cosine for Mt Mt i along X-axis, Y-axis and Z-axis are sin(π − θi ) cos ψi , sin(π − θi ) sin ψi 3

3

and cos(π − θi ), respectively.

−−−→ −−−−→ Define the unit vectors with the same direction as Ai Mt i and Mt Mt i be λ and κ respectively. Then we can get 3

3

λ = (sin φi cos ϕi , sin φi sin ϕi , cos φi )

(5a)

κ = (sin (π − θi ) cos ψi , sin (π − θi ) sin ψi , cos(π − θi ))

(5b)

the cosine value of angle β i is

cos βi

−−−→ −−−→ Ai Mt i · Mt Mt i 3  =λ·κ = −−−→3   −−−→ Ai Mt i Mt Mt i  3

3

(6)

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J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

Fig. 3. Orientation of the AUV.

−−−→ −−−−→ Namely instead of vectors Ai Mt i and Mt Mt i , we can use their unit vectors to measure the cosine value of β i . From Fig. 2 we 3

3

can see that βi = ∠Ai Mt i Mt . According to the cosine law and combining formula (4), the cosine value of β i can also be calculated 3 as

Mt Mt2i + Ai Mt2i − Ai Mt 2

cos βi =

3

3

2 · Mt Mt i · Ai Mt i 3

3

D2 + ti εiC 2 = i Di (ti + εi )C

(7)

where C is the sound speed estimated by formula (12). It leads to ɛi by substituting formulas (2), (3) and (6) into formula (7). PD f can be further solved out. Combining formula (4), tiPDt and ti It is noteworthy that when the AUV receives the reply from transponder ai , its orientation may have changed, as shown in −−−−→ Fig. 4. Thus in this case, we should reconsider the vectors Mt Mt i and κ . 3 −−−→ −−−−→ In Fig. 4, the orientation of AUV at time t and t3i can be denoted by 3D vectors Mt M and M Mt i respectively. It is clear that 3

−−−→ −−−→ −−−→ Mt Mt i = Mt M + M Mt i 3

(8)

3

−−−−→ −−−→ Define the unit vectors of Mt M and M Mt i be λ1 and λ2 respectively. Thus we can get 3

κ = λ1 + λ2

(9)

λ1 and λ2 can be calculated with the same principle as λ (see formula (5a)). 3.2.2. Sound speed estimation In underwater environment the sound speed varies with salinity, temperature and depth. The empirical model of sound speed is [6]

c (T, s, h ) = 1492.9 + 3(T − 10 ) − 6 · 10−3 (T − 10 )2 − 4 · 10−2 · (T − 18 )2 + 1.2(s − 35 ) − 10−2 (T − 18 )(s − 35 ) + h/61

(10)

where T, s, h are temperature, salinity and depth respectively. With formula (10), the sound speed for the AUV and transponder ai which are c(TAUV , sAUV , zAUV ) and c (Tai , sai , zai ) can be calculated after measuring the according parameters. In shallow water, the sound speed can be assumed to vary pseudo-linearly with depth. It decreases continuously and monotonically [15]. Thus it obviously obeys the uniform distribution. Define cmax = max(c (TAUV , sAUV , zAUV ), c (Tai , sai , zai )) and cmin = min(c (TAUV , sAUV , zAUV ), c (Tai , sai , zai )). The probability density function of sound speed c at interval [cmin , cmax ] is



f i (c ) =

1/(cmax − cmin ),

c ∈ [cmin , cmax ]

0,

others

(11)

and hence the mathematical expectation of sound speed is

Ei ( c ) =



cmax cmin

c fi (c )dc

(12)

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

31

Fig. 4. The case where the AUV changes its orientation.

Ei (c) is taken to approximate the sound speed. In Section 3.2.3 we will account for the rationality. 3.2.3. Distance estimation In this part we will give theoretical analysis on the rationality of using the mathematical expectation Ei (c) to approximate the sound speed for distance estimation. In order to estimate the distance dˆi between the AUV and transponder ai at time instant t, we averagely divide the OWTT tiPDt into n weeny sub-intervals. Each interval is

 = tiPDt /n, n → ∞

(13)

Since  is weeny, we can assume that the acoustic signal travels with constant speed ck , k = 1, 2, . . . , n during  . Obviously ck ∈ [cmin , cmax ]. Combined with formula (13) dˆi can be deduced as

dˆi =



 · ck

= tiPDt /n ·

n 

ck

k=1

= tiPDt ·

n 

ck /n

(14)

k=1

In formula (14) the term

n 

ck /n expresses the mean value of the sound speed at interval [cmin , cmax ], as ck occurs with equal

k=1

probability. And ck has infinite available values. Thus we have

n 

ck /n ≈ Ei (c ). And formula (14) can be rewritten as

k=1

dˆi ≈ tiPDt Ei (c )

(15)

3.3. Optimization and iterative localization The distance estimates are assumed to be disturbed by noise with Gaussian distribution as

dˆi = d (Y ) + W where d (Y ) = (d1 (Y ), d2 (Y ), . . . , di (Y ), . . . , dw

(16)

(Y ))T

is the vector of real distances between the AUV (at Mt ) and transponders

A, dˆ = (dˆ1 , dˆ2 , . . . , dˆw )T is the estimate of d(Y); di (Y ) =

(xMt − xai )2 + (yMt − yai )2 + (zMt − zai )2 and Y = (xMt , yMt , zMt )T ; W

32

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38 Table 1 Simulation settings of the used instruments. Instrument

Variable

Precision

Conductivity sensor Temperature sensor Pressure sensor Inclinometer Z-axis gyro Velocity sensor

Salinity Temperature Depth Pitch Yaw Velocity

± 0.0001 s/m ± 0.001 °C ± 0.1 bar 0.1◦ −1◦ 0.1° ± 0.2 cm/s

Algorithm 1 Levenberg–Marquardt algorithm. Initialization: k = 1; Y k = multilateration(. . . ); T

μ = 10−3 max{diag(J (Y k ) J (Y k ))}; T

E = J (Y k ) f (Y k ) ∞ −η; Iteration: 1: while E > 0 and k ≤ K do 2: 3: 4: 5: 6:

T

h = −(J (Y k ) J (Y k ) + μI )−1 J (Y k )T J (Y k ); if h ≤ η ( Y k + η ) then break; else Y k+1 = Y k + h;

7:

Q=

8:

if

F (Y k )−F (Y k+1 ) T

1/2·hT (μh−J (Y k ) f (Y k ))

Q>0

then T

9: E = J (Y k+1 ) f (Y k+1 ) ∞ − η; μ = μ max{1/3, 1 − (2Q − 1 )3 }; 10: v = 2; 11: 12: else 13: Y k+1 = Y k ; μ = μ · v; v = 2v; 14: end if 15: end if 16: k = k + 1; 17: end while Output: Yk

represents the estimation noise vector which causes ranging errors. We assume that W is i.i.d with W ∼ N(0, COV). COV is the covariance matrix of W as COV = diag(σ12 , σ22 , . . . , σi2 , . . . , σw2 ), where σi2 is the variance of the distance estimation noise based on transponder ai . In order to solve Y, we adopt the LMA [13] to minimize the sum square error of distance estimates. This nonlinear least squares optimization problem w.r.t. the variable Y is defined as

arg min d (Y ) − dˆ 2 Y

(17)

LMA starts with an initial location estimate and improves it iteratively. We take the result of multilateration method as the initial location input. Since the depth of an AUV can be measured by CTD, it needs at least three transponders (w ≥ 3) to do the multilateration. The LMA is described in the Algorithm 1 below. In LMA Yk is the estimate of Y in the kth iteration; f (Y ) = d (Y ) − dˆ and F (Y ) = 1/2 · f (Y )T f (Y ) model the optimization problem; J(Y) is the Jacobian matrix of f(Y); μ determines the descent rate of step h; v decides the growth rate of μ; K and η are user-defined parameters to help stop the iteration. The final value of Yk is taken to be the location estimate of the AUV at time instant t. 4. Simulation analysis We conduct simulations on Matlab 7.9 for performance analyses of our proposed algorithm. An AUV travels freely with velocity V in a 3D underwater area of 500 m × 500 m × 400 m. The space coordinate varies from [0, 0, 100] to [500, 500, 500]. Eight transponders are deployed in. Their coordinates vary from [0, 0, 450] to [500, 500, 500]. The communication range R is set to be 200 m. We run our algorithm 50 times for each group of data. The sound speed is set to be 1500 m/s. The precision settings of CTD, inclinometer, z-axis gyro and velocity sensor are shown in Table 1. Performance of distance estimation for RTR and SL-STTS is compared in Section 4.2. The impact of distance estimation noise W is discussed in Section 4.3. How the main causes of W, which are the measurement noise of time and angles, affect localization accuracy is analyzed in Sections 4.4 and 4.5. Afterwards the influence of AUV’s velocity is demonstrated in Section 4.6. The localization ratio under different values of R and V is shown in Section 4.7.

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

33

Average distance estimation error (m)

1 RTR

0.9

SL−STTS

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0

0.2

0.4 0.6 True value of | i| (ms)

0.8

1

Fig. 5. Average distance estimation error vs. true value of |ɛi |.

We adopt the root mean square error (RMSE)



RMSE =

1/n ·

n    Y − Yˆi 2

(18)

i=1

as the error standard, where Y is the real coordinate vector of AUV and Yˆi is the estimate of Y. n is set to be 50 as we run the algorithm 50 times. The Cramér–Rao bound (CRB) [13] is introduced to provide a benchmark for the performance of SL-STTS. 4.1. CRB CRB places a lower bound on the variance of estimators of a nonrandom factor. The bound expresses that the variance of any unbiased estimator is at least as high as the inverse of the fisher information (FIM). The FIM I(Y) of an estimator disturbed by independent Gaussian noise can be calculated with [10]



I (Y )i j = ∂ dT (Y )/∂ Yi · COV −1 · ∂ d (Y )/∂ Y j + 1/2tr COV −1 · ∂ COV/∂ Yi · COV −1 · ∂ COV/∂ Y j

(19)

where I(Y)ij is the element of the ith row and jth column of I(Y), ∂ d(Y)/∂ Yj equals the jth column of J(Y), and

  ∂ COV/∂ Y j = diag ∂ [COV ]11 /∂ Y j , ∂ [COV ]22 /∂ Y j , . . . , ∂ [COV ]ww /∂ Y j

(20)

and Yj is the jth element of Y, i.e. Y1 = xMt , Y2 = yMt and Y3 = zMt . The CRB can be computed by [10]

CRB =

3 

I−1 (Y )

ii

(21)

i=1

In the following simulations we will verify that SL-STTS meets the CRB well. 4.2. Performance comparison of distance estimation The performance of distance estimation under RTR and SL-STTS is compared in Fig. 5. We set σi2 = 10−1 and V = 2 m/s. The absolute difference between the real distance and its estimate is taken as distance estimation error. When |εi | = 0, namely PD f when tiPDt = ti , RTR and SL-STTS estimate distance with the same principle. As shown in Fig. 5, the values of average distance estimation error for RTR and SL-STTS are similar at |εi | = 0. However with |ɛi | increasing, the average distance estimation error of RTR exceeds SL-STTS and grows rapidly, while the latter is almost affected little. It is obvious because when tiPDt has larger bias PD f

against ti , RTR results in bad OWTT estimate but SL-STTS can give much more accurate one. Compared with RTR, the average ranging error of SL-STTS is declined by about 42%.

34

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38

1

10

SL−RTR SL−STTS Mean CRB 0

RMSE (m)

10

−1

10

−2

10

1

10

0

−1

10

−2

10

−3

10 2 i

10

−4

10

(m)

Fig. 6. RMSE vs. variance of distance estimation noise.

2

10

SL−RTR SL−STTS Mean CRB

1

10

Optimal−ToA

RMSE (m)

EKF−ESSP 0

10

−1

10

−2

10

−4

10

−5

10

−6

10 2 1

−7

10

−8

10

(s)

Fig. 7. RMSE vs. variance of time measurement noise.

4.3. Distance estimation noise and RMSE In this experiment, we analyze how the distance estimation noise W affects localization accuracy. In order to compare localization performance with RTR, we also run our algorithm with RTR technology instead of our proposed accurate sound travel time solution to calculate the OWTT, and we call it SL-RTR. For simplicity, σi2 is set equal to each other and distance independent. Thus the second term of formula (19) is 0. The velocity of AUV is set to be 2 m/s. As the results shown in Fig. 6, in general the RMSE of SL-STTS meets the mean CRB however SL-RTR floats over it. SL-STTS performs 23% better than SL-RTR. With decreasing the noise variance, the values of RMSE for both SL-RTR and SL-STTS show a decline, however the latter downs much faster. In other words, the localization accuracy is sensitive to distance estimation noise, which verifies the significance of precise ranging. In Fig. 5 we have verified that high performance sound travel time solution brings accurate distance estimates. Combined with Fig. 6, we can further conclude that high performance sound travel time solution contributes to accurate location estimates.

J. Li et al. / Computers and Electrical Engineering 50 (2016) 26–38 −7 2 =10 1

a

35 −6 2 =10 1

b

1.5

4.5

1.2

3.5

4 SL−STTS RMSE (m)

RMSE (m)

SL−STTS

3

SL−RTR 0.9

Optimal−ToA EKF−ESSP

0.6

SL−RTR

2.5

Optimal−ToA EKF−ESSP

2 1.5 1

0.3

0.5 0

0 1

10

0

10

−1

−2

10

−3

10 2 2

−4

10

1

10

0

10

−1

10

−2

10

10 2 2

(deg)

−3

10

−4

10

(deg)

2 =10−5 1

c 10

8

RMSE (m)

SL−STTS SL−RTR

6

Optimal−ToA EKF−ESSP

4

2

0 1

10

0

10

−1

−2

10

10 2 2

−3

10

−4

10

(deg)

Fig. 8. RMSE vs. variance of measurement noise of angles.

4.4. Time measurement noise and RMSE It should be noted that the measurement accuracy of ti and angles dominates the precision of OWTT estimates and further affects localization performance. In this experiment we simply investigate the effect of time measurement noise and add no noise of angle measurements. The localization performance is compared with the other three methods, SL-RTR, method [15] (we call it Optimal-ToA) and method [10] (we call it EKF-ESSP). V is set to be 2 m/s. The time measurement ti based on transponder ai is assumed to be disturbed by Gaussian distributed noise with zero mean and variance σ12 . As shown in Fig. 7, the RMSE of SL-STTS meets the mean CRB however that of SL-RTR floats over it. With decreasing noise variance σ12 , the values of RMSE for all these four methods go down sharply. The reason behind it is that the bias of time measurements in milliseconds may cause error of distance estimates in meters. Thus for both AUVs and transponders, it is necessary to equip clocks with high time resolution. Compared with SL-RTR, Optimal-ToA and EKF-ESSP, the localization performance of SL-STTS is improved by about 25%, 37% and 75%, respectively. 4.5. Measurement noise of angles and RMSE The input angles of SL-STTS are disturbed by noise assumed to be Gaussian distributed with zero mean and variance σ22 . In this experiment we investigate how such noise affects localization accuracy. σ22 is added to all the angle measurements and set to vary from 10−4 to 101 and V = 2 m/s. From the results shown in Fig. 8, we can observe that with fixed σ12 the RMSE of SL-STTS goes down slowly when σ22 decreases. While the other three methods present little performance change as the fact that they are irrelevant to inputs of AoA and orientation. When σ22 is fixed and σ12 is increasing, all the methods present a performance reduction. And SL-STTS works better than Optimal-ToA gradually. That is to say, SL-STTS is more immune to the time measurement noise than the other three approaches. Fig. 8 also indicates that the effect of angle measurement noise is small on the localization accuracy of SL-STTS. Namely, SL-STTS is slightly affected by the large error commonly arising in AoA and orientation measurements.

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a

b 10

4.5

9

4 3.5

SL−STTS Mean CRB

3 RMSE (m)

Percentage of error growth (%)

SL−RTR

Optimal−ToA 2.5

EKF−ESSP

2 1.5 1 0.5

8 7 6 5 4 3 2 1

0

0 1

2

3 4 Velocity of AUV (m/s)

5

6

SL−STTS

SL−RTR Optimal−ToA Algorithms

EKF−ESSP

Fig. 9. Impact of the velocity of AUV.

1 0.9

Localization Ratio (%)

0.8 0.7 0.6 0.5 0.4 R=50m

0.3

R=150m 0.2

R=200m

0.1 0 1

2

3 4 Velocity of AUV (m/s)

5

6

Fig. 10. Communication range and velocity of AUV vs. localization ratio.

4.6. Impact of the velocity of AUV Fig. 9(a) shows the RMSE as a function of V. We vary V from 1 to 6 m/s and set σ12 = 10−6 , σ22 = 10−1 . It can be found that with V varying, the values of RMSE for all the four approaches change smoothly. And the localization performance of SL-STTS is improved by about 8%, 23% and 79% compared with Optimal-ToA, SL-RTR and EKF-ESSP, respectively. The percentage of error growth is compared in Fig. 9(b). It can be observed that when V is increased from 1 to 6 m/s, the values of RMSE don’t grow too much for these four methods. The angle inputs for SL-STTS may lose accuracy under larger speed of the AUV. However in Fig. 8, it has proved that SL-STTS is slightly affected by the angle measurement noise. Furthermore, optimization of the measured data, as was performed in the counterparts, well eliminates the inaccuracy due to larger velocity. 4.7. Impact of the communication range and velocity of AUV on localization ratio The AUV receives localization packets within the timer period defined by formula (1). In this experiment we study how the communication range R in formula (1) and the velocity V of AUV affect the localization ratio, which can be calculated with

Localizationratio =

localizedtimes × 100% n

(22)

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where n is the total run times as defined in formula (18). If the AUV receives enough localization packets (at least three), it can be localized. Here we set α = 0.1 s. From the results shown in Fig. 10, we can see that when R increases, the localization ratio becomes little affected by V. In the LBL system, the value of R can reach hundreds of meters. The largest speed AUVs can achieve is only 5 m/s, which is about 300 times slower than the sound speed. And AUVs usually travel at normal speed 0.5 − 4 m/s. So the acoustic replies from transponders have arrived at the AUV before it moves out of its communication range. In other words, if the AUV moves fast enough and breaks through the communication range, however longer the timer period endures, the AUV cannot receive replies any more. It can be concluded that it is R that mainly affect the localization ratio. 5. Conclusion Range based LBL localization is sensitive to ranging accuracy. For the purpose of enhancing distance estimation precision, the SL-STTS method is presented. SL-STTS is time-synchronization free and works in shallow water (depth < 500 m). It gives more accurate OWTT estimates for distance estimation by analyzing the information of AoA and orientation of AUV. To solve the sound speed uncertainty, SL-STTS computes the mathematical expectation to approximate sound speed for distance estimation and gives theoretical analysis for its rationality. Furthermore, distance estimates are disturbed by measurement noise and need optimization. SL-STTS models the function between ranging optimization and localization. It adopts LMA to solve this function. Simulation results show that the localization performance of our proposed algorithm meets the mean CRB. And under the measurement uncertainties of angles and time, SL-STTS performs about 8–79% better than the counterparts. Its ranging accuracy is increased by 42% compared with RTR. From analyses through simulations, it is observed that the measurement noise of angles affects localization performance slightly however the time measurement noise affects it largely. In the next stage we will study more faithful noise models. We consider putting our algorithm into true underwater environment to verify the rationality and feasibility of the proposed sound speed solution. And as well, we will focus on the research of improving immunity of SL-STTS against time measurement noise in the future. Acknowledgments This research was sponsored by the National Natural Science Foundation of China under grant no. 61271125 and 61501168, Educational Commission of Hebei Province under grant no. QN2015045. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.compeleceng.2015. 11.018. References [1] Bellingham JG. Platforms: autonomous underwater vehicles. In: Steele JH, editor. 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In: Proceedings of the 2013 IEEE international underwater technology symposium (UT); 2013. p. 1–7. doi:10.1109/UT.2013.6519898. [16] Caiti A, Garulli A, Livide F, Prattichizzo D. Localization of autonomous underwater vehicles by floating acoustic buoys: a set-membership approach. IEEE J Ocean Eng 2005;30(1):140–52. doi:10.1109/JOE.2004.841432.

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[17] Karimi M, Bozorg M, Khayatian A. Localization of an autonomous underwater vehicle using a decentralized fusion architecture. In: Proceedings of the 2013 9th Asian control conference (ASCC); 2013. p. 1–5. doi:10.1109/ASCC.2013.6606302. [18] Eustice RM, Singh H, Whitcomb LL. Synchronous-clock, one-way-travel-time acoustic navigation for underwater vehicles. J Field Robot 2011;28(1):121–36. doi:10.1002/rob.20365. [19] Yang S, Thomas WK. Three-dimensional localization of a near-field emitter of unknown spectrum, using an acoustic vector sensor corrupted by additive noise of unknown spectrum. IEEE Trans Aerosp Electron Syst 2011;49(2):1035–41. doi:10.1109/TAES.2013.6494397. Jing Li is currently working towards the M.S. degree at the College of Mathematics and Information Science, Hebei Normal University, China. Her current research interests include localization and tracking in underwater acoustic networks. Han Gao is currently working towards the M.S. degree at the College of Mathematics and Information Science, Hebei Normal University, China. Her current research interests include localization in underwater acoustic networks. Shujing Zhang received her Ph.D. degree in the College of Information Science and Engineering from Ocean University of China. She is now a lecturer at the College of Vocational Technology of Hebei Normal University, China. Currently her research interests include SLAM for AUVs, machine learning and underwater acoustic networks localization. Shuai Chang is currently working towards the M.S. degree at the College of Mathematics and Information Science, Hebei Normal University, China. His current research interests include localization in wireless sensor networks, algorithm simulation. Jiaxing Chen received his Ph.D. degree in signal and information processing from Harbin Institute of Technology. He is the director of the Network Center at Hebei Normal University and a professor supervising 6 M.S. candidate students now. His current research interests include computer networks, address code design for mobile communication. ZhiHua Liu received her M.S. degree from Yanshan University, China. She is now an associate professor at College of Information and Technology of Hebei Normal University. Her current research interests include wireless and secure localization.