Tracking Golf Balls in Flight by Doppler Radar

The seminar will cover two subjects given by development engineer Jesper Brasch and development engineer Kasper Leenders Møller, both from Trackman, Vedbæk.

Doppler radar tracking and separation of signals in frequency spectrums 
By Jesper Brasch

A continuous wave (CW) doppler radar is a type of radar, which can separate and track objects in motion with a high sampling frequency, but on the other hand is blind to objects not in motion. 

At Trackman we use this technology to track, golf balls, baseballs, footballs, clubs and other equipment. In this presentation it will be shown how the Fourier transform can be applied to a CW doppler radar signal in order to track these objects, and how to apply complex window functions to deal with non stationary signals that may overlap in the Fourier spectrum. 

Tracking a Spinning Golf Ball: From Flight to Launch

By Kasper Leenders Møller 

We will explore how mathematical modelling and numerical methods can be used to analyse and reconstruct the flight of a spinning golf ball using real data from Trackman 4. Starting from Newton’s second law, we incorporate aerodynamic forces (gravity, drag, and the Magnus effect) to form a realistic model of the ball’s trajectory. This system is integrated in time using an adaptive Runge-Kutta method (RK45). We then consider the inverse problem of estimating the launch conditions from the observed trajectory data. This is formulated as a nonlinear least squares problem and solved using the Levenberg-Marquardt algorithm.

After the seminar there will be served sandwiches and beverages.