Comparison between Pseudomeasurement and DD2 filters in exoatmospheric Ballistic Missile engagement

This paper deals with the problem of exoatmospheric tracking of a Ballistic Missile (BM) from an interceptor (or pursuer) moving towards the ballistic target. During the terminal guidance phase of the engagement, the on-board seeker provides noisy measurements of range, azimuth, elevation and range rate (or Doppler). Using the available seeker observations, the position and the velocity of the target can be estimated by a nonlinear tracking filter. Filter initialization is realized by means of a ground radar that tracks the ballistic target until the first measurement from the seeker becomes available. Then a proportional navigation guidance law is applied in order to guide the path of the interceptor towards the intercept point of the purser and the BM. The performance of the interceptor missile guidance system is influenced by the seeker and the autopilot dynamics that, in this paper, are both modeled with single lag transfer functions. Effects of different kinds of nonlinearities (i.e. saturation of lateral acceleration and saturations at the seeker) in the guidance loop are considered as well. The Extended Kalman Filter (EKF) has probably been the most widely used estimation technique for this complex nonlinear filtering problem. Nevertheless it is known that the EKF, which is based on a first order Taylor approximation of the equation of motion and/or the measurement equation, has a bias in its estimate and could in addition have convergence problems; both of these drawbacks are due to the underlying approximations. In this paper two filters are compared for the problem of tracking a BM during its exoatmospheric portion of flight: the Pseudomeasurement filter and the second order divided-difference filter (DD2 filter). A full three-dimensional engagement scenario has been simulated to assess the performance of the two considered estimation techniques and to determine the miss distance accurately. The simulation results show that both filters have adequate perfo- rmance for the proposed problem.