# 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.