Localization based on two-stage treatment for dealing with noisy and biased distance measurements

Abstract

Localization can be performed by trilateration in which the coordinates of a target are calculated by using the coordinates of reference points and the distances between each reference point and the target. Because the distances are measured on the basis of the time-of-flight of various kinds of signals, they contain errors which are the noise and bias. The presence of bias can become a major problem because its magnitude is generally unknown. In this article, we propose an algorithm that combines the Kalman filter (KF) and the least square (LS) algorithm to treat noisy and biased distances measured by chirp spread spectrum ranging defined in IEEE 802.15.4a. By using the KF, we remove the noise in the measured distance; hence, the noise-eliminated distance, which still contains bias, is obtained. The next step consists of the calculation of the target coordinates by using the weighted LS algorithm. This algorithm uses the noise-eliminated distance obtained by using the KF, and the weighting parameters of the algorithm are determined to reduce the effects of bias. To confirm the accuracy of the proposed algorithm, we present the results of indoor localization experiments.