Concerning the observability of the dynamical modes, it turns our that the invariants put certain restrictions on the observation matrix for the system to be observable.
The main assumptions here are that the system is overdetermined (there exist more observed signals than sources) and that the columns of the observation matrix act as point-spreading functions (see Sect. 2).
A concept analogous to an observation matrix enabling only the measurement of displacements is then proposed.
We will analyze the model-case when the observation matrix has i.i.d.\ elements and the components of the ground-truth signal are taken independently from some known distribution.
The estimators require knowledge of the system matrix, the observation matrix and the variance of the state vector.
Secondly, we determine the optimal combination of platform orientations by minimizing the condition number of observation matrix.
Namely, the estimation algorithms use the observation matrix, the system matrix for the state variable and the crossvariance function between the state variable and the signal.
In this approach, the initial value for observation matrix B in HMM is selected based on the predictive neural network and intuitionistic fuzzy sets.
Based on observation matrix of a structure׳s frequency response, two optimal criteria are used to avoid the information redundancy of the candidate degrees of freedom.
For these systems, it is assumed that results of the discrete-time observations are available performed in the presence of bounded perturbations of the observation matrix (considered, e.g., as uncertainty of measuring device scale), and also additive errors.
The RLS Wiener estimators use the following information: (a) the system matrix; (b) the observation matrix; (c) the variance of the state vector; (d) the delay probabilities pj(k) and (e) the variance of white observation noise.
