A bound on the variance of fish abundance estimates obtained from acoustic echoes

In recent years, there has been increasing interest in acoustic techniques for estimating fish abundance. A lower bound on the variance of the abundance estimates is derived in this paper. The analysis assumes that the fish are Poisson-distributed in volume and that the estimate is obtained using independent samples from the received acoustic signal. It is shown that the variance of the estimate obtained from an echo counter satisfies the bound in low fish densities and that the variance of the estimate obtained from an echo integrator satisfies the bound in high fish densities.