An improved 3-dimensional mobile location method using volume measurements of tetrahedron

Since the deployment of base stations (BS) is far from optimum in 3D space, i.e., the length of vertical baseline between BS is relatively smaller than that of plane baseline, the geometric dilution of precision of the altitude estimate is larger than that of plane location. This paper considers the problem of 3D range location and attempt to improve the altitude estimate. We firstly use a volume formula of tetrahedron to transform the range measurements to volume measurements, then a new pseudo-linear solution is proposed based on the linear relationship between the rectangular and volume coordinates. Theory analysis and numerical examples are included to show the improved accuracy of altitude estimate of mobile location. Finally, an improved estimate of 3D mobile location is given by solving a set of augmented linear equations.