Ballistic Object Trajectory and Impact Point Estimation in the Reentry Phase from a Moving Passive Sensor

Zijiao Tian, Kaipei Yang, Meir Danino, Yaakov Bar-Shalom, Benny Milgrom

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


This article considers the problem of estimating the trajectory of a ballistic target in the reentry phase using 2-D measurements (azimuth and elevation angles) from a moving passive sensor. Previous works investigated the estimation problem of an object in the thrusting and initial ballistic phase from a single fixed passive sensor. This article shows that the 3-D trajectory in the reentry phase can be obtained by estimating the targetâ state at the end of the observation interval. The 7-d motion parameter vector (velocity azimuth angle, velocity elevation angle, drag coefficient, target speed, and 3-D position) is estimated by the maximum likelihood (ML) estimator with numerical search. Then we can predict the future position at an arbitrary time and the impact point of the target. The observability of the system for a sensor on a fast aircraft moving with constant velocity or maneuvering is verified via the invertibility of the Fisher information matrix. This is a major extension of the applicability of the recent observability proof for a stationary passive sensor observing a target in a gravitational field. The Cramer Rao lower bound for the estimated parameters is evaluated and it shows that the estimates are statistically efficient. The angle estimation performance for the ML estimator is also compared with that of the polynomial fitting method. Simulation results illustrate the effectiveness of the proposed method.

Original languageEnglish
Pages (from-to)4540-4550
Number of pages11
JournalIEEE Transactions on Aerospace and Electronic Systems
Issue number5
StatePublished - 1 Oct 2022

Bibliographical note

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  • Ballistic missile
  • maximum likelihood (ML) estimation
  • observability
  • parameter estimation
  • reentry phase


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