System and method for determining a spin axis of a sports ball

1. A method for determining a spin axis of a sports ball, comprising:

transmitting a signal, via a first radar, into a target area into which the sports ball is to be launched, the first radar including three receivers arranged so that a minimum of three receivers are not co-linear, the signal being reflected back to the receivers by the sports ball;

receiving, by the first radar, the received reflected signal via the receivers;

performing a frequency analysis on the received reflected signal received by the first radar at a first point in time to determine a frequency spectrum comprising a range of frequencies received by the first radar corresponding to differing velocities relative to the first radar of different portions of the sports ball as the sports ball is spinning;

separating the determined frequency spectrum into a plurality of frequency components; and

determining for each of the frequency components a first phase difference between signals received at a first pair of the three receivers and a second phase difference between signals received at a second pair of the three receivers and identifying a component of the spin axis of the sports ball based on the determined first and second phase differences.

2. The method of claim 1 , wherein the component of the spin axis is identified as a projection of the spin axis of the sports ball onto a plane perpendicular to a line of sight from the first radar to the sports ball.

3. The method of claim 2 , wherein the projection of the spin axis of the sports ball is identified as a line perpendicular to a line represented by the determined first and second phase differences.

4. The method of claim 1 , further comprising performing a motion compensation of the received reflected signal to subtract an average motion of the sports ball from the signal.

5. The method of claim 4 , wherein the motion compensation centers the received reflected signal around 0 Hz.

6. A method for determining a spin axis of a sports ball, comprising:

transmitting a signal, via a first radar, into a target area into which the sports ball is to be launched, the first radar including three receivers arranged so that a minimum of three receivers are not co-linear, the signal being reflected back to the receivers by the sports ball;

receiving, by the first radar, the received reflected signal via the receivers;

performing a frequency analysis on the received reflected signal received by the first radar at a first point in time to determine a frequency spectrum comprising a range of frequencies received by the first radar corresponding to differing velocities relative to the first radar of different portions of the sports ball as the sports ball is spinning;

separating the determined frequency spectrum into a plurality of frequency components; and

identifying for each of the frequency components a velocity contour line on a surface of the sports ball, each velocity contour line corresponding to a plurality of reflection points on the surface of the sports ball with the same relative velocity based on a phase difference detected between signals received by a first pair of the receivers of the first radar and signals received by a second pair of the receivers of the first radar.

7. The method of claim 6 , further comprising identifying as a projection of the spin axis of the sports ball onto a plane perpendicular to a line of sight from the first radar to the sports ball, a line perpendicular to a line represented by the determined phase differences.

8. The method of claim 6 , further comprising averaging locations positioned on each contour line to define a point within the corresponding plane, a set of points from each velocity contour line corresponding to a line perpendicular to the spin axis.

9. A method for determining a spin axis of a sports ball, comprising:

transmitting a signal, via a first radar, into a target area into which the sports ball is to be launched, the first radar including three receivers arranged so that a minimum of three receivers are not co-linear, the signal being reflected back to the receivers by the sports ball;

receiving, by the first radar, the received reflected signal via the receivers; and

performing a frequency analysis on the received reflected signal received by the first radar and, based on the frequency analysis, calculating a derivative of phase differences observed at the receivers with respect to frequency and, based on this derivative, identifying a spin axis of the sports ball.

10. The method of claim 9 , further comprising, based on the phase differences relative to the first radar, determining the spin axis of the sports ball in a world coordinate system.

11. The method of claim 9 , further comprising determining aerodynamical effects on a flight path of the sports ball based on the identified spin axis of the sports ball and a spin rate of the sports ball.

12. The method of claim 11 , further comprising generating a simulated projection of a continued flight path of the sports ball after the determination of the spin axis.

13. The method of claim 12 , further comprising providing to a camera operator an illustrated flight path of the sports ball to enhance tracking of the sports ball via a camera.

14. The method of claim 12 , further comprising automatically controlling a camera to track the sports ball based on the simulated projection of the continued flight path of the sports ball.

15. The method of claim 9 , further comprising deriving a first spin axis of the sports ball at a first point in time and a second spin axis of the sports ball at a second point in time and combining the first and second spin axes to determine a three-dimensional spin axis for the sports ball.

16. The method of claim 15 , wherein the first and second spin axes of the sports ball are combined to determine the three-dimensional spin axis for the sports ball based on an assumption that gyroscopic effects render a orientation of the three-dimensional spin axis in a world coordinate system substantially constant over time.

17. The method of claim 9 , wherein the spin axis of the sports ball is identified as a derivative vector of the phase difference with respect to frequency of a Doppler signal received from the sports ball.

18. A method for determining a spin axis of a sports ball, comprising:

transmitting a signal, via a first radar, into a target area into which the sports ball is to be launched, the first radar including three receivers arranged so that a minimum of three receivers are not co-linear, the signal being reflected back to the receivers by the sports ball;

receiving, by the first radar, the received reflected signal via the receivers; and

performing a frequency analysis on the received reflected signal received by the first radar and, based on the frequency analysis, calculating a derivative of differences of a time of receipt of signals at the three receivers with respect to frequency and, based on these derivatives, identifying a component of the spin axis of the sports ball based on the determined derivative.

19. The method of claim 18 , wherein the component of the spin axis is identified as a projection of the spin axis of the sports ball onto a plane perpendicular to a line of sight from the first radar to the sports ball.

20. The method of claim 19 , wherein the projection of the spin axis of the sports ball is identified as a line perpendicular to a line represented by the determined derivatives.

21. The method of claim 18 , further comprising performing a motion compensation of the received reflected signal to subtract an average motion of the sports ball from the signal.

22. The method of claim 21 , wherein the motion compensation centers the received reflected signal around 0 Hz.