Unobservable Systems: No Problem for Noise Identification

This paper deals with the noise identification of a linear time-varying stochastic dynamic system described by the state-space model. In particular, the stress is laid on the design of the correlation measurement difference method for estimation of the state and measurement noise covariance matrices for both observable and $\mathit{\text{unobservable}}$ systems with possibly unknown input sequence. The method provides unbiased and consistent estimates and is implemented in a publicly available MATLAB toolbox and numerically evaluated.