Abstract
This paper deals with methods of reconstructing, in the stochastic sense, the state of continuous-time dynamical systems with unknown initial conditions and subjected to random inputs. By extending to the stochastic systems the concept of n-observability with a deterministic system, the unknown stochastic states are reconstructed from the statistical knowledge of the system output during a finite time interval provided that the observation system is a scalar.
The technique of the determination of minimal, optimal observation time points is described by paying particular attention to the n-observability in the stochastic sense and the relation between sample and population qualities such as mean and covariance.
Two cases for the state reconstruction are treated such that the confidence intervals of the states are constructed (1) by using only the variances of the outputs at oprimal observation time points and (2) by using the variances and correlation function of the outputs.
In order to clarify the proposed technique for the state reconstruction a numerical example is given and the relations between the confidence intervals and the observation methods are discussed in detail.
