Abstract: This paper describes a methodological trial from a basic viewpoint based on the system theory and its simulation for the environmental noise and vibration problems. The state estimation of non-stationarily vibratory structure system through the observation of radiated noise accompanied with undesirable other vibration and background noise is discussed here, The recursive estimation algorithm is newly derived by expanding the so-called Bayes' theorem in the form of an orthogonal expansion series. Consequently, any kinds of statistics of state variables can be derived from this estimated probability density function. The validity and the effectiveness of proposed method are confirmed especially by means of digital simulation, since the present study is yet in an early stage and focussed on only the methodological viewpoint in this paper.