This paper describes a methodological trial from a basic viewpoint based on the system theoryand 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 withundesirable other vibration and background noise is discussed here.The recursive estimation algo-rithm is newly derived by expanding the so-called Bayes’theorem in the form of an orthogonal expan-sion series.Consequently,any kinds of statistics of state variables can be derived from this estimatedprobability density function.The validity and the effectiveness of proposed method are confirmedespecially by means of digital simulation,since the present study is yet in an early stage and focussedon only the methodological viewpoint in this paper. 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 may desirable other vibration and background noise is discussed. here. The recursive estimation algo-rithm is newly derived by expanding the so-called Bayes’theorem in the form of an orthogonal expanion series. Reconstructed, any kinds of statistics of state variables can be derived from this estimated probability function. validity and the effectiveness of proposed method are confirmedespecially by means of digital simulation, since the present study is yet in an early stage and focussedon only the methodological viewpoint in this paper.