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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TSP.2014.2305640, IEEE Transactions on Signal Processing

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Bayesian Tracking in Underwater Wireless Sensor Networks with Port-Starboard Ambiguity Paolo Braca, Peter Willett, Kevin LePage, Stefano Marano, and Vincenzo Matta

Abstract Port-starboard ambiguity is an important issue in underwater tracking systems with anti-submarine warfare applications, especially for wireless sensor networks based upon autonomous underwater vehicles. In monostatic systems this ambiguity leads to a ghost track of the target symmetrically displaced with respect to the sensor. Removal of such artifacts is usually made by rough and heuristic approaches. In the context of Bayesian filtering approximated by means of particle filtering techniques, we show that optimal disambiguation can be pursued by deriving the full Bayesian posterior distribution of the target state. The analysis is corroborated by simulations that show the effectiveness of the particle-filtering tracking. A full validation of the approach relies upon real-world experiments conducted by the NATO Science and Technology Organization – Centre for Maritime Research and Experimentation during the sea trials Generic Littoral Interoperable Network Technology 2011 and Exercise Proud Manta 2012, results which are also reported.

Index Terms Copyright (c) 2013 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to [email protected]. P. Braca and K. LePage are with NATO STO Centre for Maritime Research and Experimentation, La Spezia, Italy, Email: {braca/lepage}@cmre.nato.int. P. Willett is with ECE, University of Connecticut, Storrs CT, Email: [email protected]. S. Marano and V. Matta are with DIEM, University of Salerno, via Giovanni Paolo II 132, I-84084, Fisciano (SA), Italy, Email: {marano/vmatta}@unisa.it. P. Willett was supported by the U.S. Office of Naval Research under contract N000014-13-1-0231

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1053-587X (c) 2013 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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Data fusion, antisubmarine warfare, port-starboard ambiguity, multistatic active sonar, target tracking, particle filtering, underwater wireless sensor networks, autonomous underwater vehicles.

I. I NTRODUCTION AND M OTIVATION Autonomous systems have a wide range of applications [1], especially in the underwater domain where it is preferable or mandatory to avoid the human presence. Autonomous underwater vehicles (AUVs) with sensing capabilities then substitute for the human operator, and autonomously work to perform many tasks, including object detection (e.g. underwater mines) [2], [3], interferometry [4], sea state sensing (e.g. measurement of temperature, conductivity, currents, etc.) [5]–[7]. But submarine detection and tracking, referred to as anti-submarine warfare (ASW), is one of the most important applications. Active ASW systems can be classified as monostatic, when the acoustic source and receiver are co-located, as opposed to multistatic systems in which the sources and the receivers are different entities, spaced apart from each other [8]–[10]. Many ASW systems are designed according to the multistatic achitecture and the minimum multistatic configuration, consisting of a single source-receiver pair, is referred to as bistatic. Acoustic sources are hull mounted sonars and active sonobuoy sources, while common examples of receivers are towed line arrays [12]. Traditionally these arrays have been towed by submarines or frigates, however this approach is manpower intensive. More recently, alternative approaches have been suggested in which the system is made of distributed mobile and stationary sensors, such as sonobuoys and AUVs [1], [13]–[15]. In contrast with the use of standard assets, these small, low-power, and mobile devices have limited onboard processing and wireless communication capabilities. Due to their low cost and moderate hardware/software complexity, individual sensors can only perform simple local computation and communicate over a short range at low data rates. But when deployed in a large number across a spatial domain and properly interconnected, these primitive sensors can form an intelligent network achieving very high performance with significant features of scalability, robustness, reliability. An overview on underwater wireless sensor networks (WSNs) is provided in [1]. In ASW systems based upon the WSN paradigm and employing AUVs, receiving sensors have limited onboard computational capabilities and therefore linear arrays with a conventional (rather than adaptive) beamformer are employed. In this regard, one key fact is that single line array February 7, 2014


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true target (port contact)

AUV

array beampattern towed array

ghost target (starboard contact)

Fig. 1. Sketch of the PS ambiguity problem. An AUV is towing a linear array. The array beampattern has a cylindrical symmetry w.r.t. the heading of the array (typically assumed aligned to the bow of the AUV), consequently there are always two symmetric main lobes, one on the port side and another one, specularly, on the starboard side. For instance, assuming that a target is detected on the port side, there will be a ghost target on the starboard side. In other words, it is not possible to discriminate the port from the starboard. More details can be found in the classic array processing literature, e.g. see [11].

receivers are cylindrically symmetric: They cannot discriminate if a detected echo comes from the port or from the starboard, i.e., they suffer from port-starboard ambiguity, see Fig. 1. Such an ambiguity complicates the detection and tracking algorithms and may cause severe performance degradation. Indeed, ambiguities are a challenging issue in many WSN applications involving sensors with very limited capabilities, see e.g., [16], [17]. Several approaches have been proposed to overcome these difficulties, including multiline arrays, e.g. twin arrays [18] and triplet arrays [19]. However the use of multiline arrays requires the use of a higher number of hydrophones to achieve the resolution of a single line array. Given that in ASW applications the sonar system works at low and mid frequency, in order to achieve the desired directivity the minimum number of elements is often prohibitively large and the choice of a single linear towed array could be mandatory when AUVs are in use. As a consequence, with this system solution, we are faced with the port-starboard (PS) ambiguity problem, which plays as an additional source of uncertainty enriching the classical measurement-origin uncertainty (MOU) setup that is the standard reference for dealing with missed detections and false alarms in multisensor/multitarget systems [20]–[24]. The observation

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model resulting by including the PS ambiguity into the MOU model will be referred to as MOUPS. The PS ambiguous contacts (also called ghosts), as opposed to false alarms, are coherent in the sense that a tracker would always generate two tracks – the true one and the ghost – that are symmetric with respect to the array heading (see panels a1,2,3 in Fig. 3 for an illustration of this effect). Thus, in order to resolve the PS ambiguity, some degree of diversity within the collected data is needed. Since the true contacts are all located around the target, while the ghost echoes are located at the specular position with respect to the array heading, a spatial diversity can be obtained by using different sensor antennas, each with its own location/orientation with respect to the target. Indeed, if antennas’ headings are not aligned, then the ghost reports at different sensors are located at different areas of the surveillance region, and therefore they can be more easily classified as ghosts. In addition, time diversity can be exploited even with a single antenna array, provided that it is able to perform multiple scans with time-varying locations/orientations. Clearly, this latter approach is fruitful when the target dynamics are sufficiently slow as compared to these multiple scans. Any sensible observation models for ASW is inherently nonlinear, and consequently the posterior distribution is not Gaussian. One either tries to linearize the problem (leading to Extended/Unscented Kalman Filter, range-bearing converted measurements, etc. [20], [25]) or one admits the complexity and appeals to a fully Bayesian method: a particle filter [26], [27]. And if one does so, one might as well include the PS ambiguity to the observation model and solve it optimally. A very useful technique for ASW is the Target Motion Analysis (TMA), typically used for passive arrays (only bearing information), where there is no target observability, e.g. see [28], [29]. In order to “solve” the target non-observability the platform has to maneuver, using some information about the target trajectory, collecting data which allow a meaningful estimation of the target state. An analogous concept is present also in the PS ambiguity, i.e. TMA could suggest an optimal AUV maneuver plan. Clearly this is complementary to the proposed procedure: We derive the optimal Bayesian filtering to track the target state (position and velocity) under the MOU-PS model. To the best of our knowledge, this is the first attempt to derive the optimal fusion rule for multisensor tracking in the presence of measurements of uncertain origin and February 7, 2014


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port-starboard ambiguity. We first attack the problem from an analytical point of view by deriving the exact likelihood of the data under the MOU-PS model, and then analyze the performance of the tracking system via computer experiments. The final validation of the proposed approach, however, is provided by an extensive experimental campaign using real-world data collected during sea trial experiments, conducted by the NATO Science and Technology - Centre for Maritime Research and Experimentation (CMRE, formerly known as SACLANTCEN and NURC) in 2011 and 2012. The NATO research vessel (NRV) Alliance, the coastal research vessel (CRV) Leonardo, and CMRE’s underwater network with multistatic sonar system have been used during the experimentations. Some results of these underwater experimental campaigns are here reported. The paper is organized as follows. In Sect. II we formalize the PS problem in the presence of missed detections and clutter. Section III is devoted to the description of the optimal Bayesian dynamic estimation procedure, with numerical experiments described in Sect. IV. Details and results of real-world underwater experimentations are presented in Sect. V, and Sect. VI draws the conclusions. Some mathematical derivations are given in appendix. II. P ROBLEM FORMALIZATION In the ASW scenario considered here there is only one target of interest. However it is possible to have several target-like objects (e.g. large gross tonnage vessel, rocks, etc.) moving in the surveillance region. For trim notation we in this work assume only a single target, but the extension to the multi-target case is straightforward. Let us consider a WSN made of Ns sensors (AUVs towing acoustic array antennas) monitoring a certain surveillance region S inside which a single target is sailing. The WSN is tasked to estimate the target kinematic state at each time scan k. Assuming that the target and the vehicles sail in shallow water (≈ 70 − 150 m) and the sonar system works at mid-frequency (≈ 2.5 − 2.8 kHz) and long-range (≈ 1 − 15 km), the geometry can be considered approximately planar for the sound propagation and the water depth can be neglected. In fact the range distance between the target and the receivers (or source-target-receiver in the bistatic setup) are typically in the order of kilometers while in many scenarios the water depth does not exceed a few hundreds of meters, thus making the sound propagation similar to that inside a planar waveguide. Actually, the specific depths of the target, receivers and sources may become important in terms of signalFebruary 7, 2014


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to-noise ratio (SNR) due to the constructive/destructive interference in a multipath environment, and part of the current research focus on strategies that can be adopted in order to maximize (or minimize from the point of view of the target) the SNR and consequently the target detection probability [30]1 . However, in this work we neglect these effects and assume for simplicity that the problem is two dimensional, and that the SNR is uniform and constant in S, leading to false alarms uniformly distributed inside the surveyed area and to a constant detection probability. These assumptions are commonly adopted in the topical literature, see e.g., [20]. But of course these assumptions are “relaxed” by Nature herself when we test our approaches on the data set ExPOMA12, which includes quite a few additional unmodeled acoustic effects resulting from bistatic geometry, reverberation, bathymetry, etc. A. Target dynamic model In this subsection we summarize the target dynamic model, see also more details in [20]. The target state is defined in Cartesian (North-East) coordinates and expressed in terms of a Markovian process: xk = Fk (xk−1 , v k ),

(1)

where Fk (·) is in general a non-linear function valid for time k, xk is the target motion state vector and v k is the so-called process noise. While the approach developed here can be applied to any motion model, we adopt the nearly constant velocity model in virtue of the typical target’s behavior xk = F k xk−1 + Γk v k ,

(2)

where F k is the state transition matrix, Γk v k takes into account the target acceleration and other unmodeled dynamics. The term v k is typically assumed to be Gaussian with zero-mean and covariance matrix Q. In a 1D scenario xk = [xk , x˙ k ]T , where xk represents the position of the target and x˙ k its velocity, we have



Fk =  1

1 Tk 0

1





 , Γk = 

Tk2 /2 Tk



,

See also [31] for a generic problem of Bayesian search.

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y

port contact

port contact

array sensor

x sensor

array heading

starboard contact

x starboard contact

(a)

(b) y port contact array heading

x

array receiver source

starboard contact

(c)

Fig. 2. Sketch of the PS ambiguity geometries. (a) 1D monostatic geometry. (b) 2D monostatic geometry. (c) 2D bistatic geometry.

where Tk is the sampling time, and Q = σv2 . The 2D case is formalized using xk = [xk , x˙ k , yk , y˙ k ]T , xk , yk being the two components of the target position, x˙ k , y˙ k denoting the corresponding velocities, while

and Q = σv2 I.



1 Tk 0

  0  Fk =   0  0

1 0 0

0





Tk2 /2

   T 0  k    , Γk =   0 1 Tk    0 0 1 0

0



   , Tk2 /2   Tk 0

B. Measurement model for the PS problem Let us now consider the model for the measurements originated by the target. In the presence of PS ambiguity, there are two measurements originated by the target, and the system does not know in advance which of these is correct. Accordingly, the measurement function has two output measurements, say z Pk = HkP (xk , wk ) for the measurement to the left (port) of the sensor, and z Sk = HkS (xk , wk ) for that on its right (starboard). It is convenient to introduce the unambiguous measurement function Hk (xk , wk ), whose output is the (actually unknown) true measurement z k , see more details about the measurement models in [20, Sec. 1.6]. If the target is on port then HkP (xk , wk ) = Hk (xk , wk ), otherwise if the target is on starboard HkS (xk , wk ) = Hk (xk , wk ),

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yielding

  P    zk = zk ,     zS = zk , k

z Sk = gk z Pk , if targ. on port,

8

(3)

z Pk = gk z Sk , if targ. on starboard,

where gk (z) is a deterministic function mapping the contact z to its specular position with respect to the sensor heading. Note that, given that the target is on the starboard, the port contact is a deterministic function of the starboard contact, and vice-versa. How gk (·) is defined depends upon the scenario, as discussed next. 1) 1D monostatic geometry: Let us consider the geometry given in Fig. 2-(a). The sensor’s position at time scan k is denoted by pk , with this coordinate measured with respect to some predefined origin. The unambiguous measurement function Hk (xk , wk ) simply amounts to adding a noise term to the target position, namely: z k = xk + w k ,

wk ∼ N 0, σw2 ,

(4)

where wk is an additive noise and by N (µ, Σ) we denote the Gaussian distribution with mean vector µ and covariance matrix Σ, which in (4) are two scalars. In this scenario eq. (3) becomes   P S    zk = zk , zk = 2pk − zk , if xk < pk ,     z S = zk , k

(5)

zkP = 2pk − zk , if xk ≥ pk ,

and, in terms of the function gk (·), we have gk (z) = 2 pk − z. 2) 2D monostatic geometry: Let us consider the geometry given in Fig. 2-(b). At time scan k the sensor array position is denoted by pk = [pxk , pyk ]T and its heading angle by hk . By measuring the propagation time between the emission of the acoustic impulse and the received echo, and assuming known the sound propagation velocity, the target range rk can be computed; also measured is the bearing angle2 relative to array heading, say θk . The unambiguous measurement 2

In this paper we use the anticlockwise convention, however note that typically the angles in sonar systems are defined

clockwise from the North.

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function Hk (xk , wk ) is given by [20]    kxpk − pk k rk    = zk = y −1 yk −pk tan − hk θk xk −px k      wkr σ2 0 0  ∼ N   ,  r wk =  wkθ 0 σθ2 0

+ wkr + 

wkθ



,

 ,

(6)

(7)

where xpk = [xk , yk ] is the target location, while wkr and wkθ are the additive noise to the range and bearing, respectively. The two contacts arising from the PS ambiguity have the same range measurements but different bearing angles, θkP from port and θkS from starboard. Thus we have T T z Pk = rk , θkP and z Sk = rk , θkS , while eq. (3) reduces to  yk − pyk  P S P −1  ≥ hk , θk = θk , θk = −θk , if tan    xk − pxk   y   y − p k  k S P S −1  < hk .  θk = θk , θk = −θk , if tan xk − pxk

Note that it always holds θkP = −θkS with θkS ∈ [0, π], and θk ∈ [−π, π]. The deterministic function gk (z), defined in eq. (3), becomes  gk (z) = 

r

−θ



,



z=

r θ



.

(8)

3) 2D bistatic geometry: Let us consider the geometry given in Fig. 2-(c), with source and receiver not colocated. Let sk = [sxk , syk ]T denote the source position at time scan k, while the receiver array position and its heading angle are denoted by pk = [pxk , pyk ]T and hk , respectively. The receiver array measures the bistatic range bk from source to target to receiver. The unambiguous measurement function Hk (xk , wk ) is given by     p p b kxk − pk k + kxk − sk k + wk bk = , zk =  y −py tan−1 xkk −pkx − hk + wkθ θk k       2 b σ 0 0 wk  ,  ∼ N   ,  b wk =  0 σθ2 0 wkθ

(9)

(10)

where wkb and wkθ are the additive noise to the range and bearing, respectively. The PS ambiguity problem can be handled as for the monostatic case, i.e. the ambiguous contacts have the same

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bistatic range measurements but different bearing angles. Then eq. (3) for the bistatic case is characterized by the function gk (z) similar to that in eq. (8):     b b , z =  . gk (z) =  θ −θ

(11)

C. Measurement model in presence of missed detections and clutter At each time scan k a set of data is observed, whose cardinality is the number of detections. With sonar systems operating at low frequencies, as typical in ASW applications, the target can be well approximated as pointwise, and it is observed with a detection probability PD [20]. All the other echoes are clutter, independent from the target’s state, whose number is typically modeled as a Poisson random variable with rate λ. The data set Zs,k of the whole measurements for the sth sensor at time k is defined as Zs,k =

z Pi,s,k

ms,k i=1

,

(12)

where ms,k is the number of measurements. In the above, only the port contacts have been considered, since they form a sufficient statistic, in view of the deterministic dependence thereupon of the starboard contacts. Needless to say, the reverse choice (starboard in place of port) makes no difference from a statistical viewpoint. The aggregate in time of the whole data up s to k is indicated as Z1:k = Z1 , Z2 , . . . , Zk , where Zk = {Zs,k }N s=1 . Given that it is not possible

to discriminate between clutter- and target-originated measurements, the whole set Z1:k must be used to estimate the target state up to time k. The optimal inference procedure for accomplishing this task is the subject of the next section. III. O PTIMAL BAYESIAN I NFERENCE WITH PS AMBIGUITY In the Bayesian approach to dynamic state estimation, the goal is to construct the posterior probability density (pdf) of the state based on all available information, including the set of received measurements. Since this pdf embodies all available statistical information, it contains the complete solution to the estimation problem, and the optimal (with respect to any criterion) estimate of the state may be obtained from the posterior. The posterior of the target’s state (1), indicated by P (xk |Z1:k ) is given by the Bayes’ rule P (xk |Z1:k ) =

Lk (Zk |xk ) P (xk |Z1:k−1 ) , P (Zk |Z1:k−1 )

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where the prior at time k is given by P (xk |Z1:k−1 ) =

Z

P (xk |x) P (x |Z1:k−1 ) dx,

(14)

and P (xk |x) is ruled by the dynamic model (1). The scaling factor can be computed by Z P (Zk |Z1:k−1 ) = Lk (Zk |x) P (x |Z1:k−1 ) dx. Given that the sensors are conditionally independent, the likelihood Lk (Zk |xk ) can be factorized Lk (Zk |xk ) =

Ns Y

Ls,k (Zs,k |xk ) ,

(15)

s=1

where Ls,k (Zs,k |xk ) is the likelihood of the measurements observed by the sth sensor at time k, and is derived in the following subsection, based on the MOU-PS model described in Sect. II-B and II-C. The assumption of conditional independence is quite intuitive, especially if the sensors are not co-located; and it is commonly accepted in the tracking literature. Basically we have that neither are the false alarms of a sensor statistically correlated to those of the others, nor are measurement noises dependent, and that the target detection events are independent Bernoulli random variables with parameter PD . Regarding the classic “track-to-track fusion” formulation, note that even if the sensors are conditionally independent after the filtering stage the state estimates are in general dependent due to the common process noise, e.g. see [32]. In our approach we fuse and filter at the same time; the issue is obviated. Note that the data from the sensors are not identically distributed as each sensor has its own location/orientation with respect to the target, which can be time varying. This characteristic is a key feature to solve the PS ambiguity because the true contacts are all located around the target, instead the ghost contacts are located at the specular position with respect to the heading of the sensor. If sensors’ headings are not aligned then the ghost reports are located in different areas of the surveillance region and then are more likely to be false. When only a single sensor is present, the dynamic of the ghost contacts can be quite different from that of the real ones because of they would be influenced by the dynamic itself of the sensor. Then multiple dynamic sensors can be considered as the most suitable setup to solve the PS ambiguity.

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A. Derivation of the likelihood function In this subsection the sensor likelihood function Ls,k (Z |x ) is derived for the generic geometric configuration expressed in (3). The distribution of a target-originated measurement without the PS ambiguity is denoted by fs,k (z |x), see details in the Appendix. Recalling that the data set includes port-contacts only (12), the following two cases must be considered. The first one occurs when the target is on the port, so that, in view of eq. (3), z P is the true target-originated measurement. The second one corresponds to a target located on the starboard, and then z S = gk−1 z P is the correct contact. Conditioning on the target position, the distribution of a target-originated measurement with PS ambiguity is accordingly given by:   P  f if x on the port, s,k z |x ,   PS fs,k z P |x =     fs,k g −1 z P |x , if x on the starb. k Using the definitions of gk (·), it is useful to note that gk−1 z P = gk z S .

A clutter measurement is typically assumed to be distributed as a uniform in the field of view

(FOV) of the sensor, which is assumed to be approximately equal to the surveillance region S, whose length (1D case) or area (2D case) is indicated here with VS . The clutter is assumed to be independent from the target state and across time. More or less obviously, the clutter is not immune from the PS ambiguity issue. Let us denote by c the unambiguous clutter datum, and by cP and cS the port- and starboard-originated clutter contacts, respectively. Assuming that the (unambiguous) clutter datum c is generated uniformly in S, the pdf of the clutter measurement cP can be constructed as follows: fcP S (cP ) = fc cP |c on the port PP

+ fc gk (cP ) |c on the starboard

PS

(16)

where fc (· |· ) is the conditional pdf of c, and PP and PS are the probability that c has been generated on the port and on the starboard, respectively. Under the typical assumption of a symmetric FOV, it is equally likely that the clutter is generated on the starboard or on the port, namely, PS = PP = 1/2, and fc cP |c on the port = fc gk (cP )|c on the starboard = February 7, 2014


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Fig. 3. 1D geometry, the target is moving from the location −1 km to −1.5 km. No clutter or missed detections are considered. Uppermost plots, (a1 ) − (f1 ) posterior distribution across time. Middle plots, (a2 ) − (f2 ) contacts from sensors across time. Lowermost plots (a3 ) − (f3 ) target trajectory and estimated trajectories. Plots (a), single static sensor located in the origin. Plots (b) single sensor moving from 0 km to 1.5 km. (c) single sensor moving from 0 km to 2.5 km. (d) two static sensors in 0 km and 0.05 km. Plots (e) two static sensors in 0 km and 0.25 km. Plots (f ) three static sensors in 0 km, 0.25 km and 0.5 km.

2 VS−1 I(cp on the port), where I(·) is the indicator function. For ease of notation, in the following we skip the indicator function if no confusion arises. As a result, the pdf of cP is uniform, def

i.e. fcP S (cP ) = 2 VS−1 = V −1 . We are now ready to derive the overall pdf including both target-originated and clutter measurements. To this aim, it is expedient to introduce the following association events [20],

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[33]: {A0 } = {no meas. originated by the target} , {Ai } = {meas. i originated by the target} ,

i = 1, . . . , m.

By applying the law of total probability, the likelihood function can be expressed as m X Ls,k (Z |x) = Ls,k (Z |x, Ai ) P {Ai } , i=0

Assuming m > 0, we have:

1 , i = 0, Vm 1 PS z Pi |x , Ls,k (Z |x, Ai ) = m−1 fs,k V

Ls,k (Z |x, Ai ) =

P {Ai } = µc (m; λ)(1 − PD ), P {Ai } =

µc (m − 1; λ)PD , m

i > 0, i = 0, i > 0,

where µc (m; λ) is the distribution of the number of clutter with a rate λ. Then the likelihood is obtained m µc (m − 1; λ)PD X P S P fs,k z i |x Ls,k (Z |x) = mV m−1 i=1

+

µc (m; λ)(1 − PD ) . Vm

(17)

If no reports are present, i.e. m = 0, the likelihood reduces to Ls,k (m = 0 |x) = µc (0; λ)(1 − PD ).

(18)

Note that all the variables in Z are expressed in Cartesian coordinates, then the distribution of the exact target-originated measurement fs,k (z |x), for the case of the 2D monostatic and bistatic geometries, have been derived using the Fundamental Theorem of transformation of random variables [34], see details in the Appendix. An alternative approach would involve the approximation of the likelihood function, provided in [8], in which the small-error assumption is made allowing the use of the first-order linearization expression. It is possible to define the clutter pdf in the range-azimuth domain without converting the target-originated measurements. This equivalent solution would have the disadvantage that the clutter pdf is no longer “uniform” in range-azimuth, requiring an extra computational load for equation (17). February 7, 2014


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IV. PARTICLE FILTER AND NUMERICAL EXPERIMENTS The Bayesian posterior derived in the previous section is usually almost-impossible to evaluate in closed form. Many solutions are currently available to approximate it, typically via Sequential Monte Carlo methods [26], [27]. In this section, we first describe our particle-filter implementation of the tracking algorithm, and then test it on synthetic data. Algorithm 1 Particle multi-sensor filter for the PS problem At time k ≥ 1 •

Sampling Step

- For i = 1, . . . , NP , sample

- Normalise weights:

(i) ∼ q · xk−1 , Zk , (i) (i) ek P x e (i) L k Zk x x k k−1 (i) = Wk−1 . (i) (i) e k xk−1 , Zk q x

e (i) x k

f(i) set W k

(19)

PNP f(i) i=1 Wk = 1.

Resampling Step oN P n n oN P (i) (i) (i) (i) f ek . to get Wk , xk - Resample Wk , x

•

i=1

i=1

A. Particle filtering procedure for the MOU-PS While the posterior pdf (13) has optimality properties with respect to Bayesian criteria for the PS problem, no analytic solution is available, i.e. an approximate filter is required. Given the strong non-linearities present in the model (17) the most suitable approach is that of the particle representation of the posterior [26]. Assume that at time k − 1, a set of weighted particles posterior is available P (xk−1 |Z1:k−1 ) ≈

NP X i=1

n

(i) (i) Wk−1 , xk−1

o NP

i=1

representing the

(i) (i) Wk−1 δxk−1 xk−1 ,

(20)

where δy (x) is a Dirac delta function centered in y. The particle filter proceeds to approximate oNP n (i) (i) as described in the posterior at time k by a new set of weighted particles Wk , xk i=1 (i) Algorithm 1. Particles are sampled from the importance sampling distribution q · xk−1 , Zk , see details in [26]. Then particle weights are updated based on the likelihood function of the February 7, 2014


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1

Average posterior probability

0.9

0.8

0.7

0.6

0.5

(a) (b) (c) (d) (e) (f)

0.4

0.3

5

10

15

20

25

k

Fig. 4. 1D geometry with the same setup of the Fig. 3. The posterior probability that the target is on the correct side with respect to the sensor located in the Cartesian origin is computed, and its average value is obtained with over 104 Monte Carlo runs. The target trajectory is regenerated at each run in location −1 km with an initial velocity −0.5 m/s.

observed data Zk from all sensors, and the dynamic model, see eq. (19). The aggregate likelihood Lk (Zk |xk ) is given in eq. (15), and takes into account the whole sensor network information at time k. A resampling strategy is then adopted to avoid the particle degeneracy problem, e.g. see [26]. The target state estimate is given by the Minimum Mean Square Error (MMSE) that is optimal in terms of MSE def

ˆ k = E [xk |Z1:k ] = x

Z

xk P (xk |Z1:k ) dxk ≈

where the approximation is given by the particle representation.

NP X

(i)

(i)

xk W k ,

i=1

B. Examples using synthetic data We now report some numerical experiments aimed at providing a check for the theoretical analysis. We consider as a first case study the 1D geometry without missed detections and false alarms. It is considered a 1D scenario where a target is moving from the location −1 km to −1.5 km. The sampling time is constant T = 48 s. The following scenarios are studied and compared: (a) single static sensor located in the origin; (b) single sensor moving from 0 km to 1.5 km; (c) single sensor moving from 0 km to 2.5 km; (d) two static sensors in 0 km and 0.05

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km; (e) two static sensors in 0 km and 0.25 km; (f ) three static sensors in 0 km, 0.25 km and 0.5 km. In Fig. 3, we plot the posterior distribution in the uppermost plots, (a1 ) − (f1 ) across time. In the middle plots, (a2 ) − (f2 ), we depict the contacts from sensors across time. In the lowermost plots (a3 ) − (f3 ) the target trajectory and the estimated trajectories are given. Scenario (a) is a perfectly symmetric case, consequently the posterior is bimodal: There are consistently two “bumps” around the locations of the port and the starboard reports. This means that the particles are concentrated around these bumps. If we assume for simplicity that we have just two particles (NP = 2) one representing the bump on the left and the other that on the right, for a given time k the target is located in xk , and the two particles would be located around ˆ k ≈ 0. The estimated trajectory −xk and +xk with equal weight ≈ 0.5. Then we have that x is then unlikely to be disambiguated. In scenarios (b) and (c) the sensor is moving, providing time diversity in the collected data. The dynamic of the ghost contacts is vitiated by the sensor’s motion. It has to be remarked that the sensor’s velocity is higher in (c) than in (b), in fact the trajectory’s reconstruction is better for (c) than (b). In scenarios (d), (e) and (f ), multiple sensors are used, providing spatial diversity. This latter feature allows the disambiguation in all the cases. However, in (d), where the two sensors are close to each other, the distance is only 50 m, the time required to disambiguate is substantially higher than in (e), where the distance between the sensors is 250 m, and (f ), where there are three well separated sensors. In other words in case (d) the spatial diversity is lower than in (e) and in (f ). The disambiguation capacity is quantitatively provided for all scenarios (a) to (f) in Fig. 4, where we depict the posterior probability that the target is on the correct side with respect to the sensor located in the Cartesian origin. This probability is averaged using over 104 Monte Carlo runs with a target trajectory generated at each run in location −1 km with an initial velocity −0.5 m/s. The next example is a 2D monostatic scenario where the target is moving from North to South, see Fig. 5. In the panel (a) the target and estimated trajectory are depicted with the whole history of contacts. In panel (b) the root square error (RSE) is shown, in (c) the true target trajectory and the ghost target trajectory are plotted. A single sensor, affected by false alarms and missed detections, is present and its heading changes linearly from 0◦ to 180◦ . Here the time diversity is provided by the heading dynamic which forces through the ghost trajectory to be quite unlikely w.r.t. the assumption of the target dynamic, see in Fig. 5-(c) the target and ghost trajectory. Then consequently the disambiguation is obtained by the proposed tracking procedure in few steps, February 7, 2014


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(a)

(c)

5

6

4 3 2 4

y [km]

1 0 −1 −2

2 Target trajectory Estimated track Cont. AUV

−3 −4 −4

−3

−2

−1

0

1

2

3

4

5

y [km]

x [km] 0 AUV position

(b)

1

10

−2 0

RSE [km]

10

−1

10

−4

−2

10

Targ. track Ghost track Port cont. Starboard cont. Array heading

−3

10

0

10

20

30

40

50

−6 −6

−4

k

−2

0

2

4

6

x [km]

Fig. 5. 2D monostatic geometry, single AUV centered in the origin moving its heading from 0◦ to 180◦ . (a) Target trajectory, estimated trajectory, contacts from the AUV. (b) Position error between the target trajectory and the estimated trajectory. (c) Target and ghost trajectory with the relative port/starboard contacts.

see the knee in the error in Fig. 5-(b). V. S EA TRIAL EXPERIMENTATION The results reported in this section are based on an extensive experimental campaign using real-world data collected during the Generic Littoral Interoperable Network Technology 2011 (GLINT11) and the Exercise Proud Manta 2012 (ExPOMA12). Preliminary results using the GLINT11 data set are also provided in [35]. The experimental campaign has been conducted by the engineering and scientific staff of CMRE by using the technical facilities (e.g. communication systems, laboratories, etc.) on board the NRV Alliance. This latter is a 93 meters long vessel, see Fig. 6(a), which served as the command and control centre during the experiments. The CRV Leonardo has characteristics similar to those of the NRV, but is smaller (28 meters long) and then cannot navigate far away from the coast, see Fig. 6(d). She has one very silent low speed condition and enjoys the benefits February 7, 2014


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Fig. 3 Left the DEMUS source during deployment; the eight free-

(a) NRV Alliance.

(b) Echo repeater.

(c) Left, DEMUS during deployment.

Right,

DEMUS radio buoy. GATEWAY BUOY

(d) CRV Leonardo.

(e) OEX-AUV.

(f) Gateway. AIRCRAFT

1

Fig. 6. Main research equipments for the sea trials. (a) NRV Alliance is used as command and control of the sensor network system. (b) Echo repeater used to simulate an underwater target and towed by the NRV. (c) The DEMUS is the acoustic source of the multistatic network. (d) CRV Leonardo. (e) The OEX-AUV with the BENS towed-array. (f) Acoustic and RF gateway.

RF link NRV gateway buoy

DEMUS underwater data link

underwater modem

AUV

target

1

Fig. 7. Sketch of a mobile underwater ad hoc network. The components of the networks (e.g. AUVs, DEMUS, etc.) communicate using underwater or RF data link. Some gateways are used to guarantee the connectivity of the network.

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of diesel electric propulsion driving twin azimuthing thrusters and one azimuthing pump jet bow thruster controlled by a fully automated dynamic positioning and a power management system. The main tool of research for the sea trials was CMRE’s Ocean Explorer (OEX) AUV used in combination with the BENS towed-array, see Fig. 6(e). The OEX is an untethered AUV of length 4.5 m and a diameter of 0.53 m. It can operate down to 300 m. It has a maximum speed through the water, when towing the array, of 3 knots. Battery constraints limit the lifetime of any mission to about 7 hours. The OEX is equipped with two independent WHOI modems for communication of data with the command centre and for passing of information between vehicles. Underwater communications, algorithmic functioning and platform control are carried out under MOOS-IvP (Mission Orientated Operating Suite Interval Programming), the software architecture which has been developed at MIT and Oxford University. The BENS array is an adaption of the Slim Towed Array for AUV applications (SLITA) array [14] and as such based on the same underlying technology. The array has 83 hydrophones of which sets of 32 can be chosen to give a frequency coverage from 750 to 3400 Hz. Furthermore the array is equipped with 3 compasses and two depth sensors to aid with the reconstruction of the dynamics of the array. The Deployable Experimental Multistatic Undersea Surveillance (DEMUS) source is a programmable bottom-tethered source capable of high source levels based on free-flooded ring technology, see Fig. 6(c). It is equipped with a WHOI modem which allows it to be turned on and off remotely by means of another compliant acoustic modem. In this mode the source acts as a cue-able standoff source which can allow AUVs to change the overall mode of operation from, for instance, passive to active. The DEMUS source is equipped with a radio buoy so that the acoustic signals to be transmitted can be altered by means of a radio connection. It also has a GPS unit which allows a very accurate transmission time and position of the source. This level of information could be used subsequently to aid the AUV in determining its position more accurately. An echo-repeater (ER), see Fig. 6(b), towed by the research vessel NVR Alliance, or CRV Leonardo, is used in the experiment as a reproducible and controllable target. The AUVs, the DEMUS, and the command and control system on the NRV communicate using a mobile ad hoc network – underwater and radio gateways, see Fig. 7. Underwater communications are supported by a WHOI modem equipment. The data links can be acoustic February 7, 2014


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(a)

(b)

12 7.5 7

y [km]

10

6.5 6

8

y [km]

5.5

Harpo 5

5.5

6

6.5

7

7.5

x [km]

6

(c) 6 5.5

y [km]

4

2 Harpo Groucho DEMUS Target Trajectory 0

4

6

8

x [km]

5 4.5 4 Groucho

10

3.5

6

7

8

9

x [km]

Fig. 8. Sea trials GLINT11. (a) Target trajectory, bistatic setup with locations of the source (DEMUS) and receivers AUVs. (b) Locations and headings of Harpo. (c) Locations and headings of Groucho. The target consists of an echo repeater towed by the NRV Alliance.

(e.g. an AUV linked to a gateway) and radio (e.g. the NRV linked to a gateway). The AUV based processing chain which we have implemented is constrained to run on relatively low powered processing boards in order to limit power consumption within the vehicle and is designed to be robust, obviously requiring no human intervention and able to cope with occasional drop-outs of data and corrupted samples. The approach is based heavily on the signal processing chain which has been developed at CMRE for general array-based systems [15]. For speed and ease of implementation on the vehicle the beamforming and matched filtering are carried out in the frequency domain whilst the normalization, detection and contact formation is carried out in the time domain. A. Results of sea trials: GLINT11 GLINT11 experimentation held in the Ionic Sea (Calabria-Puglia, Italy) during August-September 2011. The setup of GLINT11 is given in Fig. 8, where we depict the location of the DEMUS (yellow diamond), trajectories of the AUVs, Harpo (blue circle) and Groucho (green circle) with related headings (arrow), and of the ER (black dashed line). The ER is towed by the CRV Leonardo. Locations and trajectories are referenced to a local Cartesian system. The source is located in (6.1 km, 8.2 km). The target sails from the location (8.8 km, 6.5 km)

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12

12

11

11

10

10

9

9

8

8

y [km]

y [km]


7

7

6

6

5

5

4

4

Harpo tracks Target trajectory Cont. Harpo

3

2

22

2

3

4

5

6

7

8

9

10

11

Groucho tracks Target trajectory Cont. Groucho

3

2

12

2

3

4

5

6

7

x [km]

8

9

10

11

12

x [km]

(a) Harpo

(b) Groucho

12

11

10

9

y [km]

8

7

6

5

4 Target Trajectory Estimated Track Cont. Harpo Cont. Groucho

3

2

2

3

4

5

6

7

8

9

10

11

12

x [km]

(c) Particle filtering Fig. 9. Sea trials GLINT11. Tracks generated from a standard MHT tracker using Harpo contacts (a), and Groucho contacts (b). In panel (a) and (b), ghost tracks are present in the South-East region. In panel (c,) using the particle filtering MOU-PS procedure, the ghost tracks are eliminated.

to (6.8 km, 10 km) and then goes back to the initial position (8.8 km, 6.5 km). The AUVs sail South-East of the source position and the target trajectory. The parameter values used in Alg. 1 for GLINT11 are reported in Tab. I. The duration of the experiment (the sailing time of the target) reported in Fig. 8 is approximately 2 hours. In Fig. 9 using the contacts collected respectively by Harpo, panel (a), and by Groucho, panel (b), we plot the output tracks of a multi hypothesis tracking (MHT) algorithm [20, Sec. 7.5] which

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does not take into account the PS ambiguity. Many ghost tracks are generated in the South-East region. On the other hand, the proposed particle filtering procedure, described in Alg. 1, is able to “reject” the ghost contacts in the sense that particles which follow the true trajectory have larger weight with respect to others that track ghost trajectories, see Fig. 9. It is possible to recognize that while the ghost tracks are filtered out the target trajectory is correctly estimated. It is worth noting that a heuristic AUV maneuvering plan has been proposed in GLINT11, see details in [36]: by turning a certain amount to port or starboard, the ambiguous contact’s geolocation is seen to move significantly, whereas that of the true contact is stationary. If the contacts are fed to a tracker, this discontinuity of the geolocation of the ambiguous contact may be exploited to attempt to break a track made on the ambiguous contact. In particular the preferred method used in the GLINT series of experiments has been to perform a sharp maneuver to starboard (≈ 30◦ ) followed T ≈ 5 − 10 minutes later by a sharp maneuver to port of twice (≈ 60◦ ) the starboard heading change. This maneuver after an additional T ≈ 5 − 10 minutes brings the AUV back onto its original trajectory, and a final maneuver of the original starboard heading change, again to starboard, brings the vehicle to its original heading on its original layline. Consequently almost 10 − 20 minutes were required to disambiguate using the data of a single AUV. By the algorithm developed in our paper we show that the disambiguation is perfectly performed without any delay.

Parameter

T

GLINT11

60 s

48 s −3

σv

5 10

σb

50 m 1.5

PD

0.75

NP

−2

ms

1.5 10 5 10

4

5 10

1.5

ms

−2

−2

m

2 10

−9

5 10

4

Process noise Std bistatic range

◦

Std bearing

0.85 −8

Specification

Sampling Period −3

50 m

◦

σθ λ/VS

ExPOMA12

Detection probability −2

m

Clutter density Number of particles

TABLE I PARAMETER VALUES USED IN IN THE ALGORITHM FOR GLINT11 AND E X POMA12.

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B. Results of sea trials: ExPOMA12 ExPOMA12 experimentation held in the Mediterranean Sea (Sicily, Italy) during FebruaryMarch 2012. The setup of the experiment is given in Fig. 10, where we depict the location of the DEMUS (yellow diamond), trajectories of the AUVs, Harpo (blue circle) and Groucho (green circle) with related headings (arrow), and of the ER (black dashed line). The ER is towed by the NRV Alliance. The source is located in (12.3 km, 23.2 km). The target sails from the location (16.5 km, 16.9 km) to (17.2 km, 9.8 km) and then goes to (15.8 km, 11.3 km). The AUVs sail south-east of the source position and the target trajectory. The parameter values used in Alg. 1 for ExPOMA12 are reported in Tab. I. The duration of the experiment is approximately 2 hours. The proposed filtering procedure is again able to disambiguate, rejecting the ghost contacts. It is easy to check that while the ghost reports are filtered out the target trajectory is correctly estimated. Given that the SNR, and consequently the PD , depends on the geometry of the bistatic system and on the environment, e.g. multipath time spread, reverberation, bathymetry, sound speed, etc., in Fig. 11 we report the behavior of the particle multi-sensor filter using a detection probability that is not uniform and constant, see further details in [37]. In particular the PD is derived using an acoustic model in which the bistatic SNR is computed taking into account: a closed-form flux solution for reverberation, target returns for a range-independent isovelocity waveguide, rangevarying bathymetry, separate correction for the loss due to multipath, see [38]–[42]. In Fig. 11, right-side, we recognize the so-called blanking region between the AUV and the source and also the degradation of the detection probability (< 0.3) close to the corners of the surveillance region. However, given that the target is moving in the region where PD is quite large (≈ 0.7 − 0.9) the estimated target trajectory is quite similar to that reported in Fig. 10 in which a constant PD is assumed, see Tab. I. VI. C ONCLUSION In the anti-submarine warfare scenario, affected by port-starboard ambiguity, clutter and missed detections, a novel target tracking and data fusion strategy is proposed. The estimation procedure is implemented by a particle filtering algorithm, used to approximate the Bayesian posterior of the target state. The effectiveness of the estimation procedure is verified using computergenerated data as well as real-world measurements. In particular, we report the results of February 7, 2014


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Fig. 10. Sea trials ExPOMA12. (a) Target trajectory, estimated trajectory, contacts from AUVs, Harpo and Groucho. (b) Target trajectory and estimated trajectory. (c) Bistatic setup with locations of the source (DEMUS) and AUVs. (d) Locations and headings of Harpo. (e) Locations and headings of Groucho. The target consists of an echo repeater towed by the NRV Alliance.

extensive experimental campaigns: the Generic Littoral Interoperable Network Technology 2011 and Exercise Proud Manta 2012. These experimentations involved the engineering and scientific staff of CMRE and exploited the facilities (communication tools, data analysis laboratories, etc.) on board of the NRV Alliance, and the CMRE’s OEX AUV equipped with BENS towed-array. While the state-of-the-art in the context of AUV network is a heuristic approach to disambiguation, our experiments show that the port-starboard ambiguity can be indeed resolved in an optimal way, i.e., by including the ambiguity in the analytical model of the observations and deriving the full Bayesian posterior distribution of the target state. In addition, the proposed disambiguation comes at no additional cost in terms of computational complexity, given a particle filtering implementation of the Bayesian filtering iterations. Possible directions for future studies include the adaptive optimization of the sensors’ deployment and dynamics, using techniques like dynamic programming and stochastic control.

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(a) k=50

(b) k=100 Fig. 11. Sea trials ExPOMA12. Behavior of the PF algorithm, using the ExPOMA12 data set, with the detection probability at Harpo and Groucho given by the acoustic model. Time scan k = 50 and k = 100. Right-side detection probability map for Harpo and Groucho at time scan k, Groucho and Harpo positions (white square ’’), source position (with diamond ’♦’). February 2014 DRAFT Left-side7,we report the target trajectory (dashed black line), current target position (’x’), estimated track at time k (red line

’-x’), Harpo contacts at time k (blue dots), Groucho contacts at time k (green dots), Harpo position at time k (blue square ’’), Groucho position at time k (green square ’’), source position (yellow diamond ’♦’).




27

Considering the shallow water environment the tracker can be also enhanced using optimization strategies to maximize the SNR and consequently the target detection probability. Another future work is the extension of the proposed procedure to a scenario with multiple targets. A PPENDIX A D ISTRIBUTION OF THE TARGET- ORIGINATED MEASUREMENT IN C ARTESIAN COORDINATES In this appendix the distribution fs,k (z |x ) of a target-originated measurement, without the PS ambiguity, is computed for the geometries depicted in Fig. 2 and described in Sect. II. A. 1D monostatic geometry In the case of the 1D monostatic geometry the distribution fs,k (z |x ) is simply given by a Gaussian centered in the target location x with std σw fs,k (z |x ) = N (z − x, σw2 ).

(21)

B. 2D monostatic geometry In the case of the 2D monostatic geometry the distribution of observed data, given the target state x = [x, x, ˙ y, y] ˙ T , has to be computed using the Fundamental Theorem of the random variables transformation [34]. Range and bearing measurements [r, θ]T are assumed to be distributed as a Gaussian, see (6), then the transformation from polar to the local Cartesian T system of coordinates is used [34] . The sth sensor is located in pxs,k , pys,k with heading hs,k .

The equations of the transformation are zx = pxs,k +r cos (θ + hs,k ) and zy = pys,k +r sin (θ + hs,k ). The likelihood is given by fs,k (z |x) = J(zx , zy )−1 ×

(22)

N kz − ps,k k − kxp − ps,k k , σr2 × ! ! ! zy − pys,k y − pys,k −1 −1 2 N tan − tan , σθ , zx − pxs,k x − pxs,k where xp = [x, y]T is the target position, and J(zx , zy ) = kz − ps,k k is the jacobian of the transformation.

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C. 2D bistatic geometry The bistatic range and bearing measurements [b, θ]T , assumed to be distributed as a Gaussian (9), has to be transformed into Cartesian system of coordinates. The equations of the transformation are [8] zx = pxs,k + r cos (θ + hs,k ) , zy = pys,k + r sin (θ + hs,k ) ,

(23)

where r=

b2 − ∆ 2 , 2(b − ∆ cos α)

α = tan−1

sy − pys,k sx − pxs,k

∆ = ksk − ps,k k . ! − θ − hs,k ,

Using the Fundamental Theorem of the random variables transformation [34], the likelihood is give by fs,k (z |x ) = J(zx , zy )−1 × N kz − ps,k k + kz − sk k − kxp − ps,k k − kxp − sk k , σb2 ! ! ! y y y − p z − p y s,k s,k − tan−1 , σθ2 , × N tan−1 zx − pxs,k x − pxs,k

(24)

where xp = [x, y]T is the target position, and the jacobian is given by J(zx , zy ) =

∂zx ∂zy x ∂zy − ∂z , ∂b ∂θ ∂θ ∂b

whose derivatives are given by ∂zx ∂r ∂zy ∂r = cos (θ + hs,k ) , = sin (θ + hs,k ) , ∂b ∂b ∂b ∂b ∂r ∂zx = cos (θ + hs,k ) − r sin (θ + hs,k ) , ∂θ ∂θ ∂zy ∂r = sin (θ + hs,k ) + r cos (θ + hs,k ) , ∂θ ∂θ where b2 + ∆2 − 2b∆ cos α ∂r (b2 − ∆2 ) ∆ sin α ∂r = = , , ∂b ∂θ 2 (b − ∆ cos α)2 2 (b − ∆ cos α)2 b = kz − ps,k k + kz − sk k , ! y z − p y s,k θ = tan−1 − hs,k . zx − pxs,k

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ACKNOWLEDGMENT This work has been funded by the NATO Allied Command Transformation (NATO-ACT) under the projects ACT000204 (System Concepts for Littoral Surveillance) and ACT000215 (Maritime Situational Awareness). The authors would like to thank the anonymous reviewers for valuable suggestions and corrections which allowed to improve the quality of the paper. R EFERENCES [1] I. F. Akyildiz, D. Pompili, and T. Melodia, “Underwater acoustic sensor networks: Research challenges,” Ad Hoc Networks (Elsevier), vol. 3, no. 3, pp. 257–279, Mar. 2005. [2] L. Wu, X. Tian, J. Ma, and J. Tian, “Underwater object detection based on gravity gradient,” IEEE Geosci. Remote Sens. Lett., vol. 7, no. 2, pp. 362–365, 2010. [3] D. Williams, “Label alteration to improve underwater mine classification,” IEEE Geosci. Remote Sens. Lett., vol. 8, no. 3, pp. 488–492, 2011. [4] T. Saebo, S. Synnes, and R. Hansen, “Wideband interferometry in synthetic aperture sonar,” IEEE Trans. Geosci. Remote Sens., 2013. [5] N. Leonard and J. Graver, “Model-based feedback control of autonomous underwater gliders,” IEEE J. Ocean. Eng., vol. 26, no. 4, pp. 633–645, 2001. [6] R. Sherman, J. nad Davis, W. Owens, and J. Valdes, “The autonomous underwater glider Spray,” IEEE J. Ocean. Eng., vol. 26, no. 4, pp. 437–446, 2001. [7] E. Rogers, G. JG, W. Smith, G. Denny, and P. Farley, “Underwater acoustic glider,” in Proc. of the IEEE Intern. Geosci. and Remote Sens. Symp. (IGARSS), vol. 3, 2004, pp. 2241–2244 vol.3. [8] S. Coraluppi, “Multistatic sonar localization,” IEEE J. Ocean. Eng., vol. 31, no. 4, pp. 964–974, Oct. 2006. [9] R. Georgescu and P. Willett, “The GM-CPHD tracker applied to real and realistic multistatic sonar data sets,” IEEE J. Ocean. Eng., vol. 37, no. 2, pp. 220–235, Apr. 2012. [10] H. Cox, “Fundamentals of bistatic active sonar,” in Proc. of the NATO Advanced Study Inst. Underwater Acoustic Data Process., Y. T. Chan, Ed. Norwood, MA: Kluwer, 1989. [11] H. L. Van Trees, Optimum array processing: Part IV of detection, estimation, and modulation theory. New York: Wiley, 2002. [12] S. Lemon, “Towed-array history, 1917-2003,” IEEE J. Ocean. Eng., vol. 29, no. 2, pp. 365–373, Apr. 2004. [13] M. Hamilton, S. Kemna, and D. Hughes, “Antisubmarine warfare applications for autonomous underwater vehicles: The GLINT09 sea trial results,” J. of Field Robotics, vol. 27, no. 6, pp. 890–902, 2010. [14] A. Maguer, R. Dymond, M. Mazzi, S. Biagini, and S. Fioravanti, “SLITA: a new slim towed array for AUV applications,” in Acoustics’08, 2008, pp. 141–146. [15] A. Baldacci and G. Haralabus, “Signal processing for an active sonar system suitable for advanced sensor technology applications and environmental adaption schemes.” in Proc. of the European Sign. Proc. Conf. (EUSIPCO), Sep. 2006. [16] S. Marano, V. Matta, P. Willett, and L. Tong, “DOA estimation via a network of dumb sensors under the SENMA paradigm,” IEEE Signal Process. Lett., vol. 12, no. 10, pp. 709–712, Oct. 2005.

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in multistatic AUV networks with port-starboard ambiguity,” in Proc. IEEE Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Florence, 2014. [38] C. Harrison, “Closed-form expressions for ocean reverberation and signal excess with mode stripping and Lambert’s law,” J. Acoust. Soc. Am., vol. 114, no. 5, pp. 2744–2756, 2003. [39] ——, “Closed form bistatic reverberation and target echoes with variable bathymetry and sound speed,” IEEE J. Ocean. Eng., vol. 30, no. 4, pp. 660–675, 2005. [40] ——, “Fast bistatic signal-to-reverberation-ratio calculation,” J. Comp. Acoust., vol. 13, no. 2, pp. 317–340, 2005. [41] ——, “Target time smearing with short transmissions and multipath propagation,” J. Acoust. Soc. Am., vol. 130, no. 3, pp. 1282–1286, 2011. [42] ——, “Ray convergence in a flux-like propagation formulation,” J. Acoust. Soc. Am., vol. 133, no. 6, pp. 3777–3789, 2013.

Paolo Braca received the Laurea degree (summa cum laude) in electronic engineering and the Ph.D. degree (highest rank) in information engineering from the University of Salerno, Italy, in 2006 and 2010, respectively. In 2009, he has been a Visiting Scholar at the ECE department of the University of Connecticut, USA. In 2010, he joined D’Appolonia S.p.A., Italy, as a Senior Engineer. In 2010-2011, he has been a Postdoctoral Associate at the University of Salerno. He is currently a Scientist at the Research Department of the NATO STO-CMRE (formerly SACLANTCEN and NURC). His main research interests include statistical signal processing with emphasis on detection and estimation theory, wireless sensor networks, multiagent algorithms, target tracking, and data fusion. Dr. Braca acts as a reviewer for many international journals and conferences and is a member of the Multistatic Tracking Working Group, International Society of Information Fusion. He has been a Co-organizer with Prof. Peter K. Willett of the special session Multi-Sensor Multi-Target Tracking at EUSIPCO 2013. He was the recipient of the Best Student Paper Award (second place) at FUSION 2009.

Peter Willett has been a faculty member in the Electrical and Computer Engineering Department at the University of Connecticut since 1986, following his PhD from Princeton University. His areas include statistical signal processing, detection, sonar/radar, communications, data fusion, and tracking. He is an IEEE Fellow. He was EIC for IEEE Transactions on AES, and is now EIC for IEEE Signal Processing Letters. He is associate editor for the IEEE AES Magazine plus ISIFs Journal of Advances in Information Fusion. He is a member of the IEEE AESS Board of Governors (and is now VP Pubs) and of the IEEE Signal Processing Societys Sensor-Array and Multichannel (SAM) technical committee (and is now Vice Chair). He has served as Technical Chair for the 2003 SMCC and the 2012 SAM workshop; and as Executive/General Chair for the 2006, 2008 and 2011 FUSION conferences.

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Kevin LePage Kevin LePage joined CMRE in 2008, where he has been the project leader for the Concepts for Littoral Surveillance project within the Cooperative ASW programme from 2010-2012 and the Programme Manager for that programme since 2013. In this time he has worked on the development and deployment of an autonomous active ASW prototype based on the concept of AUVs acting as receivers in a multistatic active ASW network. This demonstrator has been taken to sea 7 times since 2008, and most recently has been deployed in national experimentation with the Italian Navy twice (2011 and 2013) and twice during NATO ASW exercises (POMA12 and 13). Dr. LePage was a Research Physicist at the US Naval Research Laboratory in Washington DC from 2002 to 2008, a Senior Scientist at SACLANT ASW Research Centre (SACLANTCEN) from 1997-2002, and a Scientist and later Senior Scientist at Bolt Beranek and Newman in Cambridge MA from 1992 to 1997. He has expertise in reverberation and scattering modelling, multistatic ASW, Arctic and global scale acoustics, and structural acoustics and vibration. He received the PhD in Ocean Engineering from MIT in 1992 and a SM from that same institution in 1987. Prior to this he was a Naval Architect at DTNSDRC in Cabin John, MD. He received his BS in Naval Architecture and Marine Engineering from Webb Institute in 1983. Dr. LePage is a Fellow of the Acoustical Society of America.

Stefano Marano received the Laurea degree (summa cum laude) in Electronic Engineering and the Ph.D. degree in Electronic Engineering and Computer Science, both from the University of Naples, Italy, in 1993 and 1997, respectively. Currently he is an Associate Professor at the University of Salerno, Italy, where he formerly served as Assistant Professor. He has held visiting positions at Physics Department, University of Wales, College of Cardiff, and at Department of Electrical and Computer Engineering, University of California at San Diego, in 1996 and 2013, respectively. His areas of interest include statistical signal processing with emphasis on distributed inference, sensor networks, and information theory. In these areas he has published more than one hundred papers, including some invited, on leading international journals/transactions and proceedings of leading international conferences, and he has given several invited talks. Stefano Marano was awarded the IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION 1999 Best Paper Award for his work on stochastic modeling of electromagnetic propagation in urban environments. He also co-authored the paper winning the Best Student Paper Award (2nd place) at the 12th Conference on Information Fusion in 2009. As a reviewer, he handled hundreds of papers, mainly for the IEEE TRANSACTIONS, and was selected as Appreciated Reviewer by the IEEE TRANSACTIONS ON SIGNAL PROCESSING in the years 2007 and 2008. Stefano Marano is in the Technical Committee of the major international conferences in the field of signal processing and data fusion, and recently served as Area Chair for EUSIPCO 2011 and EUSIPCO 2013. He was in the Organizing Committee of the Ninth International Conference on Information Fusion (FUSION 2006), and in the Organizing Committee of the 2008 IEEE Radar Conference (RADARCON 2008). He is currently serving as an Associate Editor for the IEEE TRANSACTIONS ON SIGNAL PROCESSING and for the IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS.

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Vincenzo Matta received the Laurea degree (cum laude) in Electronic Engineering and the Ph.D. degree in Information Engineering from the University of Salerno, Italy, in 2001 and 2005, respectively. Currently, he is an Assistant Professor at the Department of Information & Electrical Engineering and Applied Mathematics of the University of Salerno, Italy. His research interests cover the wide area of statistical signal processing and information theory, with current emphasis on the interplay between inference and communications in distributed systems, adaptation and learning over networks, multitarget/multisensor tracking and data fusion, secrecy in communications. He has published about 80 journal papers, including some invited, on leading international journals/transactions, and proceedings of leading international conferences. Vincenzo Matta serves as an Associate Editor for the IEEE SIGNAL PROCESSING LETTERS and for the IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS.

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