Data assimilation

Data assimilation means the incorporation of data into a model. A core application of this is to keep models of chaotic systems on track and away from divergence.

Notation

Continuous

\[ \begin{align} \dot{x}_t &= \textbf{M}(x_t) & \text{non-linear}\\ \dot{x}_t &= \textbf{M}_tx_t & \text{linear}\\ \dot{x}_t &= \textbf{M}x_t & \text{time-invariant}\\ \end{align} \]

Discrete

\[ \begin{align} \dot{x}_{k+1} &= \textbf{M}(x_k) & \text{non-linear}\\ \dot{x}_{k+1} &= \textbf{M}_kx_k+\textbf{B}_ku_k & \text{linear}\\ \dot{x}_{k+1} &= \textbf{M}x_k & \text{time-invariant} \end{align} \]