pydrake.systems.estimators

class pydrake.systems.estimators.LuenbergerObserver

Bases: pydrake.systems.framework.LeafSystem

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.

The output of the observer system is \(\hat{x}\).

observed system input→

observed_system_output→

LuenbergerObserver

→ estimated_state

__init__(self: pydrake.systems.estimators.LuenbergerObserver, observed_system: pydrake.systems.framework.System, observed_system_context: pydrake.systems.framework.Context, observer_gain: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous]) → None

Constructs the observer.

Parameter observed_system:: The forward model for the observer. Currently, this system must have a maximum of one input port and exactly one output port.
Parameter observed_system_context:: Required because it may contain parameters which we need to evaluate the system.
Parameter observer_gain:: A m-by-n matrix where m is the number of state variables in observed_system, and n is the dimension of the output port of observed_system.
Precondition:: The observed_system output port must be vector-valued.

Note: The observed_system reference must remain valid for the lifetime of this system.

get_estimated_state_output_port(self: pydrake.systems.estimators.LuenbergerObserver) → pydrake.systems.framework.OutputPort

get_observed_system_input_input_port(self: pydrake.systems.estimators.LuenbergerObserver) → pydrake.systems.framework.InputPort

get_observed_system_output_input_port(self: pydrake.systems.estimators.LuenbergerObserver) → pydrake.systems.framework.InputPort

L(self: pydrake.systems.estimators.LuenbergerObserver) → numpy.ndarray[numpy.float64[m, n]]: Provides access via the short-hand name, L, too.

observer_gain(self: pydrake.systems.estimators.LuenbergerObserver) → numpy.ndarray[numpy.float64[m, n]]: Provides access to the observer gain.

pydrake.systems.estimators.SteadyStateKalmanFilter(*args, **kwargs)

Overloaded function.

SteadyStateKalmanFilter(A: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], C: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], W: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], V: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous]) -> numpy.ndarray[numpy.float64[m, n]]

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.

Parameter A:: The state-space dynamics matrix of size num_states x num_states.
Parameter C:: The state-space output matrix of size num_outputs x num_states.
Parameter W:: The process noise covariance matrix, E[ww’], of size num_states x num_states.
Parameter V:: The measurement noise covariance matrix, E[vv’], of size num_.

Returns: The steady-state observer gain matrix of size num_states x num_outputs.
Raises: RuntimeError if V is not positive definite. –

SteadyStateKalmanFilter(system: pydrake.systems.primitives.LinearSystem, W: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], V: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous]) -> pydrake.systems.estimators.LuenbergerObserver

Creates a Luenberger observer system using the optimal steady-state Kalman filter gain matrix, L, as described above.

Parameter system:: A unique_ptr to a LinearSystem describing the system to be observed. The new observer will take and maintain ownership of this pointer.
Parameter W:: The process noise covariance matrix, E[ww’], of size num_states x num_states.
Parameter V:: The measurement noise covariance matrix, E[vv’], of size num_.

Returns: A unique_ptr to the constructed observer system.
Raises: RuntimeError if V is not positive definite. –

SteadyStateKalmanFilter(system: pydrake.systems.framework.System, context: pydrake.systems.framework.Context, W: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous], V: numpy.ndarray[numpy.float64[m, n], flags.f_contiguous]) -> pydrake.systems.estimators.LuenbergerObserver

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.

Parameter system:: A unique_ptr to a System describing the system to be observed. The new observer will take and maintain ownership of this pointer.
Parameter 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.
Parameter W:: The process noise covariance matrix, E[ww’], of size num_states x num_states.
Parameter V:: The measurement noise covariance matrix, E[vv’], of size num_.

Returns: A unique_ptr to the constructed observer system.
Raises: RuntimeError if V is not positive definite. –