Algorithm Which Approached in Outdoor position in GSM Technology using Mathematical Definations : OBJECTIVES Understand the major positioning methods and procedures for use in positioning mobile terminals in GSM networks Understand the location procedures involved in positioning the GSM mobile station and the use of location information for applications Identify the limitations of each positioning technology and use the proposed method to calculate the position of the mobile. Writing the matlab code for the Positioning and understanding the functionality of the program. Finally, conclude the proposed method is providing better solution compared with other methods. Preface This report has been written in December 2003 in a four–week project at the IT University of Copenhagen under the supervision of Mr. John Sørensen, Head of MMT Studies and Mr. Zoltan safar, Assistant professor. All the world is brought together with the word Communication. There has been a rapid change in the world, when the communication started between people from telephones to the present world with Mobile phones. This Mobile phones has changed the daily lives. Now the increased demand of Mobile phones had created,´the FCC requirement of operators of mobile communication need to locate the mobile callers for emergency assistance. This lead the operators to examine the cellular positioning techniques. Features of GSM signals relevant to positioning are analyzed and the results are achieved by the authors positioning trials (annexure 1). Acknowledgements We would like to thank the Board of studies for giving us this opportunity to prove ourselves in doing this project successfully. We also extend our sincere thanks to our project supervisor Mr. John Sørensen, Head of MMT Studies and Mr.Zoltan safar for his valuable Suggestions during the project period. With his perfect scheduling of tasks, we were able to complete the project successfully in time. Review of OUTDOOR POSITIONING METHODS The positioning method system are the methods which calculate the position of the mobile station depending on the location whether it is far or near. We can propose 2 method based on the location 1. self – positioning 2. remote positioning in self positioning methods the positioning receiver makes its signal measurements from the sensors which are used to determine its self position in remote positioning methods the mobile station is the transmitter and the sensors are the receiver. In this the calculation are make to calculate the pasotion of the mobile station. It is called remote positioning system because the mobile station is located remote to the sensors Positioning methods We find various techniques to find the position of system. For all this positioning methods, we require the basic measurements between sensors and the mobile, which will be helpful to calculate the position of the mobile system given above.The basic measurements are (propagation time, Time difference of Arrival(TDOA), angle of arrival(AOA),and Carrier phase). In this positioning techniques it uses various mathematical algorithms to get the accurate position of the mobile station. The proposed mathematical algorithm uses large number of sensors, thus making maximum number of approximations to calculate the mobile positon