Patent Publication Number: US-7719469-B2

Title: Device and method for position measurement by means of linear doppler shifts generated

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a device and to a method for providing information about an object location by observing a Doppler frequency response regarding the object location such as may be employed, for example, for determining the positions of game devices, in particular balls. 
   2. Description of Prior Art 
   For quite some time, various interest groups have wished to study and understand the sequence of movements of moving objects and/or persons, which requires an exact indication of the object&#39;s position both in space and time. What is of particular interest here are, among other things, game balls, in particular in commercialized types of sport, such as footballs, or soccer balls, which are highly accelerated in three-dimensional space, as well as tennis or golf balls. The question of who was the last to touch the object of the game, how it was hit, and in which direction it was accelerated further may be decisive for the outcome of the game, depending on the type of game. 
   Game devices that are used in high-performance sports, such as tennis balls, golf balls, footballs and the like, nowadays can be accelerated to extremely high speeds, so that a detection of the object during the movement requires highly sophisticated technology. The technical means employed so far—mainly cameras—either completely fail to meet the requirements set forth above, or meet them only to an insufficient degree. Also, hitherto known methods for position finding by means of various transmitter and receiver combinations still leave a large error margin with regard to the spatial resolution of the position indication, with regard to the ease of use of the transmitter/receiver components required, and above all with regard to evaluating the data obtained by means of the transmitter/receiver system, so that it is not yet possible, or at least requires a large amount of effort, to evaluate the results obtained from this data as fast as possible. 
   It is not only in the field of commercial sports, where movable game devices may be employed, but it is also in the personal field that users have become more and more used to electronic devices indicating various pieces of information to give a user feedback as to how he/she has affected an object, or to provide him/her with information about whether, for example, a game device has crossed a pitch line. 
   Current statistics methods in commercial applications, such as of the German first football division (Bundesliga), work with recording relatively simple statistics, such as the percentage of ball contacts of a team or the number of corners, free kicks or fouls. 
   On the other hand, there have been means, for example in tennis, where there is a very plannable, clearly arranged environment with only two players, which measure, for example, the speed of the tennis ball at the serve, such that a viewer is in a position to assess whether a serve was “hard” or “soft”. 
   What is problematic about such speed measurements which may occur by optical methods is the fact that they do not function within an environment where there is a muddle of players, such as on a football pitch where there are not only two persons being active, but 22 persons, who, in addition, are not positioned in more or less the same place but may form any constellation on the pitch. On the other hand, particularly in football, it is interesting, both for the feedback of the players in training and for the viewers to know, for example, how fast a ball is flying or whether there is a goal situation or an offside situation at hand. 
   Thus, a multiplicity of tasks, for example locating a ball in a football match, presuppose knowledge of positions of objects. In a football match, for example, one of the most controversial topics is whether or not, in critical situations, the ball has crossed the goal line. For this purpose, it is necessary that the ball&#39;s position at the goal line can be measured with an accuracy of about +/−1.5 cm. 
   There are numerous localization methods based, for example, on optical two-dimensional or three-dimensional sensor having an evaluation system, an exploitation of the known radar principle or of a principle of radio localization. 
   One principle of radio localization is the localization of objects by electromagnetic wave propagation. For example, a receiver is integrated into an object to be localized or mounted to an object to be localized, the receiver being able to send data to a central transmitting/receiving device upon request. Thereafter, a position of the object is calculated from signal delay times and/or from differences between at least two signals received at different antennas. 
   Currently available localization methods based on optical 2D or 3D sensors having an evaluation system, or based on the use of conventional radio localization methods, entail high investment and maintenance cost, sensitivity toward environmental conditions and a large outlay in terms of adapting the evaluation algorithms. To achieve fine resolution of a position determination, systems using conventional radio localization are not suitable, since with a small geometrical expansion, differences of various signal delay times are hardly measurable any more. The requirements placed upon system for localizing objects thus are not met, or are met only to an insufficient degree, with regard to economy, robustness, clock time and object independence, for exact position determination, for example, within a range of a few centimeters. 
   SUMMARY OF THE INVENTION 
   The object of the present invention is thus to provide an improved but, at the same time, low-expense concept for localizing objects. 
   In accordance with a first aspect, the invention provides a device for providing information about an object location within a location determination area wherein the object is positioned, it being possible to associate a first coordinate with the object location, the device including: 
   a sequential transmitter and/or receiver having at least one antenna for sequentially transmitting or receiving periodic signals having a carrier frequency at various locations; and 
   a location determiner for determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting or receiving the periodic signal at the zero crossing in relation to the object location. 
   In accordance with a second aspect, the invention provides a movable object for position determination within a location determination area, including: 
   a transmitter for transmitting periodic signals having a carrier frequency. 
   In accordance with a third aspect, the invention provides a movable object for position determination in a location determination area, including: 
   a receiver for receiving periodic signals from a sequential transmitter having at least one antenna for sequentially transmitting the periodic signals having a carrier frequency at various locations; and 
   a location determiner for determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting the periodic signal at the zero crossing in relation to the object location. 
   In accordance with a fourth aspect, the invention provides a position determination system, including: 
   a device for providing information about an object location within a location determination area wherein the object is positioned, it being possible to associate a first coordinate with the object location, including 
   a sequential receiver having at least one antenna for sequentially receiving periodic signals having a carrier frequency at various locations, 
   a location determiner for determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when receiving the periodic signal at the zero crossing in relation to the object location; and
 
an object, the position of which may be determined, having
 
a transmitter for transmitting a periodic signal having the carrier frequency.
 
   In accordance with a fifth aspect, the invention provides a position determination system, including: 
   device for providing information about an object location within a location determination area wherein the object is positioned, it being possible to associate a first coordinate with the object location, including 
   a sequential transmitter having at least one antenna for sequentially transmitting periodic signals having a carrier frequency at various locations; and 
   a location determiner for determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when receiving the periodic signal at the zero crossing in relation to the object location; and
 
an object, the position of which may be determined, having
 
a receiver for receiving periodic signals from the sequential transmitter having the at least one antenna for sequentially transmitting periodic signals having the carrier frequency at various locations,
 
a location determiner for determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting the periodic signal at the zero crossing in relation to the object location.
 
   In accordance with a sixth aspect, the invention provides a method for providing information about an object location within a location determination area wherein the object is positioned, it being possible to associate a first coordinate with the object location, the method including the steps of: 
   sequentially transmitting or receiving periodic signals having a carrier frequency at various locations using at least one antenna; and 
   determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting or receiving the periodic signal at the zero crossing in relation to the object location. 
   In accordance with a seventh aspect, the invention provides a position determination method including the steps of: 
   transmitting a periodic signal having a carrier frequency; 
   sequentially receiving the periodic signal having the carrier frequency at various locations using at least one antenna; and 
   determining a first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when receiving the periodic signal at the zero crossing in relation to the object location. 
   In accordance with an eighth aspect, the invention provides a position determination method including the steps of: 
   sequentially transmitting a periodic signal having the carrier frequency at various locations using at least one antenna; 
   receiving the periodic signal having the carrier frequency; and 
   determining a first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting the periodic signal at the zero crossing in relation to the object location. 
   In accordance with a ninth aspect, the invention provides a computer program having a program code for performing the method for providing information about an object location within a location determination area wherein the object is positioned, it being possible to associate a first coordinate with the object location, the method including the steps of:
         sequentially transmitting or receiving periodic signals having a carrier frequency at various locations using at least one antenna; and   determining the first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting or receiving the periodic signal at the zero crossing in relation to the object location,
 
when the computer program runs on a computer or a microcontroller.
       

   In accordance with a tenth aspect, the invention provides a computer program having a program code for performing the position determination method including the steps of:
         transmitting a periodic signal having a carrier frequency;   sequentially receiving the periodic signal having the carrier frequency at various locations using at least one antenna; and   determining a first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when receiving the periodic signal at the zero crossing in relation to the object location,
 
when the computer program runs on a computer or a microcontroller.
       

   In accordance with an eleventh aspect, the invention provides a computer program having a program code for performing the position determination method including the steps of:
         sequentially transmitting a periodic signal having the carrier frequency at various locations using at least one antenna;   receiving the periodic signal having the carrier frequency; and   determining a first coordinate of the object location on the basis of a zero crossing of a Doppler frequency response which may be associated with the first coordinate of the object location, the first coordinate of the object location corresponding to a coordinate of that location of the at least one antenna which it has when transmitting the periodic signal at the zero crossing in relation to the object location,
 
when the computer program runs on a computer or a microcontroller.
       

   The present invention is based on the findings that an exact and low-effort determination of a position of an object may be achieved when Doppler frequency shifts of the periodic signal are generated using at least one antenna for sequential transmission or reception of periodic signals having a carrier frequency at different locations, in relation to an object location, and when a coordinate of the object location is determined on the basis of a zero crossing of the Doppler frequency shifts, it being possible to associate the zero crossing with the coordinate of the object location. The coordinate of the object location corresponds to a coordinate of that location of the at least one antenna which it has when transmitting or receiving the periodic signal at the zero crossing of the Doppler frequency shifts in relation to the object location. 
   In accordance with the invention, by means of a linear movement of an antenna or by means of a simulated linear movement by a plurality of antennas and by transmitting and/or receiving a periodic signal to or from the object whose location is to be determined, a Doppler frequency response with regard to the object location is achieved. 
   In accordance with an embodiment of the present invention, the object whose position is to be determined emits a periodic signal having a carrier frequency f c . Along the location determination area, there is positioned, for example, a linear antenna array having a plurality of antennas, the number of antennas co-determining a location resolution area in relation to the location determination area and/or their mutual distances. For simulating an antenna movement, each antenna of the plurality of antennas is sequentially operated as a receive antenna, in accordance with the invention. The simulated antenna movement direction extends along a line tangentially to a circle around the location of the object. Positive Doppler frequencies arise when a radial component of the speed vector {right arrow over (v)} does not disappear, i.e. a projection of speed vector {right arrow over (v)} to the connecting line between the object location and the location of that antenna which is being operated as the receive antenna. Due to the fact that a different antenna, respectively, of the plurality of antennas is operated as the receive antenna in a sequential manner, an angle between the speed vector {right arrow over (v)} of the simulated antenna movement and the location connecting line between the object location and the location of that antenna which is currently acting as the receive antenna will change. Thus, the magnitude and the direction of the projection of speed vector {right arrow over (v)} to the location connecting line will also change. Thus, one will obtain a time curve of Doppler frequencies which will exhibit a zero crossing precisely when the location connecting line is perpendicular, or at least approximately perpendicular, to the speed vector v. Since the coordinates of the individual antennas of the plurality of antennas are known, the zero crossing of the Doppler frequency response may thus be associated with a coordinate of the object location. This coordinate may be derived from the coordinate of that antenna which during the reception of the periodic signal sees no, or approximately no Doppler frequency. 
   If a sufficient number of antennas are used in relation to the location determination area, so that distances between the antennas are small, a resolution of an inventive location determination system may be increased. If, for example, the plurality of antennas are arranged in the form of a linear antenna array in parallel with a touch line of a football pitch in a football match, the ball movements, for example, may be tracked throughout the match in the form of the ball height. Thus, decisions may be made easier for a referee, such as decisions about corner kicks, goal decisions or offside decisions. 
   In accordance with a further embodiment of the present invention, a second coordinate of the object to be localized may be determined, for example, in that one observes the inclination of the temporal frequency response in the zero crossing of the Doppler frequency response. If the object to be localized is positioned, for example, near the line of motion of the at least one antenna, or of the antenna array, a inclination of the Doppler frequency response will be considerably steeper in the area of the zero crossing than if the object is spaced further apart from the motion axis of the at least one antenna, or of the antenna array. 
   Thus, with the inventive concept, a first coordinate of an object to be localized may be determined in that the zero crossing of the Doppler frequency response is determined, and a second coordinate of the object to be localized may be determined in that one observes the inclination of the Doppler frequency response in the zero crossing. 
   In accordance with further embodiments of the present invention, an increased level of reliability of the inventive concept may be achieved in that the inventive location determination system is constructed in a redundant manner, for example. This means that, for example, not only one antenna array is arranged in parallel with a first touch line of a pitch, but that, in addition, a second antenna array is arranged in parallel with a second touch line. In addition, further antenna arrays may be mounted in parallel with the two bylines, for example. Due to the fact that, thus, four values are determined for one ball position, the level of reliability of the location determination system may be considerably increased. 
   In accordance with further embodiments of the present invention, the at least one antenna, or the plurality of antennas, may also be used to sequentially transmit periodic signals having a carrier frequency f c  to various locations. With these embodiments, the object to be localized will have a respective receiver and the location determination means for determining the coordinates of the object location arranged therein, on the basis of the zero crossing of the Doppler frequency response. Such a scenario, where the location determination takes place within the object to be localized is feasible, for example, when an energy supply of the object to be localized is uncritical. 
   Thus, the inventive concept provides the possibility of determining the position of an object, and the possibility of determining a movement of the object on the basis of associating a zero crossing of a Doppler frequency response with a first coordinate of the object location. 
   Embodiments of the present invention have the advantage that a determination of the position of an object, in particular of a movable object, such as a game device, may be effected without any intervention into the activity of a ball game. 
   A further advantage of the present invention is that the position determination may be realized at low expense. 
   There is no necessity of any complicated evaluation algorithms, nor of any high-effort measures for synchronizing transmit and receive units. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     These and other objects and features of the present invention will become clear from the following description taken in conjunction with the accompanying drawing, in which: 
       FIG. 1  shows a schematic block diagram of a device for providing information about an object location in accordance with an embodiment of the present invention; 
       FIG. 2  shows a schematic representation of an antenna movement and/or a simulated antenna movement along a location determination area for generating a Doppler frequency response in accordance with an embodiment of the present invention; 
       FIG. 3  shows a schematic representation of the wiring of an antenna array for generating a simulated antenna movement in accordance with an embodiment of the present invention; 
       FIG. 4  shows a representation of various Doppler frequency responses for different positions of the object to be localized in the location determination area, in accordance with an embodiment of the present invention; and 
       FIG. 5  is a schematic representation of a system for determining the position of a football on a football pitch, in accordance with an embodiment of the present invention. 
   

   DESCRIPTION OF PREFERRED EMBODIMENTS 
   With regard to the following description, one should note that in the various embodiments, functional elements which are identical or have identical actions exhibit identical reference numerals, and that the descriptions of these functional elements are thus interchangeable within the various embodiments presented below. 
     FIG. 1  shows a schematic block diagram of a device  100  for providing information about an object location in a location determination area having a means  110  with at least one antenna  120  and a location determination means  130 . Means  110  is coupled to means  130 . 
   Means  110  having the at least one antenna  120  serves to sequentially transmit or receive periodic signals having a carrier frequency f c  at various locations to generate a Doppler frequency response. Sequential transmission or reception at various locations may be achieved in that, in accordance with an embodiment of the present invention, an antenna is physically moved, for example, from one location to another by a sledge on a rail. 
   In further preferred embodiments of the present invention, an antenna movement, and thus a Doppler frequency response, is simulated in that means  110  comprises a plurality of antennas, for example a linear antenna array, and in that the individual antennas of the plurality of antennas are operated sequentially as transmit or receive antennas, respectively. This configuration offers the advantage that any mechanical stress due to physical motion may be reduced. 
   The location determination means  130  serves to determine a first coordinate of the object location based on a zero crossing of the Doppler frequency response, it being possible to associate the zero crossing with the first coordinate of the object location. The first coordinate of the object location corresponds to a coordinate of the at least one antenna  120  of means  110 , the at least one antenna  120  taking up said object location in relation to the object to be localized when transmitting or receiving the periodic signal at the zero crossing. 
   If the at least one antenna  120  of means  110  is used for sequentially receiving periodic signals, in accordance with a preferred embodiment of the present invention, the location determination means  130  will be directly, i.e., for example by means of cables, coupled to means  110 . If an antenna array is used, the individual antennas of the array will be preferably connected to a receiver and/or transmitter by cables of equal lengths, respectively, or by cables of at least calculable lengths, respectively. 
   In accordance with embodiments of the present invention, the at least one antenna  120  may be operated as a transmit antenna. In this configuration, the location determination means  130  is preferably located within or at the object to be localized. In this case, means  110  and location determination means  130  are preferably coupled via a radio link between the at least one transmit antenna  120  and the object to be localized. 
   In accordance with further embodiments of the present invention, location determination means  130  is further configured to determine, in addition to the first coordinate, a second coordinate of the object location on the basis of an inclination of the Doppler frequency response in the zero crossing. 
   For a more detailed illustration of the inventive concept,  FIG. 2  depicts a location determination area  200 , the location determination area  200  being representable by an x axis and y axis. Within the location determination area  200 , an object to be localized  210  is positioned at an object location having a first coordinate x 0  and a second coordinate y 0 . In parallel with the x axis on the edge of, or outside the location determination area  200 , there is a linear antenna array  120  having a plurality of individual antennas, of which only two are designated by reference numerals  120   a  and  120   b  for clarity&#39;s sake. 
   For simulating an antenna movement, the individual antennas of antenna array  120  are connected, in quick succession, as active receive antennas, respectively, in accordance with one embodiment of the present invention. Initially, for example, antenna  120   a  is switched as the active receive antenna at a time T o . After a duration of ΔT, i.e. at a time T o +ΔT, antenna  120   a  is switched off, and second antenna  120   b  is used as the active receive antenna. After a further duration ΔT, antenna  120   b  is switched off, and the next antenna is switched as the active receive antenna, etc. 
   If a distance between the individual antennas of antenna array  120  is d in each case, the scenario depicted in  FIG. 2  results in a simulated antenna speed v=d/ΔT in parallel with the x axis of the location determination area  200  from the right to the left. Thus, the speed vector {right arrow over (v)} will point from the right to the left along the antenna array. The measurement accuracy of the inventive concept may be increased by increasing the number of antennas in relation to the location determination area  200 , and/or by reducing the distance d of the antennas. In addition, an increase in the simulated speed v and/or a reduction of the time duration ΔT will also have positive effects on the measurement accuracy. 
   The individual receive antennas of antenna array  120  receive, in accordance with one embodiment of the present invention, replica, which sequentially vary in time, of the periodic signal having the carrier frequency f c  which has been emitted by the object to be localized. The various replica exhibit different phases of the periodic signal. On this topic,  FIG. 3  shows a potential wiring of antenna array  120  so as to obtain therefrom a Doppler frequency response with the plurality of antennas of antenna array  120 . 
     FIG. 3  shows antenna array  120  having individual antennas  120   a  and  120   b  connected to a switching device  320  via cables, only two of which are provided by reference numerals  300   a  and  300   b  for clarity&#39;s sake. Switching device  320 , in turn, is coupled to a filtering means  330 , at the output of which a filter output signal is provided. 
   Cables  310   a ,  310   b  are preferably equal in length or have at least calculable lengths. Equal lengths of the cables from the antennas to the switching device  320  are advantageous for obtaining no additional different phase shifts between the individual receive branches due to signal delay times by cables  310   a, b . As has already been described above, for position measuring, the antennas of antenna array  120  are switched, for example, as active receive antennas in quick succession, in accordance with the invention. This is achieved by means of switching means  320 . Thus, a fast linear movement along the line defined by the antenna array is simulated electronically. This simulated movement creates the Doppler effect. The change in the frequency of waves of any kind while a signal source is moving toward or away from an observer is referred to as the Doppler effect. In the event of the approximation, the frequency will increase, in the opposite case it will decrease. 
   The signal applied at the input of filtering means  230  because of the switching of the antennas in a temporally sequential manner comprises phase jumps at time intervals of ΔT. The phase jumps of the replica of the carrier signal having the carrier frequency f c  are generally different from one another between two adjacent antennas, respectively, of antenna array  120 . In a linear antenna array comprising N antenna elements, a signal comprising (N−1) phase jumps and/or phase differences Δθ 1 , . . . , Δθ N-1  will result at the input of filtering means  330 . (N−1) discrete Doppler frequencies f D,1 , . . . , f D,N-1  may be determined from the (N−1) phase differences Δθ 1 , . . . , Δθ N-1 . The n th  (n=1, 2, . . . , N−1) phase difference Δθ n  may be calculated to yield 
                     Δ   ⁢           ⁢       θ   ⁢             n       =     2   ⁢           ⁢   π   ⁢           ⁢       f   c     ·     d   c     ·           ⁢   cos     ⁢           ⁢     α   n         ,           (   1   )               
wherein α n  signifies the angle between speed vector {right arrow over (v)} and the location connecting vector of the n th  antenna and the object location (x 0 , y 0 ). On the basis of the connection d=v·ΔT, the following results from equation (1) for the n th  Doppler frequency at the n th  antenna
 
   
     
       
         
           
             
               
                 
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   It may be seen from equation (2) that at that x coordinate where speed vector {right arrow over (v)} is perpendicular to the location connecting vector, the Doppler frequency disappears because of the cosine term, and/or a Doppler frequency response has a zero crossing across the antennas of antenna array  120 . In addition, a maximum Doppler frequency results at f D,max =v/c·f c . 
   Thus, for the situation depicted in  FIG. 2 , a zero crossing of the Doppler frequency response will result for that antenna whose x coordinate equals the x coordinate x 0  of the object  210  to be localized. 
   To obtain a continuous Doppler frequency response from the discretely calculated Doppler frequencies f D,n  (n=1, 2, . . . , N−1), an interpolation may be made by means an appropriate interpolation between the discrete Doppler frequencies f D,n . Thus, in accordance with an embodiment of the present invention, means  330  may comprise an A/D converter and a digital filtering means to perform the above-described steps to obtain a continuous Doppler frequency response. 
   In accordance with a further embodiment of the present invention, filtering means  330  may also comprise an analog bandpass filter having a passband of 2f D,max  around carrier frequency f c , so that an analog continuous signal having a frequency range of f c ±f D,max  is applied at the output of filtering means  330 . This filtered, analog signal present at the output of filtering means  330  will then also exhibit the Doppler frequency response described. 
   To illustrate the various Doppler frequency responses for the different positions (x 0 , y 0 ), (x 0 , y 1 ), (x 0 , y 2 ), indicated in  FIG. 2 , of the object  210  to be localized, the Doppler frequency responses resulting from the different positions are depicted in  FIG. 4  by way of example. 
     FIG. 4  shows three Doppler frequency responses  400   a ,  400   b ,  400   c  which may be associated with the positions (x 0 , y 0 ), (x 0 , y 1 ), (x 0 , y 2 ), indicated in  FIG. 2 , of the object to be localized  210 . The Doppler frequencies are in a range of ±f D,max  around carrier frequency f c . Thus, the zero crossing of the Doppler frequency response will be located where the curves have a frequency value of f c . Since for the positions (x 0 , y 0 ), (x 0 , y 1 ), (x 0 , y 2 ), indicated in  FIG. 2  by way of example, of the object to be localized, the x coordinate x 0  is identical in each case, the three Doppler frequency responses shown in  FIG. 4  all have their zero crossings at x=x 0 . 
   However, the Doppler frequency responses have different inclinations in an area around the zero crossing at x=x 0 , which is due to the various y coordinates. If the object location is positioned relatively close to the antenna array  120 , such as the location having coordinates (x 0 , y 1 ), the inclination will have a relatively large value within a range around the zero crossing of the respective Doppler frequency response  400   b . On the other hand, if an object is spaced away from the antenna array  120  at a relatively far distance, as is the case for the location having coordinates (x 0 , y 2 ), the inclination of the resulting Doppler frequency response will be relatively low in the range around its zero crossing, as is shown for curve  400   c . The explanation for this is found in the cosine term of equation (2). For a location near the antenna array  120 , angles α n  are mostly very small, except for a small range around x coordinate x 0 . On the other hand, for locations which are spaced away from the antenna array  120  at a relatively large distance, angles α n  are mostly relatively large, accordingly. 
   Thus, depending on the x, y coordinate of an object  210  to be localized, a specific and unambiguous Doppler frequency response results from antenna array  120 . The x position of the object  210  to be localized which may comprise a transmitter for the periodic signal is measured by determining the zero crossing of the Doppler frequency curve. The y position may be determined by the inclination and/or the curvature of the Doppler frequency response at the zero crossing. 
   It shall be mentioned at this point that a second coordinate, or a y coordinate, may be determined in an unambiguous manner only if a two-dimensional location determination area is defined. Generally, the inclination of the Doppler frequency response in the zero crossing indicates a location which may be positioned on a cylinder, speed vector {right arrow over (v)} of the linear antenna motion describing the longitudinal axis of the cylinder. For an unambiguous location determination within a two-dimensional location determination area it is therefore advantageous for the longitudinal axis of the cylinder, i.e. speed vector {right arrow over (v)}, to be positioned at the edge of, or outside the location determination area. However, if the longitudinal axis of the cylinder is positioned within the two-dimensional location determination area, unambiguous determination of the second coordinate is not readily possible due to the rotational symmetry of a cylinder. 
   In addition, an exact position determination within a three-dimensional location determination area is also possible with the inventive concept. If a three-dimensional location determination area is defined by a coordinate system having three coordinate axes (x, y, z) perpendicular to one another, respectively, the inventive concept may be used to perform a location determination for an object to be located within the three-dimensional space by arranging, for example, an antenna array to be parallel to the x axis, and by arranging a second antenna array to be perpendicular thereto and parallel to the z axis. As has already been described above, the first antenna array may be used to perform a two-dimensional location determination (x and y coordinates), and the second antenna array may be used to determine, for example, the remaining third coordinate (z coordinate). However, the antenna arrays are preferably positioned at the edge of, or outside the three-dimensional location determination area. 
   Also, for three-dimensional location determination, the use of a two-dimensional antenna matrix is feasible which may be arranged, for example, in parallel with a (x, z) plane at the edge of or outside a three-dimensional location determination area. 
   In addition, mention shall be made that the linear movement for achieving the Doppler effect may not only be simulated electronically, but that this movement may actually also be brought about physically. In an embodiment of the present invention, it is feasible, for example, for one individual antenna to be moved to and fro in parallel with a coordinate axis at the edge of a location determination area on a motion device, such as a sledge guided on rails. If the antenna movement is actually realized physically, or mechanically, additional electronic processing of the periodic signals received may be dispensed with, since in this case a signal received will exhibit a continuous frequency response and will have no phase jumps. However, in practice one will only be able to achieve moderate speeds with a mechanical motion device. 
   As has already been mentioned above, a resolution capability of the inventive concept may be increased by increasing the speed of the linear movement, or of the simulated linear movement. In a system wherein the linear movement is simulated electronically, this may be effected by faster sequential switching of the individual antennas. In accordance with embodiments of the present invention, this preferably results in simulated speeds of v&gt;c/1000, c standing for the speed of light. 
   If the speed is, e.g., v=c/100, and if the carrier frequency of the periodic signal is f c =2.4 GHz, a maximum-magnitude Doppler frequency shift of f D,max =24 MHz will result. If antennas of an antenna array have a mutual distance of, e.g., d=10 cm, and if they are switched to be active in a temporally sequential manner by means of a switching device  320  so as to simulate an antenna movement, the switching time ΔT will amount to about 33 ns for simulating the speed of v=c/100. 
   In addition, mention shall be made that the antennas of an antenna array and/or the antenna on a moved sledge may not only serve as receive antennas for a periodic signal emitted by the object to be localized, but that in accordance with further embodiments of the present invention, they may also act as transmit antennas. In this configuration, the object to be localized requires a respective receiver so as to be able to determine, with an inventive location determination means, at least one coordinate of the object location on the basis of the zero crossing of the Doppler frequency response. If the object location determined by the object to be localized is to be made available, for example, to a central computer, the object to be localized will additionally require, e.g., a radio transmitter to transmit the object location determined to the central calculating unit. 
   In accordance with an embodiment of the present invention, it is possible to measure in advance relevant positions and/or the associated Doppler frequency responses of an object at a desired accuracy within a location determination area, and to associate the measured values and/or Doppler frequency responses, for example, in a so-called lookup table, with the respective object coordinates, and to store them. Of course, it is equally feasible for Doppler frequency responses regarding object positions to be calculated, in accordance with a further embodiment of the present invention, in the location determination area by means of mathematical formulae, so as to subsequently be associated, in a lookup table, with the respective object coordinates. If, subsequently, a Doppler frequency response is measured for any location of the location determination area, these measured values may then be compared with the values and/or Doppler frequency responses from the lookup table which have been measured, or calculated, and stored in advance, and thus they may possibly be associated with an object location. 
   If a position of an object to be localized is to be determined in a particularly reliable manner, it is also possible to provide, around a location determination area, several inventive means having at least one antenna for sequentially transmitting or receiving periodic signals having a carrier frequency f c  at various locations. As has already been described above, these means may be antenna arrays, for example. In this respect,  FIG. 5  shows a schematic structure of a position determination system for a game device, or, in a football match, for a ball. 
     FIG. 5  shows a football pitch  500  corresponding to a location determination area, to a first antenna array  120 - 1  in parallel with a first touch line of football pitch  500 , to a second antenna array  120 - 2  in parallel with a second touch line of football pitch  500 , to a third antenna array  120 - 3  in parallel with a first byline of football pitch  500 , and to a fourth antenna array  120 - 4  in parallel with a second byline of football pitch  500 . 
   With the system depicted in  FIG. 5 , the position of the game ball may be determined in a redundant manner. This is effected by means of the above-described inventive concept in such a manner that, for example, all four antenna arrays  120 - 1  to  120 - 4  act as receive arrays and are controlled at the same time. A location determination means, not shown, subsequently obtains four Doppler frequency responses corresponding to the four antenna arrays  120 - 1  to  120 - 4 , all of which can ideally be associated with the same object location. With systems based on radio localization, however, it may generally occur that imprecise results with regard to a position determination may be achieved due to reflections or shadowing of the radio waves. If, for example, one of the four antenna arrays  120 - 1  to  120 - 4  provides an imprecise or ambiguous result, it is very likely that at least one other of the remaining antenna arrays will provide a precise result which may then be used for determining the position. A potential plausibility check could be, for example, an inclination and/or symmetry observation of the Doppler frequency response to the left and to the right of the zero crossing. For example, if the Doppler frequency response exhibits an inclination on one side of the zero crossing which differs from that on the other side, respectively, this indicates insufficient measurement accuracy. For example, the receive signals of specific antennas of the antenna array may fail and/or be corrupted due to reflections and/or shadowing. If a Doppler frequency response of an antenna array does not stand up to a plausibility check, the Doppler frequency response of a further antenna array may be used as the basis. 
   In the position determination system depicted in  FIG. 5 , it is also feasible for the four receive antenna arrays  120 - 1  to  120 - 4  to not be controlled simultaneously, but sequentially in time. During a first time interval, the first antenna array  120 - 1  will thus be active, during a second time interval, the second antenna array  120 - 2  will be active, etc. 
   As has already been described above, the antenna arrays  120 - 1  to  120 - 4  may also be used as transmit antenna arrays if a respective receive and location determination means is present within the ball. When using only a carrier frequency f c , however, in this embodiment of the present invention, the transmit antenna arrays are preferably operated in successive time intervals, since otherwise the receive signals of the various antenna arrays  120 - 1  to  120 - 4  will superimpose one another within the ball, and signal differentiation will thus be rendered more difficult. If a different carrier frequency is used for each array, the transmit antenna arrays may also be operated simultaneously, and the signals may be separated by a respective filtering device. 
   Further possibilities of using the inventive concept are naturally also to be found in other sports where, for example, critical goal decisions and/or line decisions are to be made. 
   Using the inventive concept for determining positions is also feasible in other fields, such as logistics. In the field of logistics, the task often is to localize objects in warehouses, for example. To this end, warehouses may similarly be equipped with antenna arrays and/or movable individual antennas so as to be able to determine positions of objects of interest. The inventive method described may be employed, for example, within the framework of a RF-ID system, objects to be localized being equipped with passive or active RF-ID transponders. 
   It shall be pointed out, in particular, that the inventive scheme may also be implemented in software, depending on the circumstances. The implementation may be performed on a digital storage medium, in particular a disk or a CD with electronically readable control signals which may cooperate with a programmable computer system and/or microcontroller in such a manner that the respective method is performed. Generally, the invention thus also consists in a computer program product having a program code, stored on a machine-readable carrier, for performing the inventive method when the computer program product runs on a computer and/or microcontroller. In other words, the invention may thus be realized as a computer program having a program code for performing the method, when the computer program runs on a computer and/or microcontroller. 
   While this invention has been described in terms of several preferred embodiments, there are alterations, permutations, and equivalents which fall within the scope of this invention. It should also be noted that there are many alternative ways of implementing the methods and compositions of the present invention. It is therefore intended that the following appended claims be interpreted as including all such alterations, permutations, and equivalents as fall within the true spirit and scope of the present invention.