Design And Implementation Of Multidimensional Scaling-based Indoor Positioning System

With the development of the Internet of things,getting users' location in time has become the key for many applications.However,good positioning results in the indoor environment could not be obtained by the Global Positioning System(GPS).Therefore,many scholars have devoted themselves to the study of indoor positioning.Multidimensional Scaling(MDS)algorithm is a kind of data analysis technology,which is used to transform the relationship between data into the distance between nodes,and it is easy to be expanded and implemented.Therefore,this thesis studies indoor positioning system based on MDS.The relative distribution map is output by MDS,so coordinate transformation of the target node is required.MDS Householder algorithm firstly takes three anchor nodes as a group to obtain all possible coordinate transformation parameter,and then the optimal parameter combination is selected to transform the target node.All possible node combinations in this algorithm are exhausted,so positioning time will decrease rapidly with the increase of the number of anchor nodes.In this thesis,all anchor nodes are utilized to obtain coordinate transformation parameters.First simulation and formula derivation are used to prove that the output node graph of MDS may have a mirror image relationship with the actual graph but no stretching relationship,and then the stretching factor in the two-dimensional space coordinate transformation model is optimized for flip factor(different value represents whether roll),finally the new coordinate transformation model and Particle Swarm Optimization(PSO)were combined to obtain the coordinate transformation parameters.The improved algorithm takes the sum of squares of distance difference before and after coordinate transformation of anchor nodes as fitness function to measure the matching degree.The four coordinate transformation parameters with the minimum fitness function are used for coordinate transformation.In addition,in order to avoid the calculation of different inversion matrices and further improve the efficiency of coordinate transformation,this thesis fixed the coordinate inversion mode at the Xaxis.The improved algorithm can improve the precision and efficiency of coordinate transformation.The performance of the improved MDS algorithm is verified by computer simulation and actual test.The real-time performance of the improved algorithm is improved and is less affected by the number of anchor nodes.On the core i5 processor + Kingston 8G memory hardware platform,when the number of anchor nodes is less than 10,the average positioning time is less than 100 milliseconds.