State estimation and reconstruction of unknown inputs with arbitrary relative degree via a predefined-time algebraic solver

•Unknown inputs are estimated without imposing relative-degree-related conditions.•The scheme employs an original predefined-time stable algebraic solver.•Implementation does not require to apply a state transformation on the system.•The system does not need to be affine in the unknown inputs.•The proposed observer has been shown to outperform an extended Kalman–Bucy filter.