Abstract: This paper describes a fundamental consideration on our works on the design of general Bayes' filters for the state estimation of non-stationary, non-linear, and non-Gaussian environmental sound and vibration systems. We have discussed an essential point of several Bayes' filters proposed by using the orthogonal or non-orthogonal expansion form of Bayes' theorem. They can estimate any kinds of statistics of arbitrary function type of state variables including the lower and the higher order statistics connected with the Lx evaluation index in the environmental sound and vibration systems. Here, we have mainly focussed on giving the fundamental viewpoints of their design policies. Some new estimation methods and new results not yet published ar included.