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A mathematical model is presented for describing the behavior of fish in a water tank. The state equation includes nonlinear terms representing the main causes for fish motion, and has five non-measurable parameters. The parameters are estimated by using the observation data of a water tank experiment and by applying the least squares algorithm. The validity of the model is in-vestigated by testing the whiteness of the residual of the state equation, and also by comparing the simulation result with the experimental result. Consequently, the modeling procedure becomes clearer than the previous one, and a detailed part of the model is improved. Further, it is found from the result of parameter estimation that about a thousand points of time series data are needed for the convergence of the estimation process.

Least squares parameter estimation in fish behavior model.