The kinematics of the human ankle is commonly modeled as a biaxial hinge joint model. However, significant variations in axis orientations have been found between different individuals and also between different foot configurations. For ankle rehabilitation robots, information regarding the ankle kinematic parameters can be used to estimate the ankle and subtalar joint displacements. This can in turn be used as auxiliary variables in adaptive control schemes to allow modification of the robot stiffness and damping parameters to reduce the forces applied at stiffer foot configurations. Due to the large variations observed in the ankle kinematic parameters, an online identification algorithm is required to provide estimates of the model parameters. An online parameter estimation routine based on the recursive least-squares (RLS) algorithm was therefore developed in this research. An extension of the conventional biaxial ankle kinematic model, which allows variation in axis orientations with different foot configurations had also been developed and utilized in the estimation algorithm. Simulation results showed that use of the extended model in the online algorithm is effective in capturing the foot orientation of a biaxial ankle model with variable joint axis orientations. Experimental results had also shown that a modified RLS algorithm that penalizes a deviation of model parameters from their nominal values can be used to obtain more realistic parameter estimates while maintaining a level of estimation accuracy comparable to that of the conventional RLS routine.