Multilateration localization in the presence of anchor location uncertainties

Multilateration is a fundamental localization technique for wireless sensor network applications. Classical multilateration techniques typically assume that the anchor locations are known and error free, an assumption that is always not valid in practice. Although the popular total least squares (TLS) method is able to take into account such errors in general, it requires that the noise components in the formulated data matrices be identically, independently distributed. In multilateration localization, however, it can be shown that the noise components in the formulated equations are algebraically related. In this paper, we formulate multilateration for sensor localization based on the use of the constrained total least squares (CTLS) method. By assuming that distance measurement errors are relatively small and can be neglected, we show that the CTLS solution leads to a weighted least squares problem. Computer simulations are used to demonstrate the effectiveness and performance of the proposed technique.