Dynamics of Naval Craft - System Identification 
upon the form of the equations that will be orare as- 
sumed for representing the motion of the system. 
Therefore the basic foundation underliying system 
identification as a means of representing the vehicle 
dynamics has (at least) the same degree of validity 
as any method of dynamic analysis that is presently 
used as a model of vehicle behavior. 
What is done in this technique is to obtain responses 
of a vehicle by measuring "'trajectories'(such as ve- 
hicle linear and angular displacements, velocities 
accelerations, etc.) following different types of dis- 
turbances. With the formulated mathematical model, 
values for the unknown parameters are then sought 
so that the solutions to the dynamic equations give a 
best fit to the data, where this best fit is defined by 
minimizing the mean square error between the solu- 
tion of the equations using these coefficients and the 
actual data record itself. The procedure can be ap- 
plied to data from both full scale and model scale 
trajectory observations, thereby increasing its uti- 
lity for correlation and validation purposes of par- 
ticular mathematical simulations of naval vehicles. 
Obtaining stability derivatives from full scale tra- 
jectories has been standard practice in the aircraft 
industry from its inception, and this has ordinarily 
been done by various means of data analysis that are 
primarily based upon the assumption that the equa- 
tions arelinear.In addition to considerations of non- 
linearity which are important for certain naval craft 
the sensitivity of some modes of motion of particular 
craft (such as hydrofoils, SES craft, etc.) to surface 
wave disturbances requires consideration of the in- 
fluence of random forcing functions, sensor errors 
and other ''noisy'' disturbances applied to the system 
and its measured motion responses. These different 
effects then require particular techniques for their 
analysis, and the present paper will provide a des- 
cription of the analysis methods as well as the re- 
sults obtained when the methods are applied to dif- 
ferent representative naval craft. 
The work described in this paper was carried out 
under the support of different agencies in the course 
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