Abstract
We present a new method for the state estimation, based on uncertainty quantification (UQ), which allows efficient numerical determination of probability distributions. We adapt these methods in order to allow the representation of the probability distribution of the state. By assuming that the mean corresponds to real state (i.e; that there is no bias in measurements), the state is estimated. UQ determines expansions of an unknown random variable as functions of given ones. The distributions may be quite general-namely, Gaussian/normality assumptions are not necessary. In the framework of state estimation, the natural given variables are the measurement errors, which may be partially or totally unknown. We examine these situations and we show that an artificial variable may be used instead the real one. We examine three approaches for the determination of the probability distribution of the state: moment matching (MM), collocation (COL) and variational (VAR). We show that the method is effective to calculate by using two significant examples: a classical discrete linear system containing difficulties and the Influenza in a boarding school. In all these examples, the proposed approach was able to accurately estimate the values of the state variables. The approach may also be used for non-additive noise and for the determination of the distribution of the noise.