Estimation of multiple skydiving jumps with unscented Kalman filtering

Abstract

This study investigated multiple skydiving jumps and applied the unscented Kalman filter (UKF) to develop a real-time state estimation of the skydiving physics model with gravitational and drag forces. In addition, experimental datasets were prepared by measuring the altitude change with the skydiving duration. Subsequently, the UKF and measured datasets were compared to assess the performance of the UKF according to fluctuations in the falling velocity or missing dataset. We observed that the UKF could predict the falling altitudes with various error ranges (−122.5−1.2 m) against the measured values at the end of skydiving points. Based on classical physics incorporated into the estimation model, the falling velocity should be monotonously increased, primarily owing to constant gravitational acceleration. Meanwhile, velocity fluctuation can be generated from the variation in drag forces due to the vertical air current. The UKF estimation was influenced by fluctuations in the falling velocity (8.8–20.3 m/s), missing datasets for 0–44 s, and/or the specifications of the initial estimates. Additionally, this study monitored the wind velocity approaching the skydiver vertically and the skydiver's heart rate. The measured wind velocity exhibited similar trends to the falling velocity with overall errors of 6.7 and 11.9 m/s (0.2% and 0.4%). Low correlations (R2 ≈ 0.11–0.47) were observed between the skydiving activities as falling speeds and the heart rates of the skydiver. Based on the measured and modeled data, the pressures at the terminal free falling and parachute descent were approximately 1500 and 6 N/m2, respectively.