Abstract
We use Bayesian linear regression to estimate aerodynamic coefficients from trajectory data containing measurement noise and error. The third polynomial is employed to interpolate two-dimensional trajectory data of a non-rotating table tennis ball. Each term in the polynomial is obtained as a posterior distribution. From the third polynomial, we investigate the time variations of the drag and lift coefficients. In Bayesian linear regression, the distributions of the coefficients of the polynomial including the optimal solution are obtained. It is found that two hyperparameters have significant impact on the estimation of the posterior distribution: the variance of the prior distribution in Bayes' theorem and that of observation which indicates the extent of error in linear regression. We set the prior variance for each term of the polynomial and estimate the coefficients. By normalizing the data, we can produce a more accurate polynomial. Compared to the polynomial without the normalization, there are distinct differences in the distributions for the third and constant terms. This shows that these two coefficients have large impact on the formation of the polynomial. Furthermore, based on the relationships between the estimated terms, it is found that the constant and first terms have the strongest negative correlation. In addition, by expressing the aerodynamic coefficients as probability distributions, it become possible to interpret stochastically the measurement errors.
