Analysis of TOA localization with heteroscedastic noises

This paper focuses on the problem of source localization using time-of-arrival (TOA) measurements. Differently from the existing studies assuming that TOA measurement noises are independent and identically distributed, we deal with more practical TOA measurements suffering from heteroscedastic noises due to different physical distances between a source and multiple sensors. Consequently, the variance of the heteroscedastic noise is distance-dependent. From the information point of view, the distance-dependent variance contains certain information about the source location, and as such helps to improve localization accuracy. In this paper, we theoretically analyze the impact of the heteroscedastic noises on localization accuracy, and conclude that using the extra information in the distance-dependent variance does not significantly improve the estimation accuracy under low noise levels. Furthermore, considering the fact that TOA measurements are normally accurate, we propose a lightweight localization scheme based on the existing two-stage maximum likelihood (TSML) method. Finally, a simulation analysis confirms our theoretical study, and shows that the accuracy of the proposed localization scheme is comparable to the Cramer-Rao lower bound (CRLB) given moderate TOA measurement noises.