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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">measurement difference method</i> for estimation of the state and measurement noise covariance matrices for both <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">observable</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unobservable</i> 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.