Inputs

sys

LTI model.

l

State feedback matrix.

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 (w). If argument known is omitted or empty, no inputs u are known.

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 estimator.

Block Diagram

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

Remarks

The argument type is for discrete-time systems only. If set to ’current’, the follwong prediction-correction scheme is used:

 ^           ^
 x*(k+1) = A x(k) + B u(k)
    ^      ^        -1
    x(k) = x*(k) + A   L (y(k) - C x*(k) - D u(k))

The inverse fo the system matrix in the above equations is required for maintaining the desired observer error dynamics given by (A - LC).

The advantage of this structure is that the current measurement y(k) is used for the current estiamted state and not for the next allowing the estimator to react to system disturbances faster. L is the observer feedback matrix for the common observer structure with the matrix (A - LC) being asymptotically stable, i.e. has eigenvalues strictly within the unit circle.

See also: kalman, lqe, place

Source Code: estim