## 3 Proposed Architecture
### Particle Filter (PF) with Time Difference of Arrival (TDOA) Measurement  
To estimate the movement of the acoustic signal source, we use the TDOA measurement obtained from the acoustic sensors. Four acoustic sensors including one reference sensor are used to estimate the position of the target in a three-dimensional space. The proposed PF is based target position estimation using TDOA measurements obtained in this structure. The PF is a method of probabilistically estimating the state of a target using N particles, also called the Monte Carlo method. Unlike the extended KF and unscented KF, the PF has strength in non-Gaussian and non-linear systems. The proposed algorithm is scalable to the number of sensors, and it is applicable even if the number of sensors is increased as shown in Figure 3. The proposed architecture uses four sensors which is minimum number of sensors required to detect a target in three-dimensional space or can use more than minimum number of sensors. The PF processing can operated on the GPU using each sensor node set, and the proposed architecture can detect multiple targets in parallel using acoustic signal. \[s_{k}=As_{k-1}+p_{k} \tag{1}\]  
\[z_{k}=h(s_{k})+v_{k} \tag{2}\]  
\[r_{a}(s_{k})=\mid u_{k}-s_{a}\mid, \tag{3}\]  
\[r_{ab}(s_{k})=cT_{ab}(s_{k})=r_{a}(s_{k})-r_{b}(s_{k})\]  
\[T_{ab}(s_{k})=\frac{1}{c}(r_{a}(s_{k})-r_{b}(s_{k})) \tag{4}\]  
\[h_{ab}(s_{k})=\frac{1}{c}r_{ab}(s_{k}) \tag{5}\]  
Figure 1: Proposed GPU based accelerated algorithm. Figure 2: Accelerated signal processing for large amounts of data using GPU. \[H(s_{k})=[h_{ab}(s_{k})\ h_{ac}(s_{k})\...\ h_{aX}(s_{k})]^{T} \tag{6}\]  
First, the state of the system used at PF processing is defined as follows. The state of the moving target is defined as a uniform speed motion. In this case, the system state equation for estimating the current state \(s_{k}\) in a previous state \(s_{k-1}\) is expressed by Equation (1), where \(s_{k}\) denotes a position vector of the three-dimensional space at time k. A denotes a state transition equation matrix, and \(p_{k}\) denotes process noise. The observation model, which represents the relationship between the state of the system and the measured value, is defined by Equation (2), where \(z_{k}\) denotes measured value and \(v_{k}\) denotes measurement noise. In this study, we propose accelerating the position estimation of the target using TDOA measurements, and the measured value \(z_{k}\) is a TDOA measurement obtained from the signal input to each acoustic sensor. In Equation (2), the relation between the system state and the TDOA measurements is represented by \(h\), and it can be obtained from the following procedure. The distance between the target and the sensor is defined by \(r_{a}(s_{k})\) in Equation (3). Also the reference sensor for obtaining the TDOA measurement is defined as \(s_{a}\), where \(u_{k}\) is the position vector of the target and \(s_{a}\) is the position vector of the \(a\)th sensor. As shown in second line of Equation (3), \(r_{ab}\) is displacement value between distance to \(s_{a}\) and \(s_{b}\) from target, which can be represented with the velocity of source wave 'c' multiplied by the TDOA value between sensor \(s_{a}\) and \(s_{b}\). Figure 3's left one shows the reference sensor and the other sensor. TDOA measurements used for the PF are obtained between reference sensor \(s_{a}\) and the other sensor. Equation (4) is used to obtain the TDOA measurement value by using the distance from each reference sensor \(s_{a}\) and sensor \(s_{b}\) to the target. The velocity c is the speed of the sound wave in the water, which is 1500 m/s. Therefore, the target location estimation by applying three TDOA measurement values is described with the following equation; Equation (5) defines a relation \(h_{ab}\) between the system state and the TDOA measurement. The state from three or more TDOA measurement values are represented in Equation (6) by a matrix \(H\), where index 'a' represents reference sensor and index 'X' represents relative sensors.