Ball Tracking Using Kalman Filter and Parabolic Prediction
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Solution Overview
Problem
Existing ball tracking systems face challenges in accurately calculating the three-dimensional trajectory of a flying ball, especially in outdoor environments with noise interference and unstable lighting conditions, due to limitations in detecting small fast-moving objects like golf balls and requiring multiple cameras or wind speed data.
Innovation Solution
A ball tracking apparatus and method that includes a capturing control part, detection control part, calculation control part, prediction control part, conversion control part, acquisition control part, correction control part, and repetition control part, using a single camera to detect and track the ball by calculating initial position and velocity, predicting future positions based on a parabolic trajectory, and correcting using a Kalman filter.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Device complexity
If a single camera is used to track the ball, then device complexity is reduced, but measurement precision of the three-dimensional trajectory deteriorates
Solution Approach 1:
The patent changes the parameters being measured from simple two-dimensional image coordinates to three-dimensional position and velocity coordinates. By calculating initial position and velocity from the single camera image, and then using parabolic motion equations to predict and correct three-dimensional trajectory points, the system achieves 3D trajectory measurement without requiring multiple cameras.
Solution Approach 2:
The patent introduces an intermediary mathematical model (parabolic motion equation and Kalman filter) that bridges the gap between 2D camera observations and 3D trajectory reconstruction. The Kalman filter acts as a mediator that combines predicted trajectory points with actual observed points to calculate accurate three-dimensional position and velocity, enabling precise trajectory measurement with a single camera.
2Measurement precision
If multiple cameras are used to improve trajectory detection accuracy, then measurement precision improves, but device complexity increases
Solution Approach 1:
The patent fundamentally changes the measurement parameters from requiring multiple camera viewpoints to using single-camera two-dimensional coordinates combined with three-dimensional parabolic motion parameters. This parameter transformation allows accurate 3D trajectory reconstruction without additional cameras.
Solution Approach 2:
The patent replaces the mechanical solution of using multiple physical cameras with a mathematical-computational solution involving parabolic motion equations and Kalman filter algorithms. This substitution achieves the same trajectory detection accuracy through software processing rather than additional hardware.
3Measurement precision
If wind speed data is collected to improve trajectory accuracy, then measurement precision improves, but device complexity and ease of operation worsen
Solution Approach 1:
The patent changes the approach from directly measuring environmental parameters (wind speed) to calculating trajectory parameters (initial position and velocity) from camera images and using parabolic motion equations. This eliminates the need for additional wind sensors while maintaining trajectory accuracy.
Solution Approach 2:
The patent extracts and eliminates the requirement for external wind speed measurement devices from the system. By focusing on calculating initial position and velocity from the single camera and using parabolic motion models, the system removes the complexity of integrating multiple sensors while preserving measurement precision.
4Ease of operation
If traditional ball tracking methods are used in outdoor environments, then ease of operation is maintained, but reliability deteriorates due to noise and lighting conditions
Solution Approach 1:
The patent implements a feedback mechanism through the Kalman filter that continuously compares predicted trajectory points with actual observed ball positions. This feedback loop allows the system to correct for disturbances in outdoor environments (noise, lighting changes) by adjusting the trajectory calculation based on the difference between predicted and observed positions, thereby maintaining reliability without complicating operation.
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
Enables accurate calculation and display of a flying ball's trajectory after launch, overcoming limitations of previous systems by using a single camera and Kalman filter for precise tracking in outdoor conditions.
Implementation Method 1
a correction unit that corrects the predicted position and predicted velocity of the flying ball as a corrected position and a corrected velocity based on the predicted position, the predicted velocity, coordinates of an actual ball image, and a Kalman filter
Implementation Method 2
a prediction unit that predicts a three-dimensional position and a three-dimensional velocity of a world coordinate system of a flying ball at a specific time after the initial time as a predicted position and a predicted velocity based on the calculated initial position and the calculated initial velocity of the flying ball, and an equation indicating a parabolic shape of the flying ball
Data Source
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Figure 3~4B
Figure 5~6B
AI summary
The prediction control part 204 predicts a three-dimensional position and a three-dimensional velocity of the world coordinate system of the flying ball at a specific time after the initial time as a predicted position and a predicted velocity based on initial position and initial velocity of flying ball, and an equation indicating a parabolic shape of the flying ball. The conversion control part 205 converts the predicted position into a two-dimensional position of a camera coordinate system as a temporary position. The acquisition control part 206 specifies a flying ball image and acquires a two-dimensional position of the camera coordinate system of the flying ball image as an observation position. The correction control part 207 corrects the predicted position and the predicted velocity as a corrected position and a corrected velocity based on the predicted position and the predicted velocity, the observation position, and a Kalman filter.