This paper addresses the problem of estimating the trajectory and the launch point of a tactical ballistic missile using line of sight (LOS) measurements from one or more passive sensors (typically satellite-borne), The major difficulties of this problem include the ill-conditioning of the estimation problem due to poor observability of the target motion via LOS measurements, the estimation of the unknown launch time, and the incorporation of inaccurate target thrust profiles to model the target dynamics during the boost phase. We present a maximum likelihood (ML) estimator based on the Levenberg-Marquardt algorithm that provides both the target state estimate and the associated error covariance, taking into consideration the complications mentioned above. One important consideration in the defense against tactical ballistic missiles (TBM) is the determination of the target position and error covariance at the acquisition range of a surveillance radar located in the vicinity of the impact point. We present a systematic procedure to propagate the target state and covariance to a nominal time, when it is within the detection range of a surveillance radar to obtain a cueing region. We also provide an estimate and the error covariance of the (two dimensional) launch position, which can be used to search for the missile launch site. Monte Carlo simulation studies on typical single and multiple sensor scenarios indicate that the proposed algorithms are accurate in terms of the estimates and that the estimator calculated covariances are consistent with the errors.
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