Ball Spin Axis Estimation From Noisy 3D Flight Trajectories
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Solution Overview
Problem
Existing methods for determining the spin axis of a sports ball in flight are prone to noise and inaccuracies due to factors like wind speed observations, camera hardware limitations, and mathematical model errors, leading to unreliable trajectory predictions.
Innovation Solution
A method involving sensor data smoothing with a Savitzky-Golay filter, outlier removal, and solving an optimization problem using a Huber loss function and Broyden-Fletcher-Goldfarb-Shanno algorithm to determine the spin axis, wind vector, and spin magnitude, with automatic differentiation for real-time processing.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional trajectory measurement methods are used, then the system is simple to operate, but the measurement precision deteriorates due to noise from wind speed observations, camera hardware limitations, and mathematical model errors
Solution Approach 1:
The system performs preliminary smoothing of trajectory data using a Savitzky-Golay filter before the optimization process. This pre-processing step reduces noise in the raw measurements, allowing the optimization algorithm to converge more reliably and accurately determine spin axis parameters without requiring excessively complex real-time processing
Solution Approach 2:
The optimization algorithm acts as an intermediary between the noisy sensor measurements and the final spin axis determination. By introducing intermediate variables (spin magnitude, wind vector, lift coefficient) and using a regularization term in the loss function, the system mediates the relationship between imperfect measurements and the parameters of interest, filtering out noise while extracting meaningful information
2Measurement precision
If sophisticated sensors are used to improve measurement precision, then the spin axis determination accuracy improves, but the device complexity and cost increase
Solution Approach 1:
The system replaces expensive, high-precision sensors with more affordable, standard camera hardware. By using a regularization term in the optimization loss function and pre-smoothing trajectories with a Savitzky-Golay filter, the system compensates for the lower quality of inexpensive sensors, achieving acceptable measurement precision without requiring costly equipment
Solution Approach 2:
The system substitutes direct mechanical measurement approaches with an optimization-based computational approach. Instead of relying on complex sensor hardware to directly measure spin parameters, the system uses standard sensors to capture trajectory data and then derives spin axis information through mathematical optimization, replacing physical measurement complexity with computational processing
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
Enhances the accuracy and robustness of spin axis determination, allowing for the use of less precise sensors and providing instantaneous results, thereby improving ball trajectory prediction and equipment development.
Implementation Method 1
sensor observation data is collected by one or more of: a radar, a camera, or both. the at least a portion of an observed trajectory of the ball is smoothed using a Savitzky-Golay filter
Implementation Method 2
solving an optimization problem, wherein a three-dimensional acceleration at the selected point in three-dimensional space is used as an optimization target, and a spin axis, a spin magnitude and a wind vector are used as optimization parameters
Implementation Method 3
The spin axis of a sports ball (e.g., a golf ball, hereinafter simply referred to as a 'ball'), refers to the axis around which the ball rotates during flight. The rotation around the spin axis gives rise to a lift force acting on the ball.
Data Source
AI summary
Methods and apparatus, including computer program products, implementing, and using techniques for determining a spin axis of a ball in flight. At least a portion of an observed trajectory of the ball is obtained. The trajectory includes three-dimensional locations of the ball over time, as determined from individual observations of the ball by one or more sensors. A point in three-dimensional space is selected. An optimization problem is solved, wherein the three-dimensional acceleration at the selected point is used as an optimization target, and a spin axis, a spin magnitude and a wind vector are used as optimization parameters, and wherein the solution to the optimization problem is a combination of optimization parameter values. The spin axis determined in the solution to the optimization problem is selected as the spin axis for the ball. The spin axis is used to generate ball trajectory information for presentation on an output device.