Survey of Maneuvering
Target Tracking .
Part II: Motion Models of
Ballistic and Space Targets
X. RONG LI, Fellow, IEEE
VESSELIN P. JILKOV, Member, IEEE
Univ ersity of New Orleans
This paper is the second part in a series that provides a
comprehensive survey of maneuvering target tracking without
addressing the so-called measurement-origin uncertainty. It
surveys motion models of ballistic targets used for target tracking.
Models for all three phases (i.e., boost, coast, and reentry) of
motion are covered.
CONTENTS
I. Introduction
II. Ballistic (Coast) Flight
A. Gravity
B. Coordinate Accelerations
C. Coast Motion Models
III. Reentry
A. Aerodynamic Forces
B. Ballistic (Nonmaneuvering) RV Motion
C. Maneuvering RV Motion
D. Motion of Endo-Atmospheric Ballistic Targets
IV. Boost Phase
A. Accelerations
B. Kinematic Models
C. Dynamic Models
D. Example of A Profile-Based Model
V. Integration of BT Motion Models for Entire Trajectory
VI. Concluding Remarks
References
Appendix
Part I: Dynamic Models. IEEE T ransactions on Aer ospace and Electronic
Systems, 39, 4 (Oct. 2003), 1333—1364.
Part II: Originally published as Ballistic Target Models. In Proceedings of
the 2001 SPIE Confer en ce on Signal and Data processing of Small Targets,
vol. 4473, 559—581.
Part III: Measurement Models. In Proceedings of the 2001 SPIE Conference
on Signal and Data Pr ocessing of Small Targ ets, vol. 4473, 423—446.
Part IV: Decision-Based Methods. In Proceedings of the 2002 SPIE
Conference on Signal and Data Pr ocessing of Small Targets, vol. 4728,
511—534.
Part V: Multiple-Model Methods. IEEE Transactions on Aerospace and
Electronic Systems, 41, 4 (Oct. 2005), 1255—1321.
Manuscript received August 4, 2007; revised April 8, 2008; released
for publication August 25, 2008.
IEEE Log No. T-AES/46/1/935930.
Refereeing of this contribution was handled by W. Koch.
This research was supported in part by ARO Grant
W911NF-08-1-0409, ONR-DEPSCoR Grant N00014-09-1-1169,
Project 863 through Grant 2006AA01Z126, and Louisiana BoR
Grant LEQSF (2009-12)-RD-A-25.
Authors’ address: Dept. of Electrical Engineering, University of
New Orleans, New Orleans, LA 70148, E-mail: (xli@uno.edu).
0018-9251/10/$26.00
c
° 2010 IEEE
I. INTRODUCTION
A survey of dynamic models used in maneuvering
target tracking has been reported in [64]. It, however,
does not cover motion models used for tracking
ballistic and space targets (BT), namely, ballistic
missiles, decoys, debris, satellites, projec tiles, etc.
The primary reason for this omission is that these
models possess many distinctive features that differ
vastly from those covered in [64]. To supplement
[64], a survey of these models is presented here. To
our knowledge, such a survey is not available in the
literature.
Overall, a BT has a less uncertain motion than
many other types of powered vehicles, such as
maneuvering aircraft or agile missiles: Most BTs
follow a flight path that is largely predetermined
by the performance characteristics specific for a
target type, hence the name ballistic targets, although
some more advanced ballistic missiles can undergo
small maneuvers usually for retargeting. However,
this does not mean that the motion of a foreign BT
can be determined accurately. In fact, tracking a
foreignBTislikelytobeplaguedwithavarietyof
uncertainties, including those concerning trajectory
loft or depression, thrust profile management, target
weight, propellant specific impulse, sensor bias, and
atmospheric parameters. Many of these uncertainties
stem from the uncertainty in the target type, the
principal uncertainty in modeling the motion of a
foreign BT for the tracking purpose.
The entire trajectory of a BT is commonly
divided into three basic phases: boost (and possibly
a post-boost phase), ballistic (also known as coast),
and reentry. The boost phase is the powered,
endo-atmospheric flight, which lasts from launch to
thrust cutoff or burnout. It is followed by the ballistic
phase, which is an exo-atmospheric, free-flight motion
for most BTs, continuing until the atmosphere is
reached again. The atmospheric reentry begins when
the atmospheric drag becomes considerable and
endures until impact.
For the tracking purpose, only the most substantial
forces that may act on a BT are considered: thrust,
aerodynamic forces (most notably, atmospheric
drag and possibly lift), and gravity. Not all of these
forces are present at a le vel that significantly affects
the motion of a BT in all regimes of the trajectory.
The boost phase is characterized by a large thrust,
which in the case of rocket staging is subject to
abrupt, jump-wise changes. The effects of the drag
and gravity are also essential in this phase. After the
boost, drag is no longer present and thrust vanishes or
drops to a very low level. During the exo-atmospheric
ballistic phase the motion is governed essentially by
the gravity only. Still, small retargeting maneuvers
are possible. The reentry phase features a rapid
drag-induced deceleration with possible lateral
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