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Form state estimator given estimator gain

`est = estim(sys,L) est = estim(sys,L,sensors,known) `

`est = estim(sys,L) ` produces
a state/output estimator `est` given the plant state-space
model `sys` and the estimator gain `L`.
All inputs *w* of `sys` are assumed
stochastic (process and/or measurement noise), and all outputs *y* are
measured. The estimator `est` is returned in state-space
form (SS object).

For a continuous-time plant `sys` with equations

`estim` uses the following equations to generate
a plant output estimate
and a state estimate
, which are estimates
of *y*(*t*)=*C* and *x*(*t*),
respectively:

For a discrete-time plant `sys` with the following
equations:

`estim` uses estimator equations similar to
those for continuous-time to generate a plant output estimate
and a state estimate
, which are estimates
of *y*[*n*] and *x*[*n*],
respectively. These estimates are based on past measurements up to *y*[*n-1*].

`est = estim(sys,L,sensors,known) `
handles more general plants `sys` with both known
(deterministic) inputs *u* and stochastic inputs *w*,
and both measured outputs *y* and nonmeasured outputs *z*.

The index vectors `sensors` and `known` specify
which outputs of `sys` are measured (*y*),
and which inputs of `sys` are known (*u*).
The resulting estimator `est`, found using the following
equations, uses both *u* and *y* to
produce the output and state estimates.

Consider a state-space model `sys` with seven
outputs and four inputs. Suppose you designed a Kalman gain matrix *L* using
outputs 4, 7, and 1 of the plant as sensor measurements and inputs
1, 4, and 3 of the plant as known (deterministic) inputs. You can
then form the Kalman estimator by

sensors = [4,7,1]; known = [1,4,3]; est = estim(sys,L,sensors,known)

See the function `kalman` for
direct Kalman estimator design.

`kalman` | `kalmd` | `lqgreg` | `place` | `predict` | `reg` | `ss` | `ssest`

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