| || Input estimation algorithms for reentry vehicle trajectory estimation
Author : Liu, Cheng Yu;Wang, Huai Min;Tuan, Pan Chio
Source : Defence Science Journal ; Vol:55(4) ; 2005 ; pp 361-375
Subject : 629.7 Aeronautics
Keywords : Reentry vehicle;Trajectory estimation;Input estimation;Extended Kalman filter;Reentry vehicle tracking;Reentry vehicle trajectory;Validation models;Trajectory estimation algorithms;Simulation
Abstract : Fast and accurate estimation of trajectory is important in tracking and intercepting reentry vehicles. Validating model is a real challenge associated with the overall trajectory estimation problem. Input estimation technique provides a solution to this challenge. Two input estimation algorithms were introduced based on different assumptions about the input applied to the model. This investigation presents approaches consisting of an extended Kalman filter and two input estimation algorithms to identify the reentry vehicle trajectory in its terminal phase using data from a single radar source. Numerical simulations with data generated from two models demonstrate superior capabilities as measured by accuracy compared to the extended Kalman filter. Evaluation using real flight data provides the consistent results. The comparison between two input estimation algorithms is also presented. The trajectory estimation approaches based on two algorithms are effective in solving the reentry vehicle tracking problem.
| || Tracking the Warhead Among Objects Separation from the Reentry Vehicle in a Clear Environment
Author : Liu, Cheng-Yu ;Chen, Chi-Teh
Source : Defence Science Journal ; Vol:59(2) ; 2009 ; pp 113-125
Subject : 623.4 Armaments and Ballistics;623 Military Science and Engineering
Keywords : Input estimation;Probabilistic data assocition filter;Extended Kalman filter;Tracking algorithm;Trajectory estimation
Abstract : Separating a reentry vehicle into warhead, main body, and debris is a conventional and efficient means of producing a huge decoy and increasing the kinetic energy of the warhead. This procedure causes the radar to track the main body and debris, which radar cross section are large, and ignore the warhead, is the most important part of the reentry vehicle. The warhead is difficult to identify after separation using standard tracking criteria. This study presents a novel tracking algorithm by integrating input estimation and modified probabilistic data association filter to identify warhead among objects separation from the reentry vehicle in a clear environment. The proposed algorithm provides a good tracking capability for the warhead ignoring the radar cross section. Simulation results reveal that the errors between the updated and warhead trajectories are reduced to a small interval in a short time. Therefore, the radar can generate a beam to illuminate the right area and keep tracking the warhead all the time. This algorithm is worthy of further study and application.
| || Algorithm of Impact Point Prediction for Intercepting Reentry Vehicles
Author : Cheng-Yu Liu;Chiun-Chien Liu;Pan-Chio Tuan
Source : Defence Science Journal ; Vol:56(2) ; 2006 ; pp 129-146
Subject : 531.55 Projectiles;629.76 Rockets and Missiles
Keywords : Reentry vehicle;Trajectory estimation;Input estimation;Adaptive Kalman filter;Impact point prediction;Counterparallel guidance law
Abstract : Intercepting reentry vehicles is difficult because these move nearly at hypersonic speeds that traditional interceptors cannot match. Counterparallel guidance law was developed for defending a high speed target that guides the interceptor to intercept the target at a 180° aspect angle. When applying the counterparallel guidance law, it is best to predict the impact point before launch. Estimation and prediction of a reentry vehicle path are the first steps in establishing the impact point prediction algorithm. Model validation is a major challenge within the overall trajectory estimation problem. The adaptive Kalman filter, consising of an extended Kalman filter and a recursive input estimator, accurately estimates reentry vehicle trajectory by means of an input estimator which processes the model validation problem. This investigation presents an algorithm of impact point prediction for a reentry vehicle and an interceptor at an optimal intercept altitude based on the adaptive Kalman filter. Numerical simulation using a set of data, generated from a complicated model, verifies the accuracy of the proposed algorithm. The algorithm also performs exceptionally well using a set of flight test data. The presented algorithm is effective in solving the intercept problems.
| || Estimation of Launch and Impact Points of a Flight Trajectory using U-D Kalman Filter/Smoother
Author : Naidu, V. P. S. ;Girija G.;Raol, J. R.
Source : Defence Science Journal ; Vol:56(4) ; 2006 ; pp 451-463
Subject : 629.7 Aeronautics
Keywords : Trajectory estimation;U-D Kalman filter;R-T-S smoother;Kalman tracking flight trajectory;launch point ;Impact point;Target detection;Air defence;Kalman tracking filter
Abstract : The launch and impact points of a flight trajectory are estimated using U-D Kalman filter and Rauch-Tung-Striebel (R-T-S) smoother. Algorithms are implemented in PC MATLAB and validated using simulated data. The filter performance is evaluated in terms of state error, innovation sequence, and autocorrelation of residuals along with their theoretical bounds. The R-T-S smoother was found to generate accurate state estimates, which led to better launch point estimation. Launch and impact point prediction from real data of a guided target in ballistic mode is also evaluated.