Distance and velocity estimation of projectiles based on Doppler radar signals using a nonlinear discrete-time observer
Sonja Podjawerschek, E. Spahn, Joachim Horn, Michael Brodmann, Ralf Himmelsbach · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2010
We propose a new "quasi-global" observer design to determine the distance and velocity of projectiles in real-time. The detection of the projectile is realized by a low power Doppler radar at short distances (5m-10m). The advantage of a global observer design is the possibility to deal with large initial errors, which is important because of the usually unknown initial state of the observed system. The transformation to the nonlinear observability canonical form (NOCF) leads to linear error dynamics and this allows a traceable influence on the dynamic behaviour of the observer, which is essential for the time critical implementation on a real-time system. To benefit from these two advantages, the nonlinear system has to be transformed to the NOCF and an explicit expression of the inverse transformation has to be found. Since with this severe restriction the given problem can not be solved, we propose a numerically approximated inverse transformation in a bounded region of physical interest to allow the design of a quasi-global observer with linear error dynamics in the presented case. Based on this design the class of systems where this kind of observer can be applied has been enlarged considerably.