RESUMEN
The Linearized Auto-Localization (LAL) algorithm estimates the position of beacon nodes in Local Positioning Systems (LPSs), using only the distance measurements to a mobile node whose position is also unknown. The LAL algorithm calculates the inter-beacon distances, used for the estimation of the beacons' positions, from the linearized trilateration equations. In this paper we propose a method to estimate the propagation of the errors of the inter-beacon distances obtained with the LAL algorithm, based on a first order Taylor approximation of the equations. Since the method depends on such approximation, a confidence parameter τ is defined to measure the reliability of the estimated error. Field evaluations showed that by applying this information to an improved weighted-based auto-localization algorithm (WLAL), the standard deviation of the inter-beacon distances can be improved by more than 30% on average with respect to the original LAL method.
RESUMEN
A well known problem for precise positioning in real environments is the presence of outliers in the measurement sample. Its importance is even bigger in ultrasound based systems since this technology needs a direct line of sight between emitters and receivers. Standard techniques for outlier detection in range based systems do not usually employ robust algorithms, failing when multiple outliers are present. The direct application of standard robust regression algorithms fails in static positioning (where only the current measurement sample is considered) in real ultrasound based systems mainly due to the limited number of measurements and the geometry effects. This paper presents a new robust algorithm, called RoPEUS, based on MM estimation, that follows a typical two-step strategy: 1) a high breakdown point algorithm to obtain a clean sample, and 2) a refinement algorithm to increase the accuracy of the solution. The main modifications proposed to the standard MM robust algorithm are a built in check of partial solutions in the first step (rejecting bad geometries) and the off-line calculation of the scale of the measurements. The algorithm is tested with real samples obtained with the 3D-LOCUS ultrasound localization system in an ideal environment without obstacles. These measurements are corrupted with typical outlying patterns to numerically evaluate the algorithm performance with respect to the standard parity space algorithm. The algorithm proves to be robust under single or multiple outliers, providing similar accuracy figures in all cases.