This paper deals with the adaptive observer which estimates the states and parameters of unknown system. It is shown that the adaptive observer problem is reduced to the identification of the transformation matrix for an arbitrary designable observer. Moreover, the adaptive process of the unknown parameters is reduced to the linear optimal regulator problem. As the result, a new method is presented to obtain an appropriate adaptive process with good insight. And, in this identification, a linear filter is found to be also useful against noises in input-output data. To achieve high accuracy, a particular nonlinear filtering can improve SN ratio only in the direction of the unknown vector. Even if SN ratio of input-output data has zero dB, sufficient accuracy can be accomplished within suitable correction time. This design algorithm seems to be rather straightforward and practical. Since input sequence is required to be only sufficiently general, the method is applicable to on-line identification also.