Interacting Multiple Model Filter-based Distributed Target Tracking ...

International Journal of Control, Automation, and Systems (2014) 12(3):618-627 DOI 10.1007/s12555-013-0238-y

ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555

Interacting Multiple Model Filter-based Distributed Target Tracking Algorithm in Underwater Wireless Sensor Networks Chang Ho Yu and Jae Weon Choi* Abstract: This paper deals with the problem of accurately tracking a single target, which has various trajectories, moving through the environment of underwater wireless sensor networks (UWSNs). This paper addresses the issues of estimating the states of the target, improving energy efficiency by using a distributed architecture. Each underwater wireless sensor node composing the UWSNs is batterypowered, so the energy conservation problem is a critical issue. This paper provides algorithms increasing the energy efficiency of each sensor node by using the proposed Wake-Up/Sleep (WUS) scheme. An interacting multiple model (IMM) filter is applied to the proposed distributed architecture in order to cope with a target maneuver. Simulation results illustrate the performance of the proposed tracking filter according to the various target maneuver patterns. Keywords: IMM filter, Target tracking, UWSNs, Kalman filter, WUS scheme.

1. INTRODUCTION Advances in micro electromechanical systems (MEMS) and wireless technologies have allowed for the emergence of inexpensive micro-sensors with embedded processing and communication capabilities [1]. Sensor networks consist of many of these micro-sensors communicating with one another over wireless links. Wireless sensor networks (WSNs) are emerging technology for monitoring physical world with a densely deployed network of sensor nodes. The main advantages of WSNs include its low cost, rapid deployment, selforganization, and fault tolerance. It can be used in a variety of applications, such as environment monitoring, traffic monitoring in intelligent transportation systems, industrial sensing and diagnostics, healthcare, navigation and control of mobile robots, and military surveillance. But there are many constraints for the environment of WSNs, one of the main constraints for WSNs is the energy. It typically is impractical to replace the battery on each sensor node, so the lifetime of the network is tied to the battery life. Currently many researchers argue __________ Manuscript received May 29, 2013; revised December 7, 2013; accepted January 24, 2014. Recommended by Editorial Board member Chan Gook Park under the direction of Editor Myotaeg Lim. This work was supported by Defense Acquisition Program Administration and Agency for Defense Development under the contract UD110007DD and also supported by the Financial Supporting Project of Long-term Overseas Dispatch of PNU’s Tenuretrack Faculty, 2011. Chang Ho Yu is with the School of Mechanical Engineering and Research Institute of Mechanical Technology, Pusan National University, Busan 609-735, Korea (e-mail: changhoyu@pusan. ac.kr). Jae Weon Choi is with the School of Mechanical Engineering, Pusan National University, Busan 609-735, Korea (e-mail: choijw @pusan.ac.kr). * Corresponding author. © ICROS, KIEE and Springer 2014

for the need to study the problem of energy-aware target tracking for WSNs [2]. The target tracking algorithms can be divided into 2 main approaches. One approach is to use a centralized architecture, where all sensor measurements are sent to a central processing station. However, this architecture demands significant bandwidth for communication of every node’s sensor measurements, which can put a strain on the node battery lifetime [1]. Another issue with a centralized architecture is the lack of robustness and reliability. To reduce the communication burden, a distributed architecture is preferred for WSNs. In a distributed architecture, a sensor node is chosen near the target position as a processing node, and a subset of local sensors in the network is chosen to collect sensor data while the remaining sensors are placed in a power-saving sleep mode. An added advantage using a distributed architecture is its robustness to network changes and node failures [3]. The maneuvering target tracking problem with multiple sensor nodes in WSNs is an inherent multisensor data fusion problem, through which we combine measurements from different sensor nodes, remove inconsistencies, and pull all the information together into one coherent structure. Various data fusion schemes and techniques have been proposed for combining measurements from many sensing nodes with limited accuracy and reliability, to achieve better accuracy and more robustness [4]. Although there are many applications on target tracking problems [6-14], few papers can be found on collaborative maneuvering target tracking in WSNs. And an interacting multiple model (IMM) filter for the maneuvering target tracking [6] is applied to the traditional centralized architecture [7,9-11], but rarely to the distributed architecture. Most of centralized architectures rely on expensive sensors with intensive real time computation demand and large processing

Interacting Multiple Model Filter-based Distributed Target Tracking Algorithm in Underwater Wireless Sensor Networks

delay compared to the target tracking in a distributed architecture [15]. When an IMM algorithm was applied to a multi-platform multi-sensor tracking system, several distributed versions were proposed by Chang and BarShalom [16-18]. A distributed estimation scheme with uncertain models has been derived [16]. A distributed estimation problem which took into account both model and measurement origin uncertainties was also presented [17,18]. But the method is time and bandwidth consuming, so it is not suitable for real-time applications. In [19], the authors decompose the overall model space into subsets, and each platform contain one of them. A distributed interacting multiple model filtering is carried out on every platform. In [20,21], the extended Kalman filter (EKF) based target tracking algorithm which is applied to a distributed architecture is proposed, this algorithm is carried out on not every platform but only valid sensor platforms by using the Wake-Up/Sleep (WUS) scheme. But only constant velocity (CV) model is used and the EKF cannot perform well when the target has high maneuvering [6]. And in [13,14], the authors consider the sensor selection in WSNs under the EKF framework for target tracking. Although it can deal with the low maneuvering by adaptively changing the sampling interval, it does not work well when the maneuvering is high. In order to yield satisfactory performance with high maneuvering targets, the tracking algorithm needs to be capable of identifying the beginning and the end of maneuver, that is the maneuver detection. The IMM filter achieves this maneuver detection by updating the mode probabilities based on the received data. The IMM filter has the ability to switch between a high process noise (or alternatively, higher order or turn) model in the presence of maneuvers and a low process noise model in the absence of maneuvers. This point gives the IMM filter its advantage over simpler estimators like the Kalman filter and EKF [6]. In this paper, a distributed IMM filter is employed to estimate the states of the target on valid sensor platforms, assuming the target moves along a variety of trajectories in underwater wireless sensor networks (UWSNs) where the existing structure of WSNs applied to underwater environment. A distributed IMM filter can combine different models which are formulated according to the maneuvering target motion characteristic so as to adapt different trajectory change and calculate the probability for each model. To realize the target tracking on valid sensor platforms, adaptive sensor selection scheme, Wake-Up/Sleep (WUS), is proposed in UWSNs. The proposed algorithm can give more accurate estimation performance and are more energy efficient. The rest of the paper proceeds as follows. Section 2 describes the problem by defining the target motion models, as well as the measurement model of the UWSNs of acoustic sensors. Section 3 proposes the adaptive sensor selection scheme, WUS, and describes the distributed target tracking architecture. In Section 4, the IMM filter based distributed target tracking algorithm is proposed estimating the states of the target. In Section 5, simulation results are presented and the performance

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evaluations of proposed algorithm are accomplished. Finally, conclusions of this paper are drawn in Section 6. 2. PROBLEM FORMULATION We consider tracking a maneuvering target in a 2-D Cartesian coordinate system through a UWSN environment. The target states include the position, velocity, and acceleration when the trajectory is moving along a variety of curve. We assume that the target has 3 kinds of models, a nearly constant velocity (CV) and a nearly constant acceleration (CA) and a nearly abrupt acceleration (AA) within a sensor sampling interval. And at each time step we select multiple sensor data for detection and generate a fused measurement. 2.1. UWSN architecture The UWSN architecture is composed of multiple underwater acoustic sensors because radio frequency (RF) signals cannot be transmitted in underwater environments. We consider an UWSN architecture with static acoustic sensor nodes for underwater event monitoring and patrolling unmanned underwater vehicles (UUVs) and submarines as mobile users accessing information from the UWSN anywhere, anytime. Static sensor nodes, settled on the bottom of the underwater, are capable of communicating with each other wirelessly over an acoustic channel and also with the UUVs and submarines. The UWSN may also be wirelessly linked up to a buoy, a mother-ship, and an offshore platform for data analysis. Fig. 1 shows such an architecture for underwater vehicles monitoring application [22]. Acoustic sensor nodes are located on the bottom of the sea and accomplish a task to detect and track the target. And these sensor nodes can achieve the only position information of the target by the acoustic channel. 2.2. Constant velocity (CV) model At the kth time step, the state vector XCV(k) is defined as X CV (k ) = [ x(k ) x (k )

y (k )

y (k )]T ,

(1)

whose elements are x position, x velocity, y position, and y velocity. A CV model [4,5] that describe the target movement with a nearly constant velocity is given by X CV (k + 1) = FCV X CV (k ) + wCV (k ),

(2)

where FCV is the state transition matrix, and wCV(k) is the

Fig. 1. Underwater vehicle monitoring architecture.

Chang Ho Yu and Jae Weon Choi

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independent process noise with zero-mean, white, Gaussian probability distribution N (0, QCV (k )). Each state transition matrix and process noise covariance matrix is FCV = diag[ F2 , F2 ],

(3) (4)

QCV (k ) = diag[Q2 , Q2 ]qCV ,

where

⎡1 T ⎤ F2 = ⎢ ⎥, ⎣0 1 ⎦

⎡T 4 / 4 T 3 / 2 ⎤ Q2 = ⎢ ⎥, 3 2 ⎣⎢T / 2 T ⎦⎥

(5)

qCV is the intensity of the process noise of the CV model, and T is the time interval between samples. 2.3. Constant and abrupt acceleration (CA/AA) models In order to cope with the maneuver of the target, CA and AA models add an acceleration component to the CV model. At the k th time step, the state vector XCA/AA(k) is defined as X CA/AA (k ) = [ x(k ) x (k )  x(k )

y (k )

y (k )

 y (k )]T ,

(6)

whose elements are x position, x velocity, x acceleration, y position, y velocity, and y acceleration. The CA/AA models [4,5] that describe the target movement with a nearly constant acceleration is given by X CA/AA (k + 1) = FCA/AA X CA/AA (k ) + wCA/AA (k ),

(7)

where the matrix FCA/AA has the same definition like the CV model and wCA/AA(k) is the independent process noise with zero-mean, white, Gaussian probability distribution with N (0, QCA/AA (k )). The state transition matrix and process noise covariance matrix for CA/AA models are FCA/AA = diag[ F3 , F3 ], QCA/AA (k ) = diag[Q3 , Q3 ]qCA/AA ,

(8) (9)

where ⎡T 4 / 4 T 3 / 2 T 2 / 2 ⎤ ⎡1 T T 2 / 2 ⎤ ⎢ ⎥ ⎢ ⎥ F3 = ⎢ 0 1 T ⎥ , Q3 = ⎢T 3 / 2 T 2 / 2 T ⎥, ⎢ 2 ⎥ ⎢0 0 1 ⎥⎦ T 1 ⎦⎥ ⎢⎣T / 2 ⎣ (10) qCA/AA is the intensity of the process noise of the CA/AA models. The process noise covariance matrix for each CA and AA model is almost same, but the only difference is the intensities of the process noise, qCA and qAA.

2.4. Measurement model UWSNs composed of N acoustic sensor nodes are deployed at the bottom of the sea in a 2D region. The positions of sensor nodes, in Cartesian coordinates denoted by ( xi , yi ), i = 1, , N , are arbitrary but known

to the fusion center. We suppose that each sensor node si , s2 , , si , , s N provides the position information of the target at the k th time step. The measurement equation from the sensor node si for CV model is given by i zi (k ) = H CV X CV (k ) + vi (k ),

(11)

i is the measurement matrix of sensor node where H CV si and vi (k) is the independent measurement noise with zero-mean, white, Gaussian probability distribution with N (0, Ri (k )) [23]. The measurement matrix for CV model is given by

⎡1 0 0 0 ⎤ i =⎢ H CV ⎥. ⎣0 0 1 0 ⎦

(12)

The measurement equation from the sensor node si for CA/AA model is given by i zi (k ) = H CA/AA X CA/AA (k ) + vi (k ),

(13)

i is the measurement matrix of sensor where H CA/AA node si. The measurement matrix for CA/AA model is given by

⎡1 0 0 0 0 0 ⎤ i H CA/AA =⎢ ⎥. ⎣0 0 0 1 0 0⎦

(14)

The position information of the target can be achieved by using either (11) or (13). At the k th time step, UWSNs give multiple sensor measurements zi , z2 , , zi , , z N , and the accumulated measurement Z(k), which can be also achieved by using either (11) or (13), is given by 1 ⎡ z1 (k ) ⎤ ⎡ H CV X CV (k ) ⎤ ⎡ v1 (k ) ⎤ ⎢ ⎥ ⎢ ⎢ z (k ) ⎥ ⎥ 2 H X ( k ) ⎢ ⎥ ⎢ v2 (k ) ⎥ 2 CV CV ⎢ ⎥ ⎥ ⎢ ⎢  ⎥ ⎢ ⎥  ⎥+⎢  ⎥ Z (k ) = ⎢ ⎥=⎢ i ⎢ zi (k ) ⎥ ⎢ H CV X CV (k ) ⎥ ⎢ vi (k ) ⎥ ⎥ ⎢ ⎢  ⎥ ⎢ ⎥  ⎢ ⎥ ⎢  ⎥ ⎢ ⎥ ⎢ N ⎥ ⎣⎢ z N (k ) ⎦⎥ ⎣⎢ H CV X CV (k ) ⎦⎥ ⎣⎢vN (k ) ⎦⎥ 1 ⎡ H CA/AA X CA/AA (k ) ⎤ ⎡ v1 (k ) ⎤ ⎢ 2 ⎥ ⎢ ⎥ ⎢ H CA/AA X CA/AA (k ) ⎥ ⎢ v2 (k ) ⎥ ⎢ ⎥ ⎢ ⎥  ⎥ + ⎢  ⎥. =⎢ ⎢H i X (k ) ⎥ ⎢ vi (k ) ⎥ ⎢ CA/AA CA/AA ⎥ ⎢ ⎥  ⎢ ⎥ ⎢  ⎥ ⎢ N ⎥ ⎢v (k ) ⎥ ⎣⎢ H CA/AA X CA/AA (k ) ⎦⎥ ⎣ N ⎦

(15)

3. WAKE-UP/SLEEP (WUS) SCHEME This paper focuses on the distributed target tracking algorithm, so we propose an energy efficient tracking scheme. From the proposed scheme, the distributed target tracking algorithm can save the energy by reducing the communication burden. The basic idea of

Interacting Multiple Model Filter-based Distributed Target Tracking Algorithm in Underwater Wireless Sensor Networks

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(a) 3σ circle and waked-up and sleeping sensors.

Fig. 2. Distributed target tracking architecture. the distributed target tracking architecture is illuminated in Fig. 2, where the dashed circles mean the sensor detection area. At the k th time step, there exists an ellipse which shows the estimation area of the target. At the k +1th time step, a new ellipse which is predicted estimation area of the target can be achieved from the prediction step of the Kalman filter [1]. The node B is selected as the processing node because the node B is the nearest node to the center of the predicted estimation ellipse and the information of the processing node A is transferred to a new processing node B. A new processing node B collects measurements that are inside the predicted estimation ellipse. Finally at the k +1th time step, a new updated ellipse can be achieved from the Kalman filter by using the measurements inside the predicted estimation ellipse. At every time step, the same procedures continue recursively. The idea of the proposed WUS scheme is illuminated in Fig. 3. As shown in Fig. 3(a), the predicted and updated ellipses are transformed into circles because the noise features of x and y axes are assumed independent and equal. Each small dashed circle represents the detection area of a sensor node, the solid circle at leftbottom represents the updated state estimation circle which can include the state of the target with 99.73% (3σ(k)) probability at the k th time step. At the k +1th time step, a new state of the target is predicted within a large solid circle at center with 3σ(k + 1) probability. To update the state of the target, we have to take new measurement data possess the actual target information, black star symbol in Fig. 3(a), within the predicted 3σ(k +1) circle. At the k +1th time step, the distance di (k +1) between the predicted position of the target and the position of the sensor node si (k +1) can be achieved by di 2 (k + 1) = {xˆ (k + 1| k ) − si, x (k + 1)}2 + { yˆ (k + 1| k ) − si, y (k + 1)}2 ,

(16)

where xˆ(k + 1| k ) and yˆ(k + 1| k ) are the predicted x

(b) Waked-up/sleeping sensor. (c) Valid/invalid sensor. Fig. 3. Sensor wake-up strategy with 3σ circle. and y positions of the target, and si , x (k + 1) and si , y (k +1) are the x and y positions of the sensor node si (k +1). The WUS scheme illuminated in Fig. 3(b), selects n waked-up sensor nodes from N sensor nodes by judging which have the overlapping parts of the predicted 3σ(k + 1) circle. The WUS scheme can decide the existence of the overlapping parts if di (k + 1) ≤ ri (k + 1) + 3σ (k + 1),

(17)

where ri (k +1) is the detection radius of sensor node si (k +1) at the k +1th time step. n sensor nodes satisfying equation (17) are waked-up. Shown in Figs. 3(a) and 3(b), the waked-up sensor nodes are gray circles with black center. These waked-up sensor nodes can detect the target. And the others, N – n sensor nodes are changed into the sleeping mode if the overlapping parts do not exist, that is di (k + 1) > ri (k + 1) + 3σ (k + 1).

(18)

A new processing node sp (k +1) whose detection area is textile circle in Fig. 3(a), is selected by min(d1 (k + 1), , d n (k + 1)).

(19)

We can select only some sensor nodes among all sensor nodes by the proposed WUS scheme and these selected sensor nodes can detect the target by consuming the battery, and the processing node doesn’t have to communicate all of the sensor nodes. This means that a distributed target tracking algorithm with WUS scheme can save more energy for tracking compared with centralized tracking algorithms without WUS scheme. However, we have to consider the validity of these

Chang Ho Yu and Jae Weon Choi

622

multiple sensor measurements which is related with the detection radius of each sensor node. Shown in Fig. 3(c), the sensor node which can measure the actual target, black star symbol, is decided as a valid sensor, on the other hand, the sensor node which cannot measure the actual target is decided as an invalid sensor. Finally, m valid sensor nodes which can measure the actual target, provide measurements z1 (k + 1), z2 (k + 1),  , zm (k + 1) to the processing node and the processing node calculates the fused one measurement zfusion (k + 1) by considering the covariance matrices of the all valid sensor measurements recursively. Especially in Fig. 3(a), only 2 sensor nodes which can measure the actual target , black star symbol, are valid. Thus the measurement equation (15) can be modified by ⎡m −1 ⎤ zfusion (k + 1) = ⎢ ∑ Ri ( k + 1) ⎥ ⎣ i =1 ⎦ m

−1

(20)

−1

× ∑ Ri ( k + 1) zi ( k + 1), i =1

where Ri (k +1) is the measurement covariance matrix. And the fused covariance Rfusion(k +1) can be achieved by −1

⎡m −1 ⎤ Rfusion ( k + 1) = ⎢ ∑ Ri ( k + 1) ⎥ . ⎣ i =1 ⎦

(21)

The processing node updates the state of the target and the state error covariance matrix from the fused measurement zfusion(k +1) and fused measurement covariance matrix Rfusion(k +1). 4. IMM BASED DISTRIBUTED TARGET TRACKING FILTER Based on the above CV, CA, and AA model and the measurement model, the IMM filter is applied to estimate the system state variable which includes the target’s position, velocity, and acceleration under the distributed architecture. Conventionally the IMM filter consists of four major steps: interaction (mixing), filtering, calculating each mode probability, and combination. At each time step, the initial condition for the filter matched to a certain mode (a module) is obtained by mixing the state estimates of all filters at the previous time step under the assumption that this particular mode is in effect at the current time. This is followed by a regular filtering (prediction and update) step (such as KF), performed in parallel for each mode. Then, a combination (weighted sum) of the updated state estimates of all filters yields the state estimate. The probability of a mode being in effect plays a key role in the weighting of the mixing and the combination of states and covariances [6,24]. In this section, for distributed target tracking, the IMM filter based on sensor node selection scheme is proposed. The proposed filter structure is depicted in Fig. 4. Each step is explained in detail through sub-sections.

Fig. 4. Structure of IMM based distributed target tracking filter. 4.1. Mixing probabilities and interaction At k th time step, the mixing probability is given by µ s|t ( k | k ) =

1 Φ s|t µ s (k ), ct

(22)

where s and t means each mode and Φ s|t is the mode transition probability between mode s and mode t, and μs(k) is the probability of mode s at k th time step. And ct is the normalization constant, defined by N

ct = ∑ Φ s|t µ s (k ).

(23)

s =1

By using the mixing probability µ s|k (k | k ), the interacted initial conditions for mode t at k th time step are given by N

xˆtinitial (k | k ) = ∑ xˆs (k | k ) µ s|t (k | k ), s =1 N

(24)

{

Ptinitial (k | k ) = ∑ µ s|t (k | k ) s =1

×[ Ps (k | k ) + ( xˆs (k | k ) – xˆsinitial (k | k )) (25)

}

×( xˆs (k | k ) – xˆsinitial (k | k ))T ] .

4.2. Prediction and Filtering At k +1th time step, equation (24) and (25) are used as the input of model-matched filter t, and each prediction and filtering step is accomplished by adapting the Kalman filter under the proposed sensor node selection scheme. The predicted state estimate and its covariance in model-matched filter t are given by xˆt (k + 1| k ) = Ft xˆtinitial (k | k ), Pt (k + 1| k ) = Ft Pt

initial

(26) T

(k | k ) Ft + Qt (k ).

(27)

The updated state estimate and its covariance in model-matched filter t can be given by two steps:

Interacting Multiple Model Filter-based Distributed Target Tracking Algorithm in Underwater Wireless Sensor Networks

Step 1: Shown in Fig. 4, if there are not either wakedup sensor nodes or valid sensor nodes, the updated state estimate and its covariance is defined by xˆt (k + 1| k + 1) = xˆt (k + 1| k ),

(28) (29)

Pt (k + 1| k + 1) = Pt (k + 1| k ).

Step 2: Shown in Fig. 4, if there are both waked-up sensor nodes and valid sensor nodes, the updated state estimate and its covariance is calculated by xˆt (k + 1| k + 1) = xˆt (k + 1| k ) + Gt (k + 1)rt (k + 1),

Pt (k + 1| k + 1) = [ I − Gt (k + 1) H t ] Pt (k + 1 | k ),

(30) (31)

where Gt (k +1) is the Kalman gain matrix and rt (k +1) is the residual which is defined by t (k + 1) − zˆt (k + 1 | k ), rt (k + 1) = zfusion

(32)

and the predicted measurement zˆt (k + 1) is given by zˆt (k + 1| k ) = H t xˆt (k + 1| k ).

(33)

The covariance of the residual rt (k +1) is given by t St (k + 1) = H t Pt (k + 1 | k ) H tT + Rfusion (k + 1 | k ),

Gt (k + 1) = Pt (k

−1

+ 1) .

(34)

(35)

4.3. Calculating mode probability The mode probability µt (k +1), which can be calculated by using the residuals of each sub-filter, is given by t µt (k + 1) = p ⎡⎣ M t (k + 1) | Z valid (k + 1) ⎤⎦

= p ⎡⎣ M t (k + 1) |

t zfusion (k

t + 1), Z valid (k ) ⎤⎦

t t p ⎡ zfusion (k + 1) | M t (k + 1), Z valid (k ) ⎤⎦ = ⎣ t t p ⎡⎣ zfusion (k + 1) | Z valid (k ) ⎤⎦

×

t p ⎡⎣ M t (k + 1) | Z valid (k ) ⎤⎦

t t p ⎡⎣ zfusion (k + 1) | Z valid (k ) ⎤⎦

N

×∑ Θ s|t µ s (k ),

(36)

s =1

where Mt (k +1) is the hypothesis that the movement of t the target agrees with the model Mt, and Z valid (k + 1) is the accumulated all measurements until k +1th time step. t t p[zfusion ( k + 1) | M t (k + 1), Z valid (k )] can be calculated by t t p ⎡⎣ zfusion (k + 1) | M t (k + 1), Z valid (k ) ⎤⎦

=

1 (2π )

M

| St (k + 1)

(37)

⎛ 1 ⎞ × exp ⎜ − rt (k + 1)T St−1 (k + 1)rt (k + 1) ⎟ . 2 ⎝ ⎠

4.4. Combination At k +1th time step, the final output can be achieved by the combination of the different mode update results, which are given by N

thus, the Kalman gain matrix Gt (k +1) is calculated by + 1| k ) H tT St (k

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xˆ ( k + 1| k + 1) = ∑ xˆt ( k + 1| k + 1) µt ( k + 1),

(38)

P (k + 1| k + 1) = ∑ µt (k + 1){Pt (k + 1| k + 1)

(39)

t =1 N

s =1

+[ xˆt (k + 1| k + 1) – xˆ(k + 1| k + 1)] ×[ xˆt (k + 1| k + 1) – xˆ(k + 1| k + 1))T ]}.

5. SIMULATIONS The target is assumed to move at the bottom of the sea in the X – Y plane of the Cartesian coordinate frame with the initial position of [2000 2000]Tm, and to move along the sinusoidal trajectory from the right to the left, shown in Fig. 5. The monitored field is 4000 m×2000 m and assumed to be covered by uniformly placed underwater acoustic sensor nodes. It is also assumed that the each underwater acoustic sensor node can collect the target position only by the acoustic channel, the locations of all underwater acoustic sensor nodes are already known.

t t p ⎡ zfusion (k + 1) | M t (k + 1), Z valid (k ) ⎤⎦ = ⎣ t t p ⎡⎣ zfusion (k + 1) | Z valid (k ) ⎤⎦ N

{

t × ∑ p ⎡ M t (k + 1) | M s (k ), Z valid (k ) ⎦⎤ ⎣ s =1

}

t ×p ⎡ M s (k ) | Z valid (k ) ⎤⎦ ⎣

t t p ⎡ zfusion (k + 1) | M t (k + 1), Z valid (k ) ⎤⎦ = ⎣ t t p ⎡⎣ zfusion (k + 1) | Z k −1 ⎤⎦ Z valid (k + 1) N

t × ∑ Θ s|t p ⎡⎣ M s (k ) | Z valid (k ) ⎤⎦ s =1

t t p ⎡ zfusion (k + 1) | M t (k + 1), Z valid (k ) ⎤⎦ = ⎣ t t p ⎡⎣ zfusion (k + 1) | Z valid (k ) ⎤⎦

Fig. 5. Sensor node distribution and real target trajcectory.

Chang Ho Yu and Jae Weon Choi

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Fig. 6. Waked-up and valid sensor nodes based on CV model.

Fig. 7. Waked-up and valid sensor nodes based on CA model.

We apply the proposed distributed target tracking algorithm including the WUS scheme to the tracking of a moving target through the UWSN environments. We evaluate the performance of the proposed algorithm by computer simulations. 5.1. Simulation conditions We assume the time interval T as 0.1 sec and the intensities of the process noise qCV, qCA, and qAA as 2 m2/sec4, 4 m2/sec4, and 10 m2/sec4. And the measurement covariance matrix Ri (k) is assumed as ⎡122 0 ⎤ 2 Ri (k ) = ⎢ ⎥m . ⎢⎣ 0 122 ⎥⎦

(40)

Each initial state error covariance matrix Pt (0) for model-matched filter t is assumed as PCV (0) = 102 I (4 × 4) m 2 , 2

(41) 2

PCA (0) = PAA (0) = 10 I (6 × 6) m .

(42)

The detection radius ri of sensor node si is assumed 150 m and the detection radius of all sensor nodes is assumed same. The displacement between each sensor node is assumed 200 m and the mode transition probability Φ s|t is given by Φ s|t

0 ⎤ ⎡ 0.85 0.15 ⎢ = ⎢ 0.33 0.34 0.34 ⎥⎥ . ⎢⎣ 0 0.15 0.85 ⎥⎦

(43)

And 500 Monte-Carlo simulation is executed. 5.2. Simulation results Fig. 6 shows the waked-up and valid sensor nodes based on CV model. Every sampling time several sensor nodes are waked-up which are indicated as ‘*’ symbol and a few sensor nodes among the waked-up sensor nodes are decided as valid which are indicated as ‘o’ symbol. Figs. 7 and 8 show the waked-up and valid sensor nodes based on each CA and AA model. Each symbol notation is similar with Fig. 6. Shown in Figs.

Fig. 8. Waked-up and valid sensor nodes based on AA model. 6~8, proposed distributed tracking algorithm is carried out on not every sensor platform but only valid sensor platforms by using the WUS scheme and results in a efficient energy saving. From these valid sensor nodes, the proposed filter can update the state of the target by the Step 2. If there are no both waked-up and valid sensor nodes, the proposed filter can update the state of the target by Step 1. Recursively, these procedures are performed every sampling time. As mentioned in simulation conditions, because the detection radius of sensor node is smaller than the displacement between each sensor node, every waked-up sensor node is not changed to the valid sensor node, shown in Figs. 6~8. When the target passes the region near 1000 m on the X coordinate after the maneuver occurs, 2 sensor nodes located on (1000 m, 2200 m) and (1000 m, 2000 m) are waked up in Fig. 6, on the other hands, other 2 sensor nodes located on (1000 m, 2000 m) and (1000 m, 1800 m) are waked up in Figs. 7~8. The different locations of each waked-up sensor node are generated by the different region passed through the prediction step for each sub-filter. Fig. 6 shows that the sensor node located on (1000 m, 2200 m), a little far from the predicted region of the real target is waked up by the CV

Interacting Multiple Model Filter-based Distributed Target Tracking Algorithm in Underwater Wireless Sensor Networks

Fig. 9. Real and estimated target trajectories. model based sub-filter, and this waked up sensor node has an poor effect on the tracking performance. On the contrary, Fig. 7 shows that the sensor node located on (1000 m, 1800 m), close to the predicted region of the real target is waked up by the CA model based sub-filter, finally this properly waked up sensor node increases the tracking performance. The only difference between CA and AA model based sub-filters is the intensities of the process noise, qCA and qAA, thus Fig. 8 shows the similar results with the Fig. 7. When the target passes the region near – 800 m on the X coordinate after another maneuver occurs, similar analyses can be achieved. In Fig. 6, two sensor nodes located on (– 800 m, 2000 m) and (– 800 m, 1800 m) are waked up, on the other hands, in Figs. 7~8, other 2 sensor nodes located on (– 800 m, 1800 m) and (– 800 m, 1600 m) are waked up. The different locations of each waked-up sensor node are also generated by the different region passed through the prediction step for each sub-filter. Fig. 6 shows that the sensor node located on (– 800 m, 2000 m), a little far from the predicted region of the real target is waked up by the CV model based sub-filter, and this waked up sensor node also has an poor effect on the tracking performance. On the contrary, Fig. 7 shows that the sensor node located on (– 800 m, 1600 m), close to the predicted region of the real target is waked up by the CA model based sub-filter, finally properly waked up sensor node increases the tracking performance. Fig. 9 shows the real and estimated target trajectories and proves that IMM based distributed target tracking filter can perform more successfully than KF based algorithm. From the combination of outputs based on each model, the proposed filter provides mixed state and covariance of the target in distributed architecture every sampling time. Fig. 10 shows the position RMSE comparison between IMM and KF. When the target converts its direction, which means the maneuver happening, the RMSE increases and after the filter estimates the state of the target successfully, the RMSE decreases. And the target reconverts its direction, the RMSE also increases and decreases. Recursively, these procedures are continued. Fig. 10 shows the position RMSE of IMM based

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Fig. 10. RMSE of target position estimate.

Fig. 11. RMSE of target velocity estimate.

Fig. 12. RMSE of target acceleration estimate. distributed target tracking filter is much smaller than KF based algorithm because of the combination of outputs based on each model. Figs. 11 and 12 show the velocity and acceleration RMSE comparison between IMM and KF. Fig. 13 shows the mode probability of each model such as CV, CA, and AA. As shown in Fig. 13, when the target performs the linear motion, mode probability of

Chang Ho Yu and Jae Weon Choi

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[5] Fig. 13. Mode probability of each model. CV model is high, and mode probability of AA model is low. On the other hand, in case of direction change of the target, mode probability of CV model is low and mode probability of AA model is high. In addition, the mode probability of CA model is almost same during the simulation period because the acceleration magnitude of the target in the case of direction change is high, over almost 50 m/sec2, which means the high maneuver and it is not suitable for the CA model. Shown in Figs. 9~12, proposed distributed IMM filter performs much better than the distributed KF. The distributed KF cannot cope with the target maneuver sensitively, so results in the performance decline. On the other hand, proposed distributed IMM filter copes with the target maneuver effectively and produces good performances by interacting the multiple models. The results indicate that the proposed filter has a good performance in the environment of distributed architecture, and that it has advantages in calculating future target positions such as are required in combat management systems.

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6. CONCLUSIONS This paper has presented a distributed tracking algorithm for a single moving target through UWSNs, and the issues of estimating the state of the target and improving energy efficiency by applying a Kalman filter in a distributed architecture. To estimate the states of the target, we have proposed the energy efficient tracking algorithm using the WUS scheme for a distributed target tracking, and proposed approach have saved the energy by reducing the communication burden. And to cope with the maneuver of the target, IMM filter is used and successfully estimates the state of the target in distributed architecture. And simulation results have demonstrated that, the proposed approach could guarantee the reliability and tracking accuracy.

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Chang Ho Yu received his B.S. degree in Mechanical Engineering from Pusan National University, Busan, Korea in 2002, and received his Ph.D. degree in Intelligent Mechanical Engineering from Pusan National University, Busan, Korea in 2014. He is currently a Postdoctoral Fellow in the Research Institute of Mechanical Technology, Pusan National University, Busan, Korea. His research interests include target tracking filter design, sensor localization algorithm, and guidance and control theories. He is a Member of ICROS and KSME. Jae Weon Choi received his B.S., M.S., and Ph.D. degrees in Control and Instrumentation Engineering from Seoul National University, Seoul, Korea, in 1987, 1989, and 1995, respectively. He is currently a Professor in the School of Mechanical Engineering, Pusan National University, Busan, Korea. His research interests include spectral theory for linear time-varying systems and target tracking filter design. He is a Senior Member of IEEE and AIAA, also a Member of both IFAC Technical Committees on Linear Systems and Aerospace.