# Process Models¶

## Introduction¶

As the state-transition model is nonlinear, the state-transition vector cannot be directly used to propagate the covariance forward in time. Instead the state-transition vector, \(\vec{f}\), is linearized based on the current system states and used for this task. The resulting linearization (computed from the partial derivatives of \(\vec{f}\) with respect to the system states, \(\vec{x}\)) generates a matrix referred to as the Process Jacobian, \(F\). This matrix is used to propagate the covariance, \(P\), forward in time.

The covariance estimate is also affected by the process noise, which is related to sensor-noise levels. The more process noise that exists in a system, the larger the covariance estimate will be at the next time step. This noise is reflected in the process-noise covariance matrix, \(Q\).

Formulation of these matrices are described in the following sections.