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Function Reference: kalman

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)
Function File: [est, g, x] = kalman (sys, Q, R, [], sensors, known, type)
Function File: [est, g, x] = kalman (sys, Q, R, S, sensors, known, type)

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 or empty, 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 or empty, the first m-l inputs to sys are known, where m is the total number of inputs to sys and l is the size of the quadratic matrix Q.

type

Type of the estimator for discrete-time systems. If set to ’delayed’ the current estimation is based on y(k-1), if set to ’current’ the current estimation is based on the lates mesaruement y(k). If omitted, the ’delayed’ version is created.

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

Source Code: kalman