Distance, R; 



In the next-to-Iast column of Table 1, the 

 computed relative elevation, y^, is given for every 

 time the image appears. The parameter, h, of 

 Equation 1 was calculated by taking the difference 

 between the off-bottom heights of the two fish. This 

 calculation, of course, assumes a flat bottom. The 

 horizontal component of B was assumed to be the 

 outrigger length, 42 feet. 



Table 1 reveals a marked scatter in the set of y^ 

 values for any given target. For example, the target, 

 SB3, has five computed values of y^, and the 

 difference between minimum and maximum y^ is 

 57.37 feet. The difference value, Ay^, is given in the 

 last column of Table 1 for each target. The smallest 

 Ay^ is 9.77 feet. 



Presumably, the large spread in y^ for a given 

 target is the result of (1) errors in the measurement of 

 the components of B, and (2) target points lying on 

 or near the line through the two fish. Systematic 

 errors in h could be expected since this parameter had 

 to be computed from off-bottom fish heights. Having 

 target points on or near the extension of B was 

 evidently the result of "eyeballing" the LCM-8 course 

 relative to the surface floats. 



In an attempt to estimate the magnitude of 

 average systematic and random errors in h and H 

 during the 100-foot-depth scans, a least-squares 

 computer analysis of the Table 1 data was made. A 

 FORTRAN program (Appendix B) was written to 

 determine the set, ■{ Hj, h:|, which minimizes the 

 mean-square error, e, defined by 



Distance between horizontal lines =15 meters 

 Time between vertical lines = 2 minutes 



IN 



y^y 



(7) 



where N 



number of times the target is 

 scanned 



Figure 9. Two-fish sonar-chart readout of artificial 

 target array. 



N 



Vti 



i = l 



y^ for i"^ computation 



The results are given in Table 2. The average 

 value of h is -17.25 feet, compared to -19.85 feet as 

 computed from off-bottom fish heights (Table 1). 

 The average value of H is 43.06 feet, as compared to 



