A new procedure for race analysis in swimming based on individual distance measurements

biomecanica de la natación

Comparison of starts and turns of national and regional level swimmers by individualized-distance measurements

The aim of this study was to compare the race characteristics of the start and turn segments of national and regional level swimmers. In the study, 100 and 200-m events were analysed during the finals session of the Open Comunidad de Madrid (Spain) tournament. The “individualized-distance” method with two-dimensional direct linear transformation algorithm was used to perform race analyses. National level swimmers obtained faster velocities in all race segments and stroke comparisons,although significant inter-level differences in start velocity were only obtained in half (8 out of 16) of the analysed events. Higher level swimmers also travelled for longer start and turn distances but only in the race segments where the gain of speed was high. This was observed in the turn segments, in the backstroke and butterfly strokes and during the 200-m breaststroke event, but not in any of the freestyle events. Time improvements due to the appropriate extension of the underwater subsections appeared to be critical for the end race result and should be carefully evaluated by the “individualized-distance” method.

Auto-localization algorithm for local positioning systems

This paper studies the problem of determining the position of beacon nodes in Local Positioning Systems (LPSs), for which there are no inter-beacon distance measurements available and neither the mobile node nor any of the stationary nodes have positioning or odometry information. The common solution is implemented using a mobile node capable of measuring its distance to the stationary beacon nodes within a sensing radius. Many authors have implemented heuristic methods based on optimization algorithms to solve the problem. However, such methods require a good initial estimation of the node positions in order to find the correct solution. In this paper we present a new method to calculate the inter-beacon distances, and hence the beacons positions, based in the linearization of the trilateration equations into a closed-form solution which does not require any approximate initial estimation. The simulations and field evaluations show a good estimation of the beacon node positions.

Error estimation for the linearized auto-localization algorithm

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.