Least Squares Algorithms for Time-of-Arrival-Based Mobile Location

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

“…For simplicity, we assume line-of-sight propagation between the source and all sensors such that each n i is a zero-mean white process with known variance σ 2 i [14].…”

“…It is worthy to mention that the same weighting matrix of C −1 p has been proposed in [14], which can be considered as a constrained weighted least squares calibration (CWLSC) algorithm with utilizing the constraint of x 2 + y 2 = R. We expect that the BLUE-LSC algorithm is inferior to the CWLSC scheme as the parameter relationship in θ is not exploited.…”

“…Our major findings include (i) All BLUE realizations of the LLS algorithm have identical estimation performance as long as the (M − 1) linear equations correspond to the independent set [10]; (ii) The covariance matrices of the position estimates in the BLUE-LLS scheme with the independent set and the BLUE version of the LSC algorithm are identical. By comparing with Cramér-Rao lower bound (CRLB) for TOA-based localization [14], it is then shown that they are suboptimal estimators, and this result is different from the iterative BLUE estimator of [13] which gives maximum likelihood estimation performance; and (iii) Among the BLUE-LLS and BLUE-LSC algorithms, the latter is preferable as it involves lower computational complexity. Note that the research results can also be applied to source localization systems with received signal strength [2] measurements as they employ the same trilateration concept where the propagation path losses from the source to the sensors are measured 2 This paper is a postprint of a paper submitted to and accepted for publication in IET -Signal Processing and is subject to Institution of Engineering and Technology Copyright.…”

“…Furthermore, their suboptimality and computational requirement will be discussed. Simulation results are included in Section 3 to evaluate the estimation performance of the BLUE-LSC and BLUE-LLS algorithms by comparing with the LSC, LLS and constrained weighted LSC [14] methods as well as verify our theoretical development. Finally, conclusions are drawn in Section 4.…”

The Application of Ray-Tracing to Mobile Localization Using the Direction of Arrival and Received Signal Strength in Multipath Indoor Environments

“…Many proposed localization methods and algorithms were based on the computation of the time of arrival (TOA) [5][6][7], time differences of arrival (TDOA) [8], direction of arrival (DOA) [9][10][11] and the received signal strength (RSS) [12,13]. Conventional methods based on these four measurements increase in error with multipath propagation because they require LoS conditions between the access points and the mobile stations.…”