Abstract: Systems, methods and computer-readable media are provided for determining an effective altitude in relation to a moving sports object. In some examples, a method includes determining respective values for an air temperature, an air pressure, and a relative humidity of an environment of interest. Based on the determined respective values of the air temperature, the air pressure, and the relative humidity, an air density for the environment of interest is calculated to derive a first air density value. A second air density value is derived for a reference environment. An absolute value of a difference between the first and second air densities is compared against a preset comparison value and, based on the comparison being equal to or smaller than the preset comparison value, an output including an indicator of the effective altitude is generated.

Abstract: Systems, methods and computer-readable media are provided for determining an effective altitude in relation to a moving sports object. In some examples, a method includes determining respective values for an air temperature, an air pressure, and a relative humidity of an environment of interest. Based on the determined respective values of the air temperature, the air pressure, and the relative humidity, an air density for the environment of interest is calculated to derive a first air density value. A second air density value is derived for a reference environment. An absolute value of a difference between the first and second air densities is compared against a preset comparison value and, based on the comparison being equal to or smaller than the preset comparison value, an output including an indicator of the effective altitude is generated.

Abstract: Systems, methods and computer-readable media are provided for tracking a moving sports object. In one example, a method of tracking a moving sports object includes calibrating a perspective of an image of a camera to a perspective of a Doppler radar for simultaneous tracking of the moving sports object, and tracking the moving sports object simultaneously with the camera and Doppler radar. The method may further comprise removing offsets or minimizing differences between simultaneous camera measurements and Doppler radar measurements of the moving sports object. The method may also include combining a camera measurement of an angular position of the moving sports object with a simultaneous Doppler measurement of a radial distance, speed or other measurement of the moving sports object.

Abstract: Systems, methods and media are provided for golf ball spin axis measurement. In one example, a method comprises detecting a launched golf ball, receiving reflected Doppler signals from the golf ball by a radar device having an array of multiple receiver pairs, demodulating the spin-induced signals from the received signals, determining a time delay between the demodulated signals for the receiver pairs in the array, calculating an average time delay for the multiple receiver pairs, calculating a spin axis of the golf ball from the time delay values, outputting a spin axis value to an external system, and storing the spin axis value in a database.

Abstract: Systems, methods and media are provided for golf ball spin axis measurement. In one example, a method comprises detecting a launched golf ball, receiving reflected Doppler signals from the golf ball by a radar device having an array of multiple receiver pairs, demodulating the spin-induced signals from the received signals, determining a time delay between the demodulated signals for the receiver pairs in the array, calculating an average time delay for the multiple receiver pairs, calculating a spin axis of the golf ball from the time delay values, outputting a spin axis value to an external system, and storing the spin axis value in a database.

Abstract: Systems and methods for ball spin rate measurement are described. Some embodiments provide a method whereby a phase-demodulated difference signal of a projectile in flight is received, such as from a Doppler radar system. A first periodic component of the phase-demodulated signal is detected, the first periodic component having a plurality of bipolar pulses, with each of the pulses having a first portion during which an apparent speed of the projectile is greater than a nominal speed of the projectile, and each of the pulses having a second portion during which the apparent speed of the projectile is less that the nominal speed of the projectile. A period of the first periodic component is detected, and the spin rate of the projectile in flight is determined based on the period of the first periodic component.

Abstract: Spin rate measurement utilizing periodic phase modulation of the radar Doppler signal reflected from a golf ball is described. Some embodiments provide a method to directly measure the ball spin rate caused by the symmetrical structure of the golf ball seam, using the dielectric lens effect of a practical sports ball to magnify the modulating effect of a non-homogeneous feature on the ball, and utilizing the specific pattern of modulation caused in this manner.