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: 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 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 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 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, determining one of the physical locations to be an origin of the golf ball based on the distance measure(s) and two types of separately estimated errors, wherein a first of the two types of separately estimated errors affects ball positional error for the initial observations, and a second of the two types of separately estimated errors affects an angle of the extrapolated trajectory; and presenting golf ball data on a display device associated with the origin of the golf ball.

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 three-dimensional object tracking includes, in at least one aspect, a method including: obtaining three-dimensional positions of objects registered by a detection system configured to allow more false positives so as to minimize false negatives, forming hypotheses using a filter that allows connections between registered objects when estimated three-dimensional velocity vectors roughly correspond to an object in motion in three-dimensional space, eliminating a proper subset of the hypotheses that are not further extended during the forming, specifying at least one three-dimensional track of at least one ball in motion in three-dimensional space by applying a full three-dimensional physics model to data for the three-dimensional positions used in the forming of at least one hypothesis that survives the eliminating, and outputting for display the at least one three-dimensional track of the at least one ball in motion in thr