Fish target strength estimation using multiple echo statistics

Abstract

When fish strength is estimated indirectly from the sounder echo amplitudes, the inverse techniques of solving the so-called “single-beam integral equation” are quite satisfactorily used. This approach needs prior knowledge of the beam pattern PDF, as it represents the kernel of the integral equation to be solved and is usually calculated under the assumption of a uniform spatial distribution of fish. However, it may be shown that in some cases this assumption is not necessarily justified. For instance, when the density of fish increases, one receives multiple echoes from the same single fish in successive transmissions, which results in observing so-called fish echo traces. Typically used fish counting methods are either simple direct echo counting statistics or fish traces statistics [1]. Increased fish concentration is not only the reason of multiple echo formation resulting in the fish traces in consecutive pings. As it is easily seen from the geometry of the phenomenon, even a relatively low-density fish aggregation forms multiple echoes and, hence, fish traces if the vessel (or fish) relative speed is low enough and the beam pattern angular width (sampling volume) is large enough. In some situations, the uniform assumption works properly only for the cases of large numbers of samples. Taking into account this phenomenon, the accuracy of the solution can be improved by including the fish traces counting statistics in calculating the beam pattern PDF. In this paper, two different models of fish traces statistics are investigated: one assuming the vessel movement with stationary fish and the other with a stationary vessel and moving fish. Both approaches are modeled numerically and verified experimentally using the data obtained from a dual-beam system. The comparison of both approaches, i.e., for single echo traces and multiple echoes, is carried out using Windowed Singular Value Decomposition (WSVD) and Expectation Maximization and Smoothing (EMS) inverse techniques of fish target strength estimation in both the absolute domain (backscattering length estimation) and the logarithmic domain (target strength estimation).