kalman

Design Kalman filter for state estimation.

Syntax

• [kalmf, L, P, M, Z] = kalman(sys, Q, R, N)
• [kalmf, L, P, M, Z] = kalman(sys, Q, R, N, sensors, known)

Input argument

• sys - Plant model with process noise: state-space model.
• Q - Process noise covariance: scalar or matrix.
• R - Measurement noise covariance: scalar or matrix.
• N - Noise cross covariance: scalar or matrix.
• sensors - Measured outputs of sys: vector.
• known - Known inputs of sys: vector.

Output argument

• kalmf - Kalman estimator: state-space model
• L - Filter gains: matrix
• P - Steady-state error covariances: matrix
• M - Innovation gains of state estimators: matrix
• Z - Steady-state error covariances: matrix

Description

[kalmf, L, P] = kalman(sys, Q, R, N) generates a Kalman filter using the provided plant model sys and noise covariance matrices Q, R, and N.

The function calculates a Kalman filter suitable for application in a Kalman estimator, as depicted in the following diagram.

Example

A = [11.269   -0.4940    1.129; 1.0000         0         0;0    1.0000         0];
B = [-0.3832;  0.5919;  0.5191];
C = [1 0 0];
sys = ss(A,[B, B], C, 0);
Q = 1;
R = 1;
[kEst, l, p, m, z] = kalman(sys, Q, R, [])

See also

care, dare.

History

Author

Allan CORNET