The Optimizing Selection And Error Analysis Of Position Reference Nodes In Smart Space

Context awareness can provide the user with important context information in smart space, which is about 80 percent mainly related to position. Consequently the problem of position is playing an important role in context awareness. Many behaviors of the device is related to its position, for example, track the user’s position in real-time, turning on the light near the user automatically, or transferring the phone to the nearest user, and so on. All the application should be capable to determine the user’s position in a room, and the relative position with other devices. To accurately obtain the position information is the key to finish the positioning service, therefore how to simply, efficiently, accurately acquire the user’s position information, and being able to provide the positioning service to user, is one of the basis problems in smart space.In the process of the positioning of the unknown node in the smart space, time error and relative position of reference nodes are the main causes of affecting the unknown nodes’ position error. With regards to the position error caused by the position of reference node, the position of unknown node in the smart space is decided by reference to several position reference nodes. Therefore the problem that how to choose the most optimum reference node among all the reference nodes in order to reduce the position error to the great extend becomes the main topic of this paper.In the positioning service of two dimensional space, two arithmetic operators theorems on two dimensional space are put forward on the basis of non-existence of position error. Arithmetic operators theorems provide a fast way of computing the position of unknown node. In the existence of position error in the process of positioning, reference nodes optimizing selection theorem in two dimensional space is proposed on the basis of analyzing the position error areas. This theorem shows that optimization selection of reference nodes will minimize the position error in the process of indoor positioning. Meanwhile this theorem builds up theoretical foundation for the layout and selection of reference nodes in indoor environment. Based on this, the research on the problem of position error limit caused by positioning the unknown nodes several times is conducted. Correspondingly the position error limit theorem is put forward, which reflects the fact that the position error can not be reduced gradually to zero when the positioning of unknown nodes involves limitless reference nodes, instead the position error will be reduced to a constant quantity. On the basis of reference nodes optimizing selection theorem and the improvement of the traditional positioning algorithm, optimization selection algorithm of reference nodes (OSRN) is produced. This algorithm is based on the relationship of the position of reference nodes and the position of unknown node. By the way of selecting optimum reference nodes in the process of calculating the unknown nodes’position, the more accurate position information can be delivered and the real-time sensitivity can be fulfilled. As a result, the requirements of positioning service from mobile users in the smart space are satisfied. All the above mentioned theorems are the basis for the mobile devices’specially reducing the position error caused by reference nodes in the process of positioning in two dimensional space.It is impossible to avoid any error in the process of positioning. On the basis of the research of positioning problem in three dimensional space, Arithmetic operators theorems are brought forward in three dimensional space, which are the theoretical foundation for the layout of position reference nodes. In the existence of position error, the study on the position error in the process of three dimensional space is conducted. According to the study results, the two theorems are produced:the first theorem of space reference nodes optimizing selection (SOSRN1) and the second theorem of space reference nodes optimizing selection (SOSRN2). These two theorems, in the respect of theory, prove that the position error is the least when the unknown nodes and position reference nodes are in certain layout in three dimensional space. Based on this, the research on the error areas caused by positioning the unknown codes several times is made and the fact is discovered that the position error gradually decreases with the number of position units increases, but the position error can not decrease unlimitedly while it will reach a constant quantity. In the smart space, due to limited resources of a ubiquitous device, the device is usually facing the application with real-time sensitivity. The traditional positioning algorithm can not be implemented for a ubiquitous device with limited resources. Meanwhile, it can not satisfy the time constrains. Therefore based on the SOSRN theorem, the position reference nodes algorithm is proposed. The space position reference nodes optimization selection (SOSRN) algorithm can promise more accurate information with positioning of unknown nodes and meet the requirement of real-time, which will make the requirements from positioning service fulfilled.Concerning the position error caused by the position reference nodes, it is mainly reduced by the optimization selection of position reference nodes. According to the results of analysing the position error caused by the relative position of reference nodes, the conclusion is made that the accuracy of position can be greatly improved by the adoption of reference nodes optimizing selection and the position error can be reduced to the least through only several times positioning. On the basis of this, the fast reference nodes optimization selection (FOSRN) algorithm and the fast space reference nodes optimization selection (FSOSRN) algorithm are brought forward. FOSRN and FSOSRN can guarantee the position accuracy and meet the requirement of real-time simultaneously, the two algorithms are especially suitable in the smart space positioning with the existence of many reference nodes.The simulation is used to verify OSRN and SOSRN algorithm in this paper. After the analysis of the data acquired and the comparison with the traditional algorithm, the conclusion is drawn that OSRN and SOSRN algorithm can meet the requirement of real-time positioning of unknown nodes in the environment with limited resources, and make position error less than the traditional algorithm, therefore the algorithm can effectively solve the positioning problem for mobile users in the smart space.