Cramer-Rao Bound Analysis of Quantized RSSI Based Localization in Wireless Sensor Networks Hongchi Shi, Xiaoli Li, and Yi Shang Department of Computer Science University of Missouri-Columbia Columbia, MO 65211, USA shih@missouri.edu Dianfu Ma College of Computer Science & Engineering Beihang University Beijing 100083, PRC Abstract Localizing sensor nodes in a distributed system of wire- less sensors is an essential process for self-organizing wire- less sensor networks. Localization is a fundamental prob- lem in wireless sensor networks, and the behavior of lo- calization has not been thoroughly studied. In this paper, we formulate the quantized received signal strength indica- tor based localization as a parameter estimation problem and derive the Cramer-Rao lower bound for the localiza- tion problem. We study the effect of quantization level and network configuration parameters on the lower bound of lo- calization error variance and understand the relationship between network configuration and localization accuracy. 1. Introduction Distributed systems with hundreds and even thou- sands of very small, battery-powered, and wirelessly- connected sensor and actuator nodes are becoming a real- ity [2].Wireless sensor networks are tightly coupled with the physical world, which is an important factor in the tasks they perform [14]. Typical tasks for wireless sen- sor networks are to send a message to a node at a given location, to retrieve sensor data from nodes in a given re- gion, and to find nodes with sensor data in a given range. Most of these tasks require knowing the posi- tions of the nodes. Sensor network localization has been a fundamental is- sue of wireless sensor networks and an area of active re- search in recent years [14]. Localization methods usually follow a three-phase localization model including distance estimation, trilateration or triangulation, and refinement [5]. In the first phase, each sensor node first uses its com- munication capability to obtain some measurements such as received signal strength indicator (RSSI) to its neigh- bors to estimate the single-hop distances and then estimates multiple-hop distances to anchor nodes using methods such as a distributed shortest-path distance algorithm. In the sec- ond phase, each sensor node uses methods like triangulation to estimate its location using distances to three or more an- chor nodes. In the third phase, each sensor node fine-tunes its location according to the constraints on the distances to its neighbors. There are range-free and range-based sensor network lo- calization algorithms [8, 13, 16]. In the range-free approach, the algorithms do not need range hardware support and are immune to range measurement errors while providing less accurate localization results. In the range-based approach, the algorithms require more sophisticated range hardware support while providing more accurate localization results than the range-free algorithms. Much less work has been done on searching and utilizing other range-related informa- tion for sensor network localization. In a point-in-triangle localization scheme [4], RSSI values are used for compar- ing distances. RSSI, measuring the RF energy received, is a type of range-related information and is supported by sen- sor node hardware such as the MOTE [19]. For the lo- calization purpose, the information provided by RSSI or similar type of measurement is less than range but more than a connectivity-only hop count, and it can be used to improve the accuracy of any range-free localization algo- rithms [7, 9]. The behavior of localization systems, which can be af- fected by uncertainties in the network operating environ- ment and the sensor node hardware and software, has not been thoroughly investigated [14]. The uncertainties can usually be statistically modelled [17], which is the basis that we can analyze the localization errors using the estima- tion theory [1, 11, 18]. Several researchers have analyzed errors of localization in sensor networks using distance in- formation added with simple Gaussian noise [6, 15], and some other researchers have analyzed errors of localization in sensor networks using quantized RSSI values with sim- ple Gaussian noise added [10]. Proceedings of the 2005 11th International Conference on Parallel and Distributed Systems (ICPADS'05) 0-7695-2281-5/05 $20.00 © 2005 IEEE