The mechanism of biomolecular motors has been elucidated using single-molecule experiments for visualizing motor motion. However, it remains elusive that how changes in the chemical state during the catalytic cycle of motors lead to unidirectional motions. In this study, we use single-molecule trajectories to estimate an underlying diffusion model with chemical-state-dependent free energy profile. To consider nonequilibrium trajectories driven by the chemical energy consumed by biomolecular motors, we develop a novel framework based on a hidden Markov model, wherein switching among multiple energy profiles occurs reflecting the chemical state changes in motors. The method is tested using simulation trajectories and applied to single-molecule trajectories of processive chitinase, a linear motor that is driven by the hydrolysis energy of a single chitin chain. The chemical-state-dependent free energy profile underlying the burnt-bridge Brownian ratchet mechanism of processive chitinase is determined. The novel framework allows us to connect the chemical state changes to the unidirectional motion of biomolecular motors.