Tracking of spiraling reentry vehicles with varying frequency using a new target dynamic model

Abstract

As ballistic targets reenter the earth’s atmosphere, they undergo rapid deceleration and may perform spiraling motion that can make accurate tracking very difficult. A variety of filter structures have been proposed for this problem, including variants of the Kalman filter. The present work employs a new target dynamic model combined with an unscented Kalman filter to yield an effective tracking solution. The new target model includes, in addition to position and velocity states, a modified drag coefficient, the target spiral frequency, and two harmonic states describing the periodic rotation of the target body around its velocity vector. The spiral frequency was allowed to have a general variation with time. The unscented Kalman filter with new target model produced very satisfactory tracking for targets with varying frequency. The sensitivity to angle measurement accuracy using a reduced set of measurements was evaluated and a threshold value was determined. Finally, tracking performance was confirmed by Monte Carlo analysis.

Keywords

Missile spiraling motion target tracking unscented kalman filter

Get full access to this article

View all access options for this article.

References

Chadwick WR. The re-entry flight dynamics of non-separating tactical ballistic missiles. In: Proceedings of the 3^rd annual interceptor technology conference, San Diego, CA, 11–14 July, 1994.

Chadwick WR. Reentry flight dynamics of non-separating tactical ballistic missiles. Naval Surface Warfare Center Dahlgren Division Technical Report NSWCDD/TR-95/218, May 1996.

Murphy

. Symmetric missile dynamic instabilities. J Guid Control Dyn 1980; 4: 464–471.

Platus

. Ballistic re-entry vehicle flight dynamics. J Guid Control Dyn 1982; 5: 4–16.

Platus

. Missile and spacecraft coning instabilities. J Guid Control Dyn 1994; 17: 1011–1018.

Zarchan

. Fundamentals of Kalman filtering: a practical approach (Progress in astronautics and aeronautics) 2000; vol. 190, Reston, VA: AIAA.

Jilkov

. Survey of maneuvering target tracking. Part V: Multiple-model methods. IEEE Trans Aerosp Electron Syst 2005; 41(4): 1255–1321.

Farrell

. Interactive multiple model filter for tactical ballistic missile tracking. IEEE Trans Aerosp Electron Syst 2008; 44(2): 418–426.

Julier

Uhlmann

Durrant-Whyte

. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 2000; 45(3): 477–482.

10.

Ristic

Farina

Benvenuti

. Performance bounds and comparison of nonlinear filters for tracking a ballistic object on re-entry. IEEE Proc Radar Sonar Navig 2003; 150(2): 65–70.

11.

Ristic

Arulampalam

Gordon

. Tracking a ballistic object on reentry. Beyond the Kalman filter: particle filters for tracking applications, Chap. 5. Norwood, MA: Artech House, 2004, pp. 85–102.

12.

Kandepu

Foss

Imsland

. Applying the unscented Kalman filter for nonlinear state estimation. J Process Control 2008; 18: 753–768.

13.

Crassidis

Markley

. Unscented filtering for spacecraft attitude estimation. J Guid Control Dyn 2003; 26(4): 536–542.

14.

Regan

Anandakrishnan

. Dynamics of atmospheric re-entry, Chap. 2. AIAA Education Series. Washington, D. C: American Institute of Aeronautics and Astronautics, 1993.

15.

Wann

van der Merwe

The unscented Kalman filter. In: Haykin

(ed.) Kalman filtering and neural networks, Chap. 7. New York: John Wiley & Sons, 2001, pp. 221–280.

16.

Ohlmeyer EJ, Menon PK and Kim J. Tracking of spiraling reentry vehicles with varying frequency using the unscented Kalman filter. In: AIAA guidance, navigation and control conference, Toronto, Ontario, Canada, 2–5 August 2010, AIAA 2010-8319.