Nonlinear set-theoretic position estimation of cellular phones

Within the existing GSM standard, several measurements are available that can be used for estimating the position of a cellular phone. First, the timing advance (TA) gives an estimate for the distance to the serving base station. Second, the signal strengths (RXLEV) of neighbouring base stations can also be interpreted as distance information. Both TA and RXLEV are subject to measurement errors caused for example by shadowing, reflections, and fast fading. Thus, a nonlinear set-theoretic estimation technique based on pseudo ellipsoids is applied. The uncertainty regions in the original space defined by the measurements are transformed into a hyperspace of higher dimension and described by pseudo ellipsoids. An approximation of the set intersection of the pseudo ellipsoids can be calculated recursively by a linear set-theoretic filter. The resulting pseudo ellipsoid is transformed back into the original space, and the position estimate is calculated as center of gravity of the resulting uncertainty region. The algorithm is evaluated based on the data of an extensive field trial in a rural area. Compared to Cell ID, the accuracy is significantly increased by using TA and RXLEV, reducing the mean error by half.