Indirect Measurement of a Bar Magnet Position Using a Hall Sensor Array

The measured magnetic induction field of a bar magnet can be used to compute or measure indirectly the position of the magnet. A model-based parameter estimation approach requires a precise induction field model and knowledge of the model error. In this paper, different analytic models describing the axial component of the induction field in front of a small cylindrical bar magnet are compared with Hall sensor array measurements and finite-element simulations. The used solenoid model matched the finite-element method simulations but requires a high numerical effort. The approximate dipole model is suitable when a proposed correction function for the estimated distance is applied and current and position are estimated simultaneously