control.lqe¶
-
control.
lqe
(A, G, C, QN, RN[, N])¶ Linear quadratic estimator design (Kalman filter) for continuous-time systems. Given the system
with unbiased process noise w and measurement noise v with covariances
The lqe() function computes the observer gain matrix L such that the stationary (non-time-varying) Kalman filter
produces a state estimate that x_e that minimizes the expected squared error using the sensor measurements y. The noise cross-correlation NN is set to zero when omitted.
- Parameters
A (2D array) – Dynamics and noise input matrices
G (2D array) – Dynamics and noise input matrices
QN (2D array) – Process and sensor noise covariance matrices
RN (2D array) – Process and sensor noise covariance matrices
NN (2D array, optional) – Cross covariance matrix
- Returns
L (2D array (or matrix)) – Kalman estimator gain
P (2D array (or matrix)) – Solution to Riccati equation
E (1D array) – Eigenvalues of estimator poles eig(A - L C)
Notes
The return type for 2D arrays depends on the default class set for state space operations. See
use_numpy_matrix()
.Examples
>>> K, P, E = lqe(A, G, C, QN, RN) >>> K, P, E = lqe(A, G, C, QN, RN, NN)
See also