Abstract
Three-dimensional fish trajectories were analysed based on acoustic telemetry collected using a large experimental tank （600 m3）and refined with a state-space model to which the Kalman filter was applied. The movements of three red sea bream fitted with acoustic transmitters （at 63, 75, and 84 kHz）were monitored simultaneously using four hydrophones. On the basis of the differences in the times at which the transmitted sound signals arrived at each hydrophone, the positions of the fish were determined as the intersections of hyperboloid functions. A performance test of this system showed that it can be used to detect transmitter positions in a three-dimensional coordinate system with mean accuracy and precision of 0.69 m and 0.02‒0.04 m, respectively, with the 63 kHz transmitter, which generated the best results. The accuracy and precision were better for horizontal measurements than for vertical measurements, and the precision degraded with increasing transmitter frequency. These results indicate that it is possible to improve the precision of the system by employing a sampling rate that is sufficient
in relation to the transmitter frequency. Because of the significant error in the measurements, the swimming trajectories were refined using estimates obtained from a state-space model and the Kalman filter. For three of the fish, the estimated horizontal trajectories remained within the boundaries representing the walls of the tank. This study demonstrates that applying a state-space model to acoustic telemetry with large error can produce results that closely approximate the actual swimming trajectories of fish.
