Extended sufficient conditions for the observation of linear time invariant systems with unknown inputs are formulated. A new observation scheme is proposed. An additional linear term ensuring global stability is included for this sake in the differentiation algorithm based on high-order sliding-modes. The global robust finite-time-convergent estimation of observable states and unknown inputs is obtained, exact in the absence of measurement noises. Under the detectability conditions the whole state is asymptotically estimated. The accuracy of the estimation in the presence of bounded deterministic Lebesgue-measurable noises and discrete sampling is worked out.