Best linear unbiased estimator approach for time-of-arrival based localisation

Abstract

A common technique for source localization is to utilize the time-of-arrival (TOA) measurements between the source and several spatially separated sensors. The TOA information defines a set of circular equations from which the source position can be calculated with the knowledge of the sensor positions. Apart from nonlinear optimization, least squares calibration (LSC) and linear least squares (LLS) are two computationally simple positioning alternatives which reorganize the circular equations into a unique and non-unique set of linear equations, respectively. As the LSC and LLS algorithms employ standard least squares (LS), an obvious improvement is to utilize weighted LS estimation. In this paper, it is proved that the best linear unbiased estimator (BLUE) version of the LLS algorithm will give identical estimation performance as long as the linear equations correspond to the independent set. The equivalence of the BLUE-LLS approach and the BLUE variant of the LSC method is analyzed. Simulation results are also included to show the comparative performance of the BLUE-LSC, BLUE-LLS, LSC, LLS and constrained weighted LSC methods with Cramér-Rao lower bound.

Source localization using block-based Wiener filter

“…Section 2 deals with the details of the proposed algorithm, which adopts a block-based Wiener filter. Section 3 discusses the experimental results in order to evaluate the estimation performance of the block-based Wiener filter algorithm by comparing it with the BLUE-LSC [5], MDS [6], SRLS [7]. Section 4 presents conclusions and directions for future work.…”

Mitigación de la Condición NLOS para Sistemas de Posicionamiento de Suscriptor Móvil usando Ponderación de Medidas y Restricciones Geométricas

“…Furthermore, an iterative process may be performed in order to minimize the function cost in (8) and achieve the maximum accuracy, and consequently the Best Linear Unbiased Estimator (BLUE) algorithm, but in general a twostep LS algorithm is adequate. Alternative formulations for the positioning problem are possible, but results in terms of accuracy are not important [22].…”

Space-time diversity for NLOS mitigation in TDOA-based positioning systems

“…Furthermore, an iterative process may be performed in order to minimize the function cost in (6) and achieve the maximum accuracy, and consequently the Best Linear Unbiased Estimator (BLUE) algorithm, but in general a two-step LS algorithm is adequate. Alternative formulations for the positioning problem are possible, but improvement in terms of accuracy is not important [8].…”

“…These expressions were derived in [10] and they will help us to construct the noise correlation matrix C n in (8), and the weighting matrix required in (7) to achieve the positioning.…”