Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects include a method including: determining at least one three dimensional trajectory for at least one golf ball hit into a three dimensional physical space based on observations by at least one golf ball sensor placed adjacent to the three dimensional physical space; calculating systemic and stochastic errors for the at least one three dimensional trajectory in accordance with variations in golf ball launching position, variations in locations for the at least one golf ball sensor, or both; and presenting a report showing a summary of the calculated systemic and stochastic errors to indicate preferred hitting positions, a different location for the at least one golf ball sensor, or both.

Abstract: A post for mounting a camera comprises a base, a tube mast, and a camera mount arranged to hold one or more cameras. A proximal end of the tube mast is connected to the base and a distal end of the tube mast is connected to the camera mount. The invention is characterised in that the base is arranged to comprise computing equipment, from which computing equipment wiring runs through the tube mast to the camera mount, and in that the base and computing equipment are encased by a cabinet configured to protect the computing equipment from exposure to weather. The invention also relates to a method for installing a post.

Abstract: Methods and systems include, in at least one aspect: determining an optical model of an object in flight using two dimensional image data obtained from a camera, determining a radar model of the object in flight using radar data obtained from a radar device, combining the radar model with the optical model to produce three dimensional location information of the object in flight in three dimensional space, comparing the three dimensional location information of the object in flight with data representing an expected ball launch, and rejecting (or verifying) the object as an actual ball launch in response to the three dimensional location information of the object in flight differing (or not differing) from the data representing the expected ball launch by a threshold amount.

Abstract: Method for providing reduced interference for at least two co-located FMCW (Frequency Modulated Continuous Wave) Doppler radars, each of said radars being used in a system to detect respective distances to and velocities of objects moving through space, can include a propagation determination step, in which expected electromagnetic wave propagation times are determined between pairs of radars; a sweep time offset synchronizing step, in which different respective sweep time offsets are selected, with respect to each radar in a first group of radars; and a sweep frequency offset synchronizing step, in which a second sweep frequency offset is selected with respect to a second group of radars, the second sweep frequency offset being relative to a sweep frequency pattern used for radars belonging to said first group. The invention also relates to a system and to a computer software product.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects include a method including determining a three dimensional trajectory based on initial observations, extrapolating the three dimensional trajectory backward in time to generate an extrapolated trajectory, calculating distance measures between the extrapolated trajectory and defined physical locations, waiting for additional observations when none of the distance measures satisfy a threshold distance, identifying one of the defined physical locations as an origin when only one of the distance measures satisfies the threshold distance and an error measure satisfies a predefined criteria, identifying one of the defined physical locations as the origin when two of the distance measures satisfy the threshold distance and only one of first and second error measures satisfies the predefined criteria, and waiting for additional observations when neither the first error measure nor the second error me

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects includes, in at least one aspect, a method including obtaining two dimensional image data of a golf ball in flight, the two dimensional image data originating from a camera; obtaining radar data of the golf ball in flight, the radar data originating from a Doppler radar device associated with the camera; interpolating the radar data to generate interpolated radar data of the golf ball in flight; and blending radial distance information derived from the interpolated radar data of the golf ball in flight with angular distance information derived from the two dimensional image data of the golf ball in flight to form three dimensional location information of the golf ball in three dimensional space.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects include a method including determining a golf ball trajectory based on observations by sensor(s), extrapolating the trajectory backward in time, calculating distance measure(s) between the extrapolated trajectory and physical locations, estimating a systemic error for observation(s), wherein the systemic error affects observed ball positions, estimating a stochastic error associated with the observation(s), wherein the stochastic error affects an angle of a trajectory determined from observed ball positions, combining the estimated systemic and stochastic errors to form error measure(s) for the distance measure(s), identifying one of the physical locations as an origin for the golf ball when the error measure(s) satisfy a criterion, and waiting for additional observations of the golf ball by the sensor(s) when the error measure(s) do not satisfy the criterion.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for pre-processing image data before 3D object tracking includes, in at least one aspect, a method including: receiving, at a first computer, image frames from a camera; identifying, by the first computer, locations of interest in the image frames; finding sequences of the locations, wherein each of the sequences satisfies a motion criterion for locations identified in at least three image frames from the camera; and sending output data for the sequences of the locations to a second computer for processing the sequences in the output data by interpolating between specified 2D positions in specific image frames for the sequences, using timestamps of the specific image frames, to produce a virtual 2D position at a predetermined point in time, which is usable for constructing a 3D track of a ball in motion.

Abstract: A method for estimating a spin of a projectile, the method comprising obtaining from a radar transceiver a first time series comprising observations of a radial velocity of the projectile relative to the radar transceiver, calculating, from the first time series, a center velocity of the projectile, extracting from the first time series a second time series comprising a variation in the first time series around the calculated center velocity estimating a frequency of the second time series, and determining the spin of the projectile WO based on the estimated frequency of the second time series.

Abstract: Methods and systems include, in at least one aspect: obtaining from a camera 2D image data of an object, obtaining from a radar device radar data of the object, combining the radar data and the 2D image data to produce 3D location information of the object, and modeling a 2D trace of the object using the 2D image data by finding an initial version of the 2D trace, receiving an initial portion of the 3D location information, extending the initial portion of the 3D location information in accordance with physical-world conditions to find at least one 3D location beyond the initial portion of the 3D location information, projecting the at least one 3D location into a 2D image plane of the camera to locate 2D region, and processing the 2D region in the 2D image data to extend the 2D trace of the object in flight.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for pre-processing image data before 3D object tracking includes, in at least one aspect, a method including: receiving, at a first computer, image frames from a camera; identifying, by the first computer, locations of interest in the image frames; finding sequences of the locations, wherein each of the sequences satisfies a motion criterion for locations identified in at least three image frames from the camera; and sending output data for the sequences of the locations to a second computer for processing the sequences in the output data by interpolating between specified 2D positions in specific image frames for the sequences, using timestamps of the specific image frames, to produce a virtual 2D position at a predetermined point in time, which is usable for constructing a 3D track of a ball in motion.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects includes, in at least one aspect, a method including: obtaining 2D camera image data of a golf ball; modeling a 2D trace of the golf ball using the 2D image data; obtaining radar speed data of the golf ball; modeling a speed of the golf ball using the radar speed data, wherein modeling the speed of the golf ball includes fitting a polynomial function to a first portion of the radar speed data and fitting an exponential function to a second portion of the radar speed data; combining the modelled speed of the golf ball with the modelled 2D trace of the golf ball to form a 3D trace of the golf ball; and outputting for display the 3D trace of the golf ball in 3D space.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for 3D flight tracking of objects includes, in at least one aspect, a method including obtaining two dimensional image data of a golf ball in flight, the two dimensional image data originating from a camera; obtaining radar data of the golf ball in flight, the radar data originating from a Doppler radar device associated with the camera; interpolating the radar data to generate interpolated radar data of the golf ball in flight; and blending radial distance information derived from the interpolated radar data of the golf ball in flight with angular distance information derived from the two dimensional image data of the golf ball in flight to form three dimensional location information of the golf ball in three dimensional space.