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Drake
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Drake
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Implementations of estimators that operate as Systems in a block diagram.
Algorithms that synthesize controllers are located in State Estimation.
Classes | |
| class | LuenbergerObserver< T > |
| 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... | |
| Eigen::MatrixXd | ObservabilityMatrix (const LinearSystem< double > &sys) |
| Returns the observability matrix: O = [ C; CA; ...; CA^{n-1} ]. More... | |
| bool | IsObservable (const LinearSystem< double > &sys, std::optional< double > threshold=std::nullopt) |
| Returns true iff the observability matrix is full column rank. More... | |
| bool | IsDetectable (const LinearSystem< double > &sys, std::optional< double > threshold=std::nullopt) |
| Returns true iff the system is detectable. More... | |
| bool drake::systems::IsDetectable | ( | const LinearSystem< double > & | sys, |
| std::optional< double > | threshold = std::nullopt |
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Returns true iff the system is detectable.
| bool drake::systems::IsObservable | ( | const LinearSystem< double > & | sys, |
| std::optional< double > | threshold = std::nullopt |
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Returns true iff the observability matrix is full column rank.
| Eigen::MatrixXd drake::systems::ObservabilityMatrix | ( | const LinearSystem< double > & | sys | ) |
Returns the observability matrix: O = [ C; CA; ...; CA^{n-1} ].
| Eigen::MatrixXd drake::systems::estimators::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.
This is a simplified form of the full Kalman filter obtained by assuming that the state-covariance matrix has already converged to its steady-state solution.
| A | The state-space dynamics matrix of size num_states x num_states. |
| C | The state-space output matrix of size num_outputs x num_states. |
| W | The process noise covariance matrix, E[ww'], of size num_states x num_states. |
| V | The measurement noise covariance matrix, E[vv'], of size num_. |
| std::exception | if V is not positive definite. |
| std::unique_ptr<LuenbergerObserver<double> > drake::systems::estimators::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.
| system | A unique_ptr to a LinearSystem describing the system to be observed. The new observer will take and maintain ownership of this pointer. |
| W | The process noise covariance matrix, E[ww'], of size num_states x num_states. |
| V | The measurement noise covariance matrix, E[vv'], of size num_. |
| std::exception | if V is not positive definite. |
| std::unique_ptr<LuenbergerObserver<double> > drake::systems::estimators::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.
Assuming system has the (continuous-time) dynamics: dx/dt = f(x,u), and the output: y = g(x,u), then the resulting observer will have the form dx̂/dt = f(x̂,u) + L(y - g(x̂,u)), where x̂ is the estimated state and the gain matrix, L, is designed as a steady-state Kalman filter using a linearization of f(x,u) at context as described above.
| system | A unique_ptr to a System describing the system to be observed. The new observer will take and maintain ownership of this pointer. |
| context | A unique_ptr to the context describing a fixed-point of the system (plus any additional parameters). The new observer will take and maintain ownership of this pointer for use in its internal forward simulation. |
| W | The process noise covariance matrix, E[ww'], of size num_states x num_states. |
| V | The measurement noise covariance matrix, E[vv'], of size num_. |
| std::exception | if V is not positive definite. |