Abstract: Examples relate to golf assistance systems for providing environmentally-adjusted club recommendations during golf play. An example system includes a communication-enabled laser range finder with distance measurement circuitry, wireless communication circuitry, wind direction input controls, and a display interface. A networked processing device comprises a processor and memory configured to execute software storing golfer-specific shot performance data normalized to baseline atmospheric conditions. The networked processing device establishes wireless communication with the communication-enabled laser range finder to receive target distance and slope measurements, obtains real-time atmospheric data including air density, temperature, humidity, and wind conditions, and calculates effective shot distances for multiple golf clubs by processing the atmospheric data with the golfer-specific shot performance data.

Abstract: Systems, methods, and computer-readable media are provided for making a weather-based club recommendation.

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 making a weather-based club recommendation.

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 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 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 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 to reduce parallax errors are provided for an antenna array having a boresight optical system. In an example embodiment, a method comprises constructing an antenna array having antenna elements disposed symmetrically around an antenna axis and providing an optical aperture in the antenna array. An optical instrument having an optical axis is arranged in or adjacent the optical aperture. A first portion of the antenna elements receives reflected signals from a target in flight. A second portion of the antenna elements receives reflected signals from the same target in flight. A direction of travel of the target is calculated based on an average of the respective signals received by the first and second portions of the antenna elements.

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: 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: 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.