Independent thesis Advanced level (professional degree), 20 credits / 30 HE credits
Traditionally direct integration of the measurements from an IMU (inertial measuring unit), measuring the acceleration and inertial angular velocity of the missile, is used to determine a missiles position and state. However, if some prior information about the missile dynamics is known, this method should be suboptimal. Combining the knowledge of the missile dynamics with the measurements should improve performance.
Of course, the complete missile dynamics are not known. A few model uncertainties are therefore added and these uncertainties are estimated by the estimator. The measurements from the IMU are not perfect and these measurement errors are also estimated. This method is called model based parameter estimation.
The problem is non linear and therefore estimators for non linear systems have been studied. The Extended Kalman filter and the Unscented Kalman filter were considered for this problem.
It was shown that using this method the performance of the position estimate compared to the traditional method, was increased. The performance gain is mainly decided by the size of the model uncertainties compared to the size of the measurement errors. All states used in the model was not observable but only jointly observable meaning that all states did not converge to their true value. Instead the error was caught in other states and the position estimate was still quite good.
Different trajectories for the missile excites different states. The trajectory both affects the impact of the IMU-errors and on the observability. The best performance was achieved for the sinus trajectory because of its excitation of the states. This knowledge might be used to improve the performance for all trajectories.
An position sensor was also added and the affects were studied. It was shown that it is possible to increase the estimation performance even if the position is measured only for a short period of time in the beginning of the trajectory. The states converged much better using the position sensor than without and this method could be used in the evaluation of fired missiles in controlled circumstances.
The Extended Kalman filter and the Unscented Kalman filter gave approximately the same estimation performance but the Extended Kalman filter was considerably faster and used in most of the analysis of the system. From this it was concluded that the performance of the position estimate is not estimator dependent but is more about the basic observability of the system.
2009. , 66 p.