Estimation of Atlantic Salmon (Salmo Salar L.) Trajectories and Swimming Speeds in a Commercial Sea Cage Using Acoustic Telemetry and the Kalman Filter

Acoustic telemetry systems equipped with multiple receiver units can determine the 3D positions of individual fish by employing the time difference of arrival (TDoA) method. However, these datasets are often temporally sparse and exhibit uncertain positioning accuracy, which limits their utility in describing continuous fish behaviour. State estimation methods can address these limitations by enhancing data accuracy through mathematical modelling. This study employs the Kalman filter to estimate fish trajectories and velocities in open-net sea cages. We used a kinematic constant velocity model as the motion model, and the observation model reflects the estimator's assimilation of Cartesian position measurements. The measurement noise of the state estimator was calculated as the sample covariance of a position dataset recorded using an acoustic telemetry tag positioned statically relative to the receivers in a cage at a commercial fish farm. The process noise was tuned so that the average normalized innovations squared (ANIS) of the estimator satisfied a 95 % confidence interval, ensuring that the estimator was consistent. The state estimator was validated using position datasets for two free-swimming salmon tracked with acoustic telemetry in the same cage as the stationary tag. The resulting estimated trajectories and velocities resemble those observed for real salmon in open-net sea cages, and the estimated speeds were close to those recorded in a previous study using Doppler shift measurements. This work represents a natural progression towards improving the accuracy with which individual fish trajectories and velocities may be estimated through acoustic telemetry in aquaculture.