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

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, connecting the optical model and the radar model in time using a timestamp derived for the camera and the radar device based on a difference between a duration required by the camera to produce an image frame and a duration required by the radar device to produce a radar reading, and producing three dimensional location information of the object in flight in three dimensional space using the optical model and the radar model connected in time using the timestamp.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for pre-processing image data before 3D object tracking include, in at least one aspect, a method including: performing object detection in uncompressed, two-dimensional image data from a camera to produce two-dimensional location data for objects of interest; processing the two-dimensional location data for the objects of interest using a motion criterion to generate possible paths data for the objects of interest; and constructing a flight track of an object in three-dimensional space, from the possible paths data and position information obtained from a sensor, by filtering out false positives in the possible paths data.

Abstract: Methods and apparatus, including computer program products, implementing, and using techniques for estimating wind velocity. Measurements are obtained, which indicate two or more trajectories traversed by flying balls. Individual wind velocity estimates are determined for the two or more trajectories, wherein the determination comprises comparing a model acceleration of the ball with an observed acceleration of the ball, derived from the measurements. The aggregated wind velocity estimate is calculated as a weighted average of the determined two or more individual wind velocity estimates. The aggregated wind velocity estimate is used for generating ball trajectory information to be presented on an output device.

Abstract: Methods and apparatus, including computer program products, implementing, and using techniques for estimating wind velocity. Measurements are obtained, which indicate two or more trajectories traversed by flying balls. Individual wind velocity estimates are determined for the two or more trajectories, wherein the determination comprises comparing a model acceleration of the ball with an observed acceleration of the ball, derived from the measurements. The aggregated wind velocity estimate is calculated as a weighted average of the determined two or more individual wind velocity estimates. The aggregated wind velocity estimate is used for generating ball trajectory information to be presented on an output device.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for tracking an object in motion includes, in at least one aspect, a method including: detecting a launch of a ball based on initial data obtained by one or more sensors, sending initial control signals that begin changing at least one of pan, tilt, or zoom for a camera based on a predicted future position of the ball, determining a trajectory of the ball in three-dimensional space based on additional data obtained by the one or more sensors after the launch, and sending additional control signals that control each of the pan, tilt, and zoom for the camera based on an expected future position of the ball along the trajectory.

Abstract: A method includes assessing errors for golf shots using observations by sensor(s), the assessing being in accordance with variations in a location for the sensor(s), and providing a map indicating at least one preferred location for the sensor(s) for use in setting up an object tracking system. Further, a method includes assessing how an estimated error affects identification of an originating location for a golf shot, including projecting a first value of the error back to the originating location and multiplying a second value of the error by a distance to the originating location, and identifying the originating location for the golf shot based on a first effect of the error and a second effect of the error. Finally, a system includes a building including tee areas, targets, and a sensor system including sensor(s), in which a dedicated sensor system is not included for any one of the tee areas.

Abstract: Methods, systems, and apparatus, including medium-encoded computer program products, for tracking an object in motion includes, in at least one aspect, a method including: detecting a launch of a ball based on initial data obtained by one or more sensors, sending initial control signals that begin changing at least one of pan, tilt, or zoom for a camera based on a predicted future position of the ball, determining a trajectory of the ball in three-dimensional space based on additional data obtained by the one or more sensors after the launch, and sending additional control signals that control each of the pan, tilt, and zoom for the camera based on an expected future position of the ball along the trajectory.

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 (from a camera) two dimensional image data of a golf ball in flight; obtaining radar data (originating from a Doppler radar device) of the golf ball in flight; fitting a curve to the radar data to generate a continuous function of time for the radar data of the golf ball in flight; determining three dimensional location information of the golf ball in three dimensional space including, for each of multiple camera observations, finding a radial distance using the continuous function and a time of the camera observation, finding a depth distance, finding a horizontal distance and finding a vertical distance to the golf ball; and providing the three dimensional location information of the golf ball in three dimensional space to augment other data before display.

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 (from a camera) two dimensional image data of a golf ball in flight; obtaining radar data (originating from a Doppler radar device) of the golf ball in flight; fitting a curve to the radar data to generate a continuous function of time for the radar data of the golf ball in flight; determining three dimensional location information of the golf ball in three dimensional space including, for each of multiple camera observations, finding a radial distance using the continuous function and a time of the camera observation, finding a depth distance, finding a horizontal distance and finding a vertical distance to the golf ball; and providing the three dimensional location information of the golf ball in three dimensional space to augment other data before display.

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 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

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, connecting the optical model and the radar model in time using a timestamp derived for the camera and the radar device based on a difference between a duration required by the camera to produce an image frame and a duration required by the radar device to produce a radar reading, and producing three dimensional location information of the object in flight in three dimensional space using the optical model and the radar model connected in time using the timestamp.

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

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 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: 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 includes, in at least one aspect, a method including obtaining (from a camera) two dimensional image data of a golf ball in flight; obtaining radar data (originating from a Doppler radar device) of the golf ball in flight; fitting a curve to the radar data to generate a continuous function of time for the radar data of the golf ball in flight; determining three dimensional location information of the golf ball in three dimensional space including, for each of multiple camera observations, finding a radial distance using the continuous function and a time of the camera observation, finding a depth distance, finding a horizontal distance and finding a vertical distance to the golf ball; and providing the three dimensional location information of the golf ball in three dimensional space to augment other data before display.

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.