navlie.lib.preintegration.PreintegratedLinearModel¶
- class navlie.lib.preintegration.PreintegratedLinearModel¶
Bases:
ProcessModelProcess model that applies a preintegrated LinearIncrement to predict a state forward in time using the equation
\[\mathbf{x}_k = \mathbf{A}_{ij} \mathbf{x}_i + \Delta \mathbf{u}_{ij}\]- evaluate_with_jacobian(x: ~navlie.types.State, u: ~navlie.types.Input, dt: float) -> (<class 'navlie.types.State'>, <class 'numpy.ndarray'>)¶
Evaluates the process model and simultaneously returns the Jacobian as its second output argument. This is useful to override for performance reasons when the model evaluation and Jacobian have a lot of common calculations, and it is more efficient to calculate them in the same function call.
- input_covariance(x: State, u: Input, dt: float) → ndarray¶
Covariance matrix of additive noise on the input.
- input_jacobian_fd(x: State, u: Input, dt: float, step_size=1e-06, *args, **kwargs) → ndarray¶
Calculates the input jacobian with finite difference.
- jacobian_fd(x: State, u: Input, dt: float, step_size=1e-06, *args, **kwargs) → ndarray¶
Calculates the model jacobian with finite difference.
- evaluate(x: VectorState, rmi: LinearIncrement, dt=None) → VectorState¶
Implementation of \({f}(\mathcal{X}_{k-1}, \mathbf{u}, \Delta t)\).
- jacobian(x: VectorState, rmi: LinearIncrement, dt=None) → ndarray¶
Implementation of the process model Jacobian with respect to the state.
\[\mathbf{F} = \frac{D {f}(\mathcal{X}_{k-1}, \mathbf{u}, \Delta t)}{D \mathcal{X}_{k-1}}\]
- covariance(x: VectorState, rmi: LinearIncrement, dt=None) → ndarray¶
Covariance matrix \(\mathbf{Q}_k\) of the additive Gaussian noise \(\mathbf{w}_{k} \sim \mathcal{N}(\mathbf{0}, \mathbf{Q}_k)\). If this method is not overridden, the covariance of the process model error is approximated from the input covariance using a linearization procedure, with the input Jacobian evaluated using finite difference.