Dynamites of Naval Craft - System Identtftcatton 
The results demonstrated here show that the present 
sequential estimation technique can provide accurate estimates of 
parameters as a means of system identification for cases where 
random-noise interference or excitation is present. For the case 
where the data was generated on a computer, and the mathematical 
model was precisely known, quite good agreement between estimat- 
ed parameter values and the true ones were demonstrated for the 
hydrofoil case. The analysis of the full scale case was partially 
successful, in that generally reasonable parameter values were 
found that yielded good tracking of observed trajectories when using 
well stabilized values of the parameter estimates. There isa 
question concerning the proper form of the equations to represent 
the depth dependence influence on the effectiveness of the controls, 
as well as a possible influence on the nature of the measured input 
data on the results, when examining the results of this system 
identification procedure. These questions aid in the development of 
more rational mathematical model representations as well as on the 
nature of data acquisition for use in this type of analysis. 
There are a number of features of this particular se- 
quential estimation technique that have been observed in the present 
work. These features are concerned with methods used to obtain 
convergence and useful solutions, as well as information on com- 
putation time requirements, It is easily seen that the computation 
time generally increases as the number of variables (including 
unknown parameters) is increased. A general rule is that the time 
increases as n3? , where n = sum of number of state variables 
in equations and the number of unknown parameters. For the pre- 
sent case of the hydrofoil problem, with n = 14, the computation 
time was 22 times longer that the ''real time'' extent of the observed 
data, and this is for the case of a sequential estimation technique 
that would minimize computation time as compared to the classical 
nonsequential estimation schemes (with the problems being run on 
a very fast large computer, the CDC 6600). This time could be 
reduced by about 50% by applying symmetry considerations to the 
Pij elements, thereby reducing the number of equations to be solv- 
ed, as mentioned previously. Another possibility is to separate the 
equations into separate sets of a smaller number of equations, 
by means of partitioning, which could then reduce the time si- 
gnificantly depending on the number of partitioned elements. These 
particular computational modifications were not carried out in this 
work due to the increased programming effort required, and the 
fact that the main objective of the work was to develop the capability 
of system identification per se. These approaches to reduce com- 
puter time remain as a further step in providing a more ''computa- 
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