DAUBIN: STATISTICAL ANALYSIS OF SHIP GENERATED NOISE 



Now, consider Equation (1) , the most simple-minded ambient noise 

 model shown during this conference: 



N 

 I = E T. S. (1) 



where 



..) = /t, 



T. = T(R.) = / T(R) 6(R. - R) dR. 



The intensity, I, at the receiving point is an incoherent sum of 

 independent signals from a set of N ships. T. is the energy trans- 

 mission from source to receiver, and S. is the source intensity of 

 the j ship. Assume further that the transmission loss is a function 

 of range only, and not a function of azimuth. Although we know this 

 to be unrealistic, nevertheless, it is not a bad approximation. 

 Hence, T. is the value of the transmission curve T at the radial 

 position of the j ship, R.. 



The problem then is to predict the statistics of the received 



intensity: its expectation, distribution and, ultimately, its power 



spectrum. These will be derived from the statistics of the two 



variables, T. and S., which are to be treated as random variables. 

 D : 



We know from statistics that the expectation value of the product 

 of random variables is given by the product of the expectation values 

 plus the statistical cross-correlation function between these vari- 

 ables times their individual standard deviations: 



Pts ''t %) 



E(I) = N (e(T) E(S) + p^g O^ oA. (2) 



An additional assumption for this part of the derivation is that the 

 correlation between the position relative to the receiving site and 



853 



