kkf.solution#

Solution data structure for Koopman Kalman Filter results.

Provides the KoopmanKalmanFilterSolution dataclass for storing and accessing filter outputs.

Classes

KoopmanKalmanFilterSolution(x_plus, x_minus, ...)

A class to store the solution of a Koopman-Kalman Filter iteration.
class kkf.solution.KoopmanKalmanFilterSolution(x_plus, x_minus, Pz_plus, Pz_minus, Px_plus, Px_minus, S, K)[source]#

Bases: object

A class to store the solution of a Koopman-Kalman Filter iteration.

This class maintains the state estimates, covariance matrices, and filter gains for both the prior (minus) and posterior (plus) estimates in both state and feature spaces.

Parameters:
x_plus#

Posterior state estimate after measurement update.

Type:

np.ndarray

x_minus#

Prior state estimate from prediction step.

Type:

np.ndarray

Pz_plus#

Posterior covariance matrix in feature space after measurement update.

Type:

np.ndarray

Pz_minus#

Prior covariance matrix in feature space from prediction step.

Type:

np.ndarray

Px_plus#

Posterior covariance matrix in state space after measurement update.

Type:

np.ndarray

Px_minus#

Prior covariance matrix in state space from prediction step.

Type:

np.ndarray

S#

Innovation (residual) covariance matrix.

Type:

np.ndarray

K#

Kalman gain matrix.

Type:

np.ndarray

Notes

The class uses the common Kalman filter notation where: - (-) denotes prior estimates before measurement update - (+) denotes posterior estimates after measurement update - Pz refers to covariances in the feature/transformed space - Px refers to covariances in the original state space

Examples

>>> solution = KoopmanKalmanFilterSolution(
...     x_plus=np.array([1.0, 2.0]),
...     x_minus=np.array([0.9, 1.9]),
...     Pz_plus=np.eye(2),
...     Pz_minus=np.eye(2) * 1.1,
...     Px_plus=np.eye(2) * 0.9,
...     Px_minus=np.eye(2),
...     S=np.eye(2) * 0.5,
...     K=np.array([[0.1, 0], [0, 0.1]])
... )
get_estimation_error()[source]#

Calculate the difference between prior and posterior estimates.

Returns:

The difference between posterior and prior state estimates.

Return type:

np.ndarray

get_feature_dimension()[source]#

Get the dimension of the feature space.

Returns:

The dimension of the feature space.

Return type:

int

get_state_dimension()[source]#

Get the dimension of the state vector.

Returns:

The dimension of the state vector.

Return type:

int

get_trace_reduction()[source]#

Calculate the reduction in uncertainty as measured by trace of covariance.

Returns:

The relative reduction in trace of the state covariance matrix.

Return type:

float

to_dict()[source]#

Convert the solution to a dictionary format.

Returns:

Dictionary containing all solution components.

Return type:

dict