# Detection of Intelligent Intruders in Wireless Sensor Networks
## 1 Introduction
### Related Works and Research Motivation  
The research literature has extensively addressed the intrusion detection problem in WSNs under different metrics and assumptions [10]. On the one hand, the problem is addressed from the perspective of WSN design and deployment based on the assumption that an intruder followsa linear intrusion path and moves inside the WSN FoI at a constant speed [10; 11; 12; 13; 14; 15; 16; 17; 18]. The focus of the research is to investigate the tradeoff between WSN settings and detection probability and to identify critical network parameters for achieving the application-specific detection probability, while minimizing network cost and/or power consumption. Under the linear intrusion model, [PERSON] _et al._[19] derive the closed form formula of detection probability and the average detection delay of mobile intruder(s), taking into consideration the sensor sleeping pattern for energy efficiency. [PERSON] _et al._[11] study the tradeoff between intrusion detection quality and power conservation and derive the mean time when a linear mobile intruder is first detected. They also provide sleep-scheduling algorithms to guarantee a minimum response time for intrusion detection and power conservation. [PERSON] _et al._[10; 13] formulate the intrusion detection problem as a line-set intersection problem and utilize integral geometry to derive the intrusion detection probability for both random and deterministic WSNs. [PERSON] _et al._[15] derive the detection probability of a linear intruder that is detected by \(k\) sensors within the maximum allowable intrusion distance in homogeneous and heterogeneous WSNs. Further, [PERSON] _et al._[20] analyze the linear intruder detection problem in a Gaussian-distributed WSN with respect to a counterpart uniformly-distributed WSN and characterize the detection probability in both single-sensing detection and multiple-sensing detection scenarios. On the other hand, the intrusion detection problem is addressed under the assumption that sensors and/or intruders are both mobile and follow some random mobility model [18]. [PERSON] _et al._[21] provide a comprehensive survey on a number of mobility models, including the random walk mobility model, the random way point mobility model, the random direction mobility model, the Gaussian-Markov mobility model, _etc._ The mobility model is to mimic the random movements of mobile sensors and/or intruders for network simulation and performance evaluations. Based on these random mobility models, [PERSON] _et al._[22] study the impact of sensor mobility on the network sensing coverage and intrusion detection probability. Their results show that sensor mobility can be exploited to improve the network sensor sensing coverage and reduce the detection time of a stationary intruder. For mobile intruders, the detection time depends on the mobility strategies of the sensors and the intruders. [PERSON] _et al._[23] address the mobile intruder detection problem in a mobile sensor network by formulating the problem as a \(k\)-barrier coverage problem. They derive the dynamic relationship for the \(k\)-barrier coverage performance in terms of the density of mobile sensors, sensing range, sensor mobility, intruder mobility, _etc._ This is done by utilizing the classical kinetic theory of gas molecules in physics for system modeling and analysis. However, to the best of our knowledge, no prior research on the intrusion detection problem in sensor networks considers the intelligence of a mobile intruder that is capable of detecting nearby sensors and attempts to circumvent detected sensors for detection avoidance. In real-life applications, an intruder is usually an intelligent mobile robot with environment learning and detection avoidance capability. This motivates us to propose two intrusion algorithms that mimic the intelligent motion and behaviors of a mobile intruder in terms of detecting and avoiding nearby sensor(s) utilizing artificial intelligence (AI) strategies.