Function File: [est, g, x] = kalman (sys, q, r)

Function File: [est, g, x] = kalman (sys, q, r, s)

Function File: [est, g, x] = kalman (sys, q, r, [], sensors, known)

Function File: [est, g, x] = kalman (sys, q, r, s, sensors, known)

Design Kalman estimator for LTI systems.

Inputs

sys

Nominal plant model.

q

Covariance of white process noise.

r

Covariance of white measurement noise.

s

Optional cross term covariance. Default value is 0.

sensors

Indices of measured output signals y from sys. If omitted, all outputs are measured.

known

Indices of known input signals u (deterministic) to sys. All other inputs to sys are assumed stochastic. If argument known is omitted, no inputs u are known.

Outputs

est

State-space model of the Kalman estimator.

g

Estimator gain.

x

Solution of the Riccati equation.

Block Diagram

                                 u  +-------+         ^
      +---------------------------->|      |-------> y
      |   +-------+     +       y  | est  |        ^
u ----+--->|      |----->(+)------>|      |-------> x
           | sys  |      ^ +      +-------+
w -------->|      |      |
           +-------+       |v

Q = cov (w, w')     R = cov (v, v')     S = cov (w, v')

See also: care, dare, estim, lqr.

Package: control