statespacemodell
Statespacemodell, or state-space model, is a mathematical framework for describing the dynamic behavior of a system using a set of internal state variables that evolve over time. The model combines a state update equation with an observation equation, capturing how inputs and disturbances affect the system and how measurements relate to its hidden state.
In discrete time, the standard form is:
Here x_k is the state vector, u_k the input vector, y_k the output vector, and w_k and
In continuous time, the corresponding representation uses differential equations:
Key concepts in state-space modeling include observability (whether the internal state can be inferred from outputs)
Estimation and filtering play a central role. For linear Gaussian models, the Kalman filter provides optimal