## 1 Introduction  
Surveillance and monitoring of battlefields is one of the most important requirements in critical times. Sometimes it is also quite risky or impossible to have direct surveillance of a real field. That is why for such surveillance tasks remote acoustic target tracking is mostly used. Remote acoustic target tracking can be done by using wireless sensor networks (WSNs). A 2-dimensional acoustic target tracking of a target object by sensed spatio-temporal information obtained using sensor nodes is a 3-dimensional problem. It is often impossible to place wireless sensor nodes in predetermined positions, and this is why in most applications motes (i.e., sensor nodes) are spread randomly in a field from the air. For the sake of simplicity in this paper, we assume that sensor nodes are spread with a uniform distribution in a field and constitute a multi-hop wireless network. Sensor nodes use distributed processing for doing target tracking. In the study reported in this paper we further ignore the signal processing aspects of target tracking using sound sensing.  
Quality of service (QoS) plays a critical role on the performability of WSNs that are used for remote target tracking. Attaining the best QoS from the application and end-user's viewpoint though requires the best possible adjustment of WSNs' parameters in support of QoS metrics. This task, namely the QoS management, is the responsibility of WSNs middleware [1]. Providing the best possible values for every QoS metric is difficult because most of the QoS metrics are mutually exclusive. For example, decreases in the sensing coverage increases the network lifetime and at the same time decreases the accuracy and precision of target tracking results [2,3]. One of the challenges in 2-dimensional acoustic target tracking is the determination of the best degree of sensing coverage for accurate target tracking. A high sensing coverage wastes the resources of WSNs while a low sensing coverage decreases the accuracy of target tracking results by producing more frequently happening outliers that greatly decrease the accuracy of the target tracking results.  
In this paper we theoretically determine the minimum best sensing coverage of WSNs for 2-dimensional acoustic target tracking that guarantees high accuracy of results without occurrence of outliers. We also present the best possible processing and fusion method that can yield more accurate results with the least sensing coverage and less communication overhead. Since we study the acoustic target tracking from a theoretical point of view in this paper, we ignore the environmental factors like humidity and temperature. The contributions of our paper are applicable to other methods of target tracking like particle filtering [4] and Kalman filtering [5].  
The rest of paper is organized as follows. Section 2 presents related work in the area of acoustic target tracking. Section 3 presents the basics of acoustic target tracking and our basic geometric based proposed method, its simulation results and pitfalls. Section 4 discusses the acoustic target tracking from a theoretical perspective and formally represents the different bases of outliers in target tracking and proposes simple solutions for one type of outliers. Section 5 introduces two extended new methods and proves that they eliminate the source of second type of outliers. Section 6 evaluates our proposed methods by reporting the results of our simulations. Section 7 concludes the paper and puts forward some future works.