Experimental verification of an interpolation algorithm for improved estimates of animal position

This article presents experimental verification of an interpolation algorithm that was previously proposed in Jaffe [J. Acoust. Soc. Am. 105, 3168-3175 (1999)]. The goal of the algorithm is to improve estimates of both target position and target strength by minimizing a least-squares residual between noise-corrupted target measurement data and the output of a model of the sonar's amplitude response to a target at a set of known locations. Although this positional estimator was shown to be a maximum likelihood estimator, in principle, experimental verification was desired because of interest in understanding its true performance. Here, the accuracy of the algorithm is investigated by analyzing the correspondence between a target's true position and the algorithm's estimate. True target position was measured by precise translation of a small test target (bead) or from the analysis of images of fish from a coregistered optical imaging system. Results with the stationary spherical test bead in a high signal-to-noise environment indicate that a large increase in resolution is possible, while results with commercial aquarium fish indicate a smaller increase is obtainable. However, in both experiments the algorithm provides improved estimates of target position over those obtained by simply accepting the angular positions of the sonar beam with maximum output as target position. In addition, increased accuracy in target strength estimation is possible by considering the effects of the sonar beam patterns relative to the interpolated position. A benefit of the algorithm is that it can be applied "ex post facto" to existing data sets from commercial multibeam sonar systems when only the beam intensities have been stored after suitable calibration.