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This paper discusses the issues of finite-time state estimation and switching signal identification for a class of switched linear system with both unknown inputs and unknown active modes. By some special state and output transformations, a reduced-order switched system is constructed such that a finite-time switched observer can be constructed, where the unknown inputs of the original system are removed. A cluster of finite-time observers are proposed for all reduced-order subsystems. Then, the state estimation of a reduced-order switched system is derived from the finite-time switched observer by choosing any small time-delay parameters, and the finite-time state estimation of the original switched system is also obtained from the estimated states of the reduced-order switched system based on the state equivalent transformation. Next, a kind of active mode identification method is proposed by minimizing the output residual norm. Finally, a simulation example is given to verify the reliability of the proposed method. [ABSTRACT FROM AUTHOR]