Estimation of parameters in the time variable dynamics of a missile from flight test data

Abstract

ESTIMATION OF PARAMETERS IN THE TIME VARIABLE DYNAMICS OF A MISSILE FROM FLIGHT TEST DATA Bengt Skarman Saab Scania Linkoping S-581 88 Sweden Missile parameters have been estimated from flight test data. The effect of firing small rocket motors perpendicular to the missile centre line was investigated. Ideally the force from the motors should have acted through the centre of gravity. Due to aerodynamic effects this was not the case. The point of action and important aerodynamic derivatives were estimated from body rates. The analysis had to handle: changing missile speed, pitch-yaw coupling due to a constant roll rate, wind disturbances and rate sensor saturation. By considering process noise statistics as constant and using.an approximate likelihood function it was possible to use existing programs for maximum likelihood identification. Introduction Maximum likelihood parameter estimation has become a widely used method for estimating aerodynamic derivatives from flight test data. The estimates are used to confirm or adjust wind tunnel test data. This paper describes an application of parameter estimation where no wind tunnel data existed. Only theoretically calculated values were available. In fact, the design of tunnel tests that could give reliable data would have been difficult. This is due to the special way of applying control forces perpendicular to the missile velocity vector with thrusters. side force centre of gravity thrusters between yaw and pitch data was introduced. Body rates in pitch and yaw were measured and telemetered. The body .rates caused by the thrusters were relatively small and therefore process noise caused by wind gusts could not be neglected in the analysis. In this paper a prediction error model for the missile is formulated. It is shown that in the case of no process noise the time variability presents no great problem when system dynamics can be described with unknown but constant parameters multiplied by known time function as air speed. With process noise present the matter is more complicated. Here two approximations are made. The Kalman filter gains are set constant and the generated and measured random process is considered to have constant statistics. This approach produces reasonable results when applied to the flight test data. Symbols A system dynamic matrix B input relation matrix C output relation matrix x state vector u control vector Y observation vector ' m measured observation vector 0 It is of main interest that attitude changes while applying side forces should be kept small. This mq implies that the side force should act through the Cm, centre of gravity. To compensate for aerodynamic effects one therefore has to place the thrusters C ~ c , nonsymmetrically relative to the centre of gravity. q The goal of the flight tests was to estimate the proper displacement and important aerodynamic M derivatives. S d To allow low cost tests the missile contained no sustain motor and thus the estimation procedure m had to handle changing speed. Furthermore the missile was not roll 'stabilized so that coupling Cupyrighl @ American Institule of Aeronautics and Astronautics, Inc., 1978. All rights reserved. noise vector process noise vector covariance matrix Kalman filter gain loglikelihood function approximate loglikelihood function deviation y A m-Y parameter vector aerodynamic derivative aerodynamic derivative aerodynamic derivative dynamic pressure air speed reference area reference length mass Ix,Iy,IZ moments of inertia P,Q,R body rates U,V,W velocity in body coordinates gx,g ,gZ components of gravity Y F thruster force k point of application of F relative to centre of gravity uw component of wind in flight direction