This paper considers the problems of the state estimation and the simultaneous unknown input and measurement
noise reconstruction for linear systems. For the linear systems only with unknown inputs, the issues of state estimation and
unknow input reconstruction are discussed when the observer matching condition is not satisfied. A reduced-order observer
is developed and a high-order sliding mode observer is proposed. After this, an unknown input reconstruction method is
developed. Then, the results are extended to be suitable for linear systems with both unknown inputs and measurement noise,
and a kind of simultaneous unknown inputs and measurement noise reconstruction method is proposed. Finally, a numerical
simulation example is given to illustrate the effectiveness of the proposed methods.