The optimized interpolation of fish positions and speeds in an array of fixed acoustic receivers

The principal method for interpolating the positions and speeds of tagged fish within an array of fixed acoustic receivers is the weighted-mean method, which uses a box-kernel estimator, one of the simplest smoothing options available. This study aimed to determine the relative error of alternative, non-parametric regression methods for estimating these parameters. It was achieved by predicting the positions and speeds of three paths made through a dense array of fixed acoustic receivers within a coastal embayment (Gaspe Bay, Quebec, Canada) by a boat with a GPS trailing an ultrasonic transmitter. Transmitter positions and speeds were estimated from the receiver data using kernel estimators, with box and normal kernels and the kernel size determined arbitrarily, and by several non-parametric methods, i.e. a kernel estimator, a smoothing spline, and local polynomial regression, with the kernel size or smoothing span determined by cross-validation. Prediction error of the kernel estimator was highly dependent upon kernel size, and a normal kernel produced less error than the box kernel. Of the methods using cross-validation, local polynomial regression produced least error, suggesting it as the optimal method for interpolation. Prediction error was also strongly dependent on array density. The local polynomial regression method was used to determine the movement patterns of a sample of tagged Atlantic salmon ( Salmo salar) smolt and kelt, and American eel (Anguilla rostrata). Analysis of the estimates from local polynomial regression suggested that this was a suitable method for monitoring patterns of fish movement.