On geolocation in ill-conditioned BS-MS layouts

The achievable accuracy for estimating the position of a mobile station (MS) in terms of the Cramer-Rao lower bound (CRLB) has been well studied and accepted. For certain class of layouts of an MS and base stations (BS), termed as ill-conditioned layouts here, the CRLB suggests that the variance of estimation errors is infinitely large. In this paper, we investigate how to overcome this problem in both analytical and algorithmic aspects. The ill-conditioned layouts are classified into two categories: layouts with an insufficient number of BS and those satisfying the condition of collinearity or coplanarity. We investigate estimation schemes and error analysis for each category. Accordingly, a geolocation method with adaptive dimensions is devised. Simulation results confirm the effectiveness of our method.