Dynamtcs of Naval Craft - System Identt fication 
noise in the surface ship case may have been more severe than noise 
that would be experienced with actual recorded data on a full scale ship, 
or in the case of model test trajectories, the indications are that the 
influence of noise tends to degrade the estimated parameter values 
given by this technique of system identification. This behavior might 
be anticipated to some extent in view of the fact that the basic analy- 
sis method makes no allowance for the presence of noise in the re- 
corded data, or noise present as a result of an arbitrary (unknown) 
random excitation. The only requirement is that the resulting diffe- 
rences between observed and predicted trajectories satisfy the mini- 
mum mean square error criterion, and that may not be sufficient 
without other ancillary conditions that would allow for the presence 
of such noise influences. More extensive investigations of the in- 
fluence of noise on the prediction capabilities of this method of system 
identification must be obtained in order to determine its limits when 
applied to such realistic cases. A discussion of the application of this 
iteration technique to a full scale case where significant noise dis- 
turbances were present is given in a later section of this paper, when 
considering techniques applicable to noisy systems. A description of 
the mathematical techniques and the results of application to different 
naval craft where noise has a significant influence is presented in 
the following sections. 
MATHEMATICAL PROCEDURES - SEQUENTIAL ESTIMATION 
TECHNIQUE 
When considering the use of system identification for cases 
where the observed data is contaminated by noise or if the system is 
excited by a random input, the method that is used is based upon a 
sequential estimation procedure that is derived as illustrated below. 
The basic problem underlying this system identification technique is 
that of estimating the state variables and the parameters in a noisy 
nonlinear dynamical system, and this problem is treated in [7] : 
which is an extension of the simpler problem where only observation 
errors ‘occur [6] . Considering the scalar case (i.e. a single state 
variable), the system is represented by 
Kode (eilc sit): wcteuatde (sept) a(t) (21) 
where u(t) is the unknown disturbance input. The measurements or 
observations of the output are 
y(t) = h(x,t) + (Measurement errors) (22) 
1647 
