Method and computer system for obtaining weighted geometric dilution of precision closed form

摘要

A method utilized in a wireless communication system having a mobile device and a plurality of base stations includes obtaining a geometric matrix according to a plurality of relative distances between the mobile device and the plurality of base stations, obtaining a weighted matrix according to the mobile device and the plurality of base stations, obtaining a weighted geometric dilution of precision according to the weighted matrix and the geometric matrix, so as to obtain a weighted geometric dilution of precision closed form, and choosing a plurality of selected base stations from the plurality of base stations according to the weighted geometric dilution of precision closed form to position the mobile device.

主权项

1. A computer system comprising:
a central processing unit; a detection module coupled to the central processing unit for detecting a plurality of base stations (i=1−n) neighboring the computer system; and a storage device coupled to the central processing unit for storing a programming code, and the programming code is utilized to instruct the central processing unit to process a method for a wireless communication system comprising a mobile device and the plurality of base stations, the method comprising: obtaining a geometric matrix asH=[e11e12e131e21e22e231⋮⋮⋮⋮en⁢⁢1en⁢⁢2en⁢⁢31]according to a plurality of relative distances between the mobile device and the plurality of base stations, whereinei⁢⁢1=x^-Xir^i,ei⁢⁢2=y^-Yir^i,ei⁢⁢3=z^-Zir^i,(Xi,Yi,Zi)represents a position coordinate of the ith base station, ({circumflex over (x)},ŷ,{circumflex over (z)}) is utilized as a simplified position coordinate, and ei12+ei22+ei32=1 is satisfied;
obtaining a weighted matrix asW=[1/σ12000001/σ22000001/σ3200000⋱000001/σn2]=[k100000k200000k300000⋱00000kn]according to the mobile device and the plurality of base stations, wherein σi represents a covariance related to a corresponding one of the plurality of base stations, and ki represents a reciprocal value of each corresponding covariance;
obtaining a weighted geometric dilution of precision (WGDOP) as WGDOP=√{square root over (tr(HTWH)−1)} according to the weighted matrix and the geometric matrix, so as to obtain a WGDOP closed form; and choosing a plurality of selected base stations from the plurality of base stations according to the WGDOP closed form, so as to position the mobile device.