Comparison of Meteorological Data With Fitted Values Extracted from Projectile Trajectory

In this report, the atmospheric conditions are found by knowing only the projectile's flight trajectory and its flight coefficients together with the initial atmospheric conditions on the ground. The test trajectories were generated as solutions of the modified point mass (MPM) equations of motion. The correct atmospheric conditions for the generated flight trajectory are obtained from data collected during a weather balloon flight. A nonlinear least squares method was then used to fit the MPM equations to the test trajectory by varying the meteorological parameters. Density, sound speed, and wind profiles agreed well. Further tests of the method involved the flight coefficients, which we perturbed to observe the corresponding variation for the fitted values. Also, Gaussian noise was introduced onto the trajectory values to simulate the uncertainty in trajectory measurements. The results of the analysis shows that the whole trajectory should be fitted, and not small trajectory segments, to obtain accurate atmospheric parameters with the location precision provided by current radar and Global Positioning Satellite System (GPS) techniques.