Detection Filters for Missile Tracking

In [3] a detection filter approach to fault detection is developed from an eigensystem assignment approach. The detection filter is an observer whose gains are constructed such that the presence of a fault induces in the measurement residuals an invariant (fixed) direction. Therefore, during a sudden maneuver of the target, although the detection filter's estimate of the state of the target is inaccurate, the target's acceleration direction can be determined by examining the detection filter residuals of the position measurement. As will be shown, a vector composed of the three position residuals has the same direction as the targets acceleration vector. Thus, while the detection filter's estimates are inaccurate in the usual sense of estimation, they seem very accurate in estimating the target's acceleration direction immediately following a maneuver. In Section 2 the essential aspects of fault detection and isolation algorithms for the missile tracking problem are presented. The definitions of detectability, separability, output stationarity and detection spaces are given. Appropriate theorems and lemmas which give the conditions under which a system and set of failures can be designed into a detection filter are presented. Given position only measurements and assumed acceleration fault directions, a detection filter is designed for the missile tracking problem which gives a one-to-one correspondence between the direction of the target's acceleration and the direction of the detection filter's position residuals. This is the subject of Section 3. The necessary conditions are checked and explicit closed-form solutions for the detection gains in terms of arbitrary eigenvalues are found. The computer simulation of the detection filter is presented in Section 4. The coordinate frame, missile and target models, the noise models and the Shiryayev Sequential Probability Ratio Test are discussed Section 5 contains the results from the simulations. The selection of the eigenvalues for the deterministic case is discussed and performance is presented. The optimal eigenvalues for the stochastic case are presented for two noise models, and performance is shown.