Department of Biomedical Engineering and Computational Science

Reentry Vehicle Tracking demonstration, 'reentry_demo'

This is a classical filtering problem, in which a space vehicle is entering the Earth's atmosphere with high speed and it's position is tracked with a sensor, which is placed on earth's surface. In figure 1 we have plotted the Earth's surface, position of sensor on it and the trajectory of the vehicle.

The dynamical model is nonlinear, and it's affected with three kinds of forces: aerodynamic drag, which is a function of vehicle speed and varies nonlinearily with altitude. Gravity causes the vehicle to accelerate toward the center of the earth. Lastly there are also random buffeting terms present, which make the estimation more difficult. The measurement model is also nonlinear, as the sensor measures the distance and the angle between it and the vehicle.

The system was estimated with first order EKF and augmented form UKF. In figure we have plotted MSEs and SDTEs of EKF in estimating x_1, x_3 and x_5 as a function of simulation time. See documentation for the discussion on results.

Files used in this example:

REENTRY_F
REENTRY_DF_DX
REENTRY_H
REENTRY_DH_DX
REENTRY_IF
REENTRY_COND
MAKE_REENTRY_DATA
REENTRY_DEMO
Dynamic model function
Jacobian of the dynamic model
Measurement model function
Jacobian of the measurement model
Inverse prediction of the dynamic model
Generates condition numbers for simulation data
Generates the simulation data for reentry dynamics
Reentry Vehicle Tracking demonstration
Figure 1

Figure 1. Sample vehicle trajectory, earth and position of radar.

Figure 2

Figure 2. MSEs and variances in estimating x_1, x_3 and x_5 using EKF and ERTS over 100 Monte Carlo runs. Results of UKF and URTS were practically identical.