Gunshot acoustic event identification and shooter localization in a WSN of asynchronous multichannel acoustic ground sensors

Abstract

Gunshot acoustic localization for military and civilian security systems has long been an important topic of research. In recent years the development of Wireless Sensor Network (WSN) systems of independent Unmanned Ground Sensors (UGS) performing distributed cooperative localization has grown in popularity. This paper considers a shooter localization approach based on gunshot Shockwave (SW) and Muzzle Blast (MB) event time and Direction of Arrival (DOA) information. The approach accounts for acoustic events Not-of-Interest (NOI), such as target hit noise, reflections and background noise. UGS perform gunshot acoustic event detection and DOA estimation independently; the information regarding every detected shot instance is sent through the WSN to the fusion node, which performs event identification and calculates the shooter’s position. The paper presents a solution to identifying SW and MB among NOI events at the stage of information fusion. The considered approach treats the information gathered from different UGS separately, and thus does not require precise synchronization between the UGS. For DOA estimation, an algorithm designed for circular microphone arrays is proposed and compared with the SRP-PHAT localization algorithm. It is shown to provide adequate DOA estimates, while being more computationally effective. The proposed shooter localization approach is tested on real signals, acquired during three live shooting experiments. It is shown to succeed in localizing the shooter’s position with a mean accuracy of 0.87 m for 30 shots at the range of 35 m, and just above 7 m for 37 shots at the range of 100 m.

Appendix

Multilateration is a technique of estimating object position coordinates based on TDOA information. For the application of shooter localization in the WSN of ground sensors, the shooter’s position can be estimated using the TDOA between the MB events, detected by different UGS. As the inter-UGS event time values are used, sufficient node synchronization and temporal, as well as spatial data validation are essential for successful operation of multilateration. Furthermore, the method is applicable only if the MB acoustic events are explicitly identified among other detected gunshot events.

The distance between UGS network node k with coordinates $\left( x_{k},y_{k},z_{k}\right)$ and the shooter can be defined as a vector length

$$\begin{aligned} d=\sqrt{\left( x_{k}-x\right) ^{2}+\left( y_{k}-y\right) ^{2}+\left( z_{k}-z\right) ^{2}}, \end{aligned}$$

(29)

where $\left( x,y,z\right)$ are the shooter’s coordinates and $k=1,\dots ,K$, where K is the total number of UGS. Thus, knowing UGS positions and times of MB event occurrence $t_{MB}$ for a detected gunshot, the TDOA $\tau _{A,B}$ can be found between two separate UGS A and B. The distance difference between UGS A and the shooter and UGS B and the shooter, $d_{A,B}$ is then calculated as

$$\begin{aligned} d_{A,B}= & {} c\cdot \tau _{A,B}=c\left( t_{MB}(A)-t_{MB}(B)\right) \nonumber \\= & {} \sqrt{\left( x_{A}\,-\, x\right) ^{2}+\left( y_{A}\,-\, y\right) ^{2}+\left( z_{A}\,-\, z\right) ^{2}}\,\nonumber \\&\quad -\,\sqrt{\left( x_{B}\,-\, x\right) ^{2}+\left( y_{B}\,-\, y\right) ^{2}+\left( z_{B}\,-\, z\right) ^{2}}, \end{aligned}$$

(30)

where (x, y, z) are shooter (MB source) coordinates and $\left( x_{A},y_{A},z_{A}\right)$ are the coordinates of UGS A, and $\left( x_{B},y_{B},z_{B}\right)$ are the coordinates of UGS B (Liu and Yang 2010). For any group consisting of G UGS the shooter is localizable by the following system of $G-1$ nonlinear equations:

where $d_{i,j}$ is the distance difference between the i-th and j-th UGS, and $G\le K$ is the number of UGS in the group. To estimate the solution to this system of nonlinear equations at least four UGS that have detected MB are needed; this yields three TDOA values $\tau _{1,2}$, $\tau _{1,3}$, $\tau _{1,4}$, and the system is solved by applying a least squares method, e.g., Levenberg-Marquardt. Various practical approaches exist, e.g., as discussed by Bancroft (1985) or by Bucher and Misra (2002). For the ground applications we could simplify the solution with constant z dimension and denote the unknown location of the shooter as (x, y); then we can use the $t_{MB}$ values from only three UGS.

Fig. 22

Shooter localization simulation results for Experiment 3 using multilateration. The theoretical node clock synchronization error is uniformly distributed within the interval of $\pm 10$ ms. Blue circles shooter positions estimated with $G=6$ UGS groups; green crosses shooter positions estimated with $G=4$ UGS groups; red diamonds true shooter positions

Table 4 Shooter position estimate mean error (ME) and standard deviation (SD) in meters

Multilateration methods for WSN highly depend on inter-node synchronization accuracy. Figure 22 presents the results of a simulation of shooter localization using multilateration for the setup identical to that of Experiment 3 (see Sect. 5). The figure illustrates the localization accuracy for all ${6 \atopwithdelims ()4}=15$ combinations of $G=4$ UGS groups and ${6 \atopwithdelims ()6}=1$ combination of $G=6$ UGS groups with the synchronization error of each UGS randomly chosen from a uniform distribution within the interval of $\pm 10$ ms. The figure shows that larger UGS groups perform with better accuracy than smaller groups with the same degree of node synchronization error. To illustrate the impact of WSN synchronization error on shooter localization accuracy, shooter position estimate mean error (ME), calculated by (28), and its standard deviation (SD) are presented for $G=4$ and $G=6$ UGS groups in Table 4. For this simulation we also use the setup of Experiment 3 and assume the WSN clock synchronization error to be in a range of $\pm 5$ ms and up to $\pm 50$ ms. The table shows that in order to obtain shooter position estimate accuracy comparable to our proposed method, the $G=6$ UGS groups should be synchronized to at least $\pm 10$ ms, and for $G=4$ UGS groups the synchronization should be within $\pm 5$ ms.