estimates from the MLE estimate differed from the true spectrum by about 20 to 

 40 percent at high- energy directions in the true spectrum when the true 

 spectrum had a finite spread (the method was nearly perfect for unidirectional 

 waves). An improvement for this problem was proposed by Pawka (1982, 1983), 

 who argued that a correction term could be added to an MLE estimate for each 

 viewing direction. The magnitude of the correction term was determined from 

 the difference between the observed cross spectrum and the cross spectrum 

 resulting from inversion of the MLE estimate. Adding the correction term to 

 the existing result provides a new MLE estimate of the directional spectrum. 

 Since this system is transcendental, a further correction can be found by 

 inverting the new MLE estimate and comparing the result to the observed cross 

 spectrum. This process is repeated until the differences are minimized. 

 Since it is iterative, this method is known as Iterative Maximum Likelihood 

 Estimation (IMLE) . Details of IMLE are described by Pawka (1982, 1983) and 

 summarized by Oltman-Shay and Guza (1984). This algorithm was used to process 

 the data described in this report. 



115 . The problem remains of confidence intervals for final frequency- 

 direction spectra. In contrast to the MLE method, there is no formal estimate 

 of error for the IMLE method. One might use a formal error computation from 

 the MLE method as a crude estimate of error in the IMLE method. However, such 

 error estimates are only measures of statistical noise and, while of value, 

 are not complete. Errors also occur because of interrelationships imposed by 

 the IMLE algorithm between a true directional distribution and a specific 

 array geometry. This algorithm is nonlinear, so it is difficult to compute a 

 general error estimate from any type of linear analysis; each true directional 

 distribution can have its own unique error distribution. 



116. Perhaps the best approach to this problem is to conduct a series 

 of tests using simulated, but realistic, directionally distributed wave 

 energy. The assumption is made that real directional distributions close in 

 shape to the simulated cases have similar error distributions and so give an 

 indication of the verity of the IMLE method. Results of such tests are 

 reported by Pawka (1983). Several hundred spectra, having one or two direc- 

 tional peaks of varying widths, were employed in this test. A five -gage array 

 was used. Typical results were that errors using the IMLE method were about 

 13 percent of the errors from the MLE method for unimodal (single peaked) 

 directional distributions and about 1 percent for bimodal distributions. This 



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