Beam pattern probability density function for multiple echo statistics

When fish target strength is estimated indirectly from single beam echo peak values the inverse techniques of solving the "single-beam integral equation" are recently quite satisfactorily used. This approach needs prior knowledge of beam pattern PDF, as it represents the kernel of the integral equation and is usually estimated under assumption of uniform spatial distribution of fish. However, it may be shown that in some cases this assumption not necessarily must be valid. For instance, when the density of fish is increased one receives multiple echoes from one fish observed in successive transmissions. Moreover, in some situations uniform assumption works properly only for the cases of large number of samples. Taking into account this phenomenon the accuracy of solution may be improved by including fish counting statistics in calculating the beam pattern PDF.