Abstract
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.
Highlights
The general implantation of Global Navigation Satellite Systems (GNSS) has triggered the development of new applications based on the user’s position. Their limited use in indoor environments [1] has created the necessity for new positioning systems able to localize in environments where GNSS signals are not available
They show that both algorithms get very similar results, being slightly better for the Parity Space (PS) algorithm in the last case
The lack of robustness of the parity space algorithm is clearly shown when two outliers are present, where the number of non valid estimations is approximately equal to the number of evaluations with two simultaneous erroneous measurements
Summary
The general implantation of Global Navigation Satellite Systems (GNSS) has triggered the development of new applications based on the user’s position. Standard least-squares regression diagnostic methods, such as Parity Space, are affected by two related phenomenons: masking (misidentification of outliers) and swamping (identification of good measurements as outliers) [14] These effects make the use of robust estimators for position calculation more appropriate. These values and their combination are usually referred in GPS bibliography as Geometric Dilution of Precision parameters (GDOP [28]) This name is based on the fact that the Jacobian matrix depends on the existing geometry of the beacons with regard to the user position
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call