Drake
drake::systems::estimators Namespace Reference

Classes

class  LuenbergerObserver
A simple state observer for a dynamical system of the form:

$\dot{x} = f(x,u)$

$y = g(x,u)$

the observer dynamics takes the form

$\dot{\hat{x}} = f(\hat{x},u) + L(y - g(\hat{x},u))$

where $$\hat{x}$$ is the estimated state of the original system. More...

Functions

Eigen::MatrixXd SteadyStateKalmanFilter (const Eigen::Ref< const Eigen::MatrixXd > &A, const Eigen::Ref< const Eigen::MatrixXd > &C, const Eigen::Ref< const Eigen::MatrixXd > &W, const Eigen::Ref< const Eigen::MatrixXd > &V)
Computes the optimal observer gain, L, for the linear system defined by

$\dot{x} = Ax + Bu + w,$

$y = Cx + Du + v.$

The resulting observer is of the form

$\dot{\hat{x}} = A\hat{x} + Bu + L(y - C\hat{x} - Du).$

The process noise, w, and the measurement noise, v, are assumed to be iid mean-zero Gaussian. More...

std::unique_ptr< LuenbergerObserver< double > > SteadyStateKalmanFilter (std::unique_ptr< LinearSystem< double >> system, const Eigen::Ref< const Eigen::MatrixXd > &W, const Eigen::Ref< const Eigen::MatrixXd > &V)
Creates a Luenberger observer system using the optimal steady-state Kalman filter gain matrix, L, as described above. More...

std::unique_ptr< LuenbergerObserver< double > > SteadyStateKalmanFilter (std::unique_ptr< System< double >> system, std::unique_ptr< Context< double >> context, const Eigen::Ref< const Eigen::MatrixXd > &W, const Eigen::Ref< const Eigen::MatrixXd > &V)
Creates a Luenberger observer system using the steady-state Kalman filter observer gain. More...