State Blocks
State Blocks (SBs) provide the Fusion
plugin with states and the models to propagate those states.
State Blocks provide a set of states,
\(\mathbf{x}\). Let \(\mathbf{x}_k\) be the Mx1 vector representing
the value of \(\mathbf{x}\) at time \(t_k\). Then the Fusion
plugin assumes that the way \(\mathbf{x}\) changes
from one time epoch to the next is well-modeled by
where \(\mathbf{g}\) is the discrete-time propagation function, and \(\mathbf{w}\) is white Gaussian noise sources.
In the special case of a linear model, \(\mathbf{g}(\mathbf{x})\) can be written \(\mathbf{g}(\mathbf{x})=\mathbf{\Phi x}\), where \(\mathbf{\Phi}\) is the Jacobian matrix of \(\mathbf{g}(\mathbf{x})\). The discrete-time process noise covariance matrix is defined as \(\mathbf{Q_d}=E[\mathbf{w}_{k}\mathbf{w}_{k}^T]\).
When a Fusion plugin wants to propagate a set of
states from \(\mathbf{x}_{k-1}\) to \(\mathbf{x}_{k}\), it queries the
State Block which provides those states for
the three elements of the dynamics model: \(\mathbf{g}(\mathbf{x})\),
\(\mathbf{\Phi}\), and \(\mathbf{Q_d}\).