In recent years, there has been an increasing demand for reliable and objective evaluation of sport specific data. The measurement and analysis of the trajectories of athletes is one possible approach to gain such insights. It allows the assessment of the physical performance and tactical behavior of athletes. Thus, it can yield helpful feedback for athletes, coaches and referees. Furthermore, spectators can be supplied with additional information about the accomplishments of their idols.
Local Positioning Systems (LPS) provide a means for the measurement of athletes' positions and motion trajectories. State-of-the-art systems use time-of-arrival or time-difference-of-arrival measurements of electromagnetic waves. These electromagnetic waves travel between antennae with fixed and known positions and mobile transponders (tags) with unknown and variable positions. Using the timing measurements from several antennae with respect to the mobile transponder, the position of the mobile transponder in the coordinate system of the local positioning system can be determined. When such a mobile transponder is attached to an object or person, the position of this object or person can be determined from the position of the mobile transponder.
Usually, directive antennae are preferred over omnidirectional antennae in order to extend the ranges of the radio coverage areas. Throughout this text, ‘range’ shall mean the maximum distance to the antenna to which the transponder may be located in order to receive electromagnetic waves from said antenna. In addition, ‘coverage area’ shall mean the area on which the transponder must be located to receive electromagnetic waves from said antenna. For the purposes of this text, ‘the transponder is within range of the antenna’ shall mean that the distance between the transponder and the antenna is short enough for the transponder to receive electromagnetic waves from said antenna. Moreover, it is understood that in addition to being within range of the antenna, the transponder needs to be on the effective coverage area of the antenna in order to receive electromagnetic waves from said antenna.
For illustrative purposes only, a radiation pattern of a typical directive antenna is given in FIGS. 1a and 1b. In particular, FIG. 1a shows the horizontal radiation pattern and FIG. 1b shows the vertical pattern. It is to be noted that radiation pattern' refers to the angular dependence of the strength of the electromagnetic waves from the antenna.
Understandably, if the mobile transponder is not within range of said antenna, or within range but not in the coverage area of a directive antenna of the LPS, no timing measurement will be available for said antenna with respect to said transponder. However, in order to allow localization of the transponder, a sufficient number of timing measurements needs to be available. In particular, to obtain a unique 2D position solution, at least three timing measurements are required, and to obtain a unique 3D position solution, at least four timing measurements are required. As a consequence, if the number of available timing measurements is not high enough, the position of the transponder cannot be determined.
Moreover, even if the number of available timing measurements is sufficient to calculate the transponder's position, it is advantageous to increase them in order to improve accuracy.
A solution for reducing the risks that a situation where the position of the transponder cannot be calculated and/or to enhance the calculation accuracy, is to increase the number of antennae in the vicinity of an area of interest on which the transponder is supposed to move. However, adding additional antennae is costly, and the number of antennae a LPS can handle is usually also limited.