Two state/fault estimation methods using terminal sliding mode (TSM) concepts are presented in this paper. In contrast with conventional sliding modes, which guarantee asymptotic convergence of non-output estimation errors and faults, TSMs enable finite time convergence of estimation errors for faults and all the states. The minimum-phase condition, as a common condition required for fault estimation, is released in the proposed methods. Method I implements fractional power of the so-called switching term to make it robust against matched faults and disturbances. Compared with previous terminal scheme, this method covers a wider class of systems. In Method II, fractional power sliding variable is considered to achieve finite time convergence of estimation errors and their derivatives. In contrast with Method I, this approach is also robust against unmatched faults. Finally, the methods are applied to an unstable aircraft model.