Abstract
This paper develops a sampling method to estimate the integral of a function of the area with a strategy to cover the area with parallel lines of observation. This sampling strategy is special in that lines very close to each other are selected much more seldom than under a uniformly random design for the positions of the parallel lines. It is also special in that the positions of some of the lines are deterministic. Two different variance estimators are derived and investigated by sampling different man made signal functions. They show different properties in that the estimator that estimate the biggest variance gives an error interval that, in some situations, may be more than ten times the error interval computed from the other estimator. It is also obvious that the second estimator underestimates the variance. The author has not succeeded to derive an expression for the expectation of this estimator. This work is motivated towards finding the variance of acoustic abundance estimates.
Highlights
This paper is about to find the variance in acoustic surveys to estimate the abundance of fish stocks
This paper develops a sampling method to estimate the integral of a function of the area with a strategy to cover the area with parallel lines of observation
This sampling strategy is special in that lines very close to each other are selected much more seldom than under a uniformly random design for the positions of the parallel lines
Summary
This paper is about to find the variance in acoustic surveys to estimate the abundance of fish stocks. Usually a ship with a downward looking echo sounder that pings sound pulses into the sea and receive sound reflections from fish, covers an area where the fish stock under estimation is supposed to be located. The author of this paper has worked with acoustic estimation of fish populations. The echo signal received from a modern echo sounder as a function of the area position of the echo sounder is an example of a function of which the area integral is necessary to estimate.
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