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This paper constructs a mathematical model of wheelchair dynamics in a data-driven manner. In particular, we focus on the forward-backward movement of the wheelchair, for which we adopt a linear-parameter-varying finite-impulse-response model. To avoid overfitting behavior, we employ the Bayesian estimation method. We show by experimental results that the constructed model reproduces the observed data more precisely than linear models. We also show the identified model is effective for the feedforward input design.