Dynamtes of Naval Craft - System Identtficatton 
variables that represent the unknown coefficients in these equations. 
The coefficients themselves are the actual variables that are sought 
in this system identification procedure, and different techniques are 
used within the course of the analysis with the understanding that the 
variables desired are the coefficients in the equations. Solutions are 
necessary for all the variables starting with estimated initial condi- 
tions, where the variables include the state variables of the system 
as well as the coefficients themselves. Errors between the calculated 
state variables and the actual measured trajectory data itself are 
determined, and then modifications of the unknown coefficients are 
obtained in this procedure. These new values are then inserted again, 
solutions obtained, modified coefficient values found, and these are 
inserted again with the method repeated, i.e. an iterative procedure. 
The main features of this method are the fact that the basic 
dynamic system itself can be nonlinear (in terms of the state variables) 
and it is not necessary to measure every response variable in order 
to obtain the values for the coefficients. Even in the case of a linear 
system, if each and every response variable, including displacements, 
velocities, and accelerations of all degrees of freedom are measured, 
then the only unknowns are the coefficients themselves which can be 
obtained from solution of a set of linear algebraic equations. However 
it is often difficult, if not impossible, to measure every variable, 
derivative, etc., as well as the fact that often such measurements 
are not very accurate due to instrument limitations. The technique 
applied here requires selecting just those variables that are easiest 
to measure and which are available, but nevertheless a certain num- 
ber of variables must be measured since in a coupled system more 
than one mode of motion applies; e.g. as an illustration, it is neces- 
sary to obtain measured data on yaw and roll responses since measur- 
ing a single mode such as yaw alone would not yield sufficient data to 
obtain information on roll coefficients, and vice-versa. 
The original derivations in [3] presented a method for deter- 
mining unknown parameters in an otherwise known dynamic system 
using only measurements of the time history of just one state variable. 
However, practical experience with large systems containing a number 
of degrees of freedom and many parameters led to a generalization of 
the procedure involving the use of an increased number of measured 
trajectory records, (as mentioned above), and this improved proced- 
ure overcame many difficulties in regard to convergence and unique- 
ness of the results. A number of applications were made to different 
vehicles, including aircraft, a surface ship, and a hydrofoil craft, 
and the results obtained are described in [4] and [5] . A description 
of the mathematical procedures, and a discussion of results obtained 
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