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BUILT-IN MATHEMATICA SYMBOL
DiscreteLQEstimatorGains[ssm, {w, v}, 
]
gives the optimal discrete-time estimator gain matrix with sampling period for the continuous-time StateSpaceModel ssm, with process and measurement noise covariance matrices w and v.
DiscreteLQEstimatorGains[{ssm, sensors}, {w, v}, ]
specifies sensors as the noisy measurements of ssm.
DiscreteLQEstimatorGains[{ssm, sensors, dinputs}, {w, v}, ]
specifies dinputs as the deterministic inputs of ssm.
Details and Options
- The standard state-space model ssm can be given as StateSpaceModel[{a, b, c, d}], where a, b, c, and d represent the state, input, output, and transmission matrices of the continuous-time system
. - The descriptor continuous-time state-space model ssm defined by
can be given as StateSpaceModel[{a, b, c, d, e}]. - The input
can include the process noise 
, as well as deterministic inputs 
. - The argument dinputs is a list of integers specifying the positions of
in 
. - The output
consists of the noisy measurements 
, as well as other outputs. - The argument sensors is a list of integers specifying the positions of
in 
. - DiscreteLQEstimatorGains[ssm, {...}, ] is equivalent to DiscreteLQEstimatorGains[{ssm, All, None}, {...}, ].
- The noisy measurements are modeled as
, where 
and 
are the submatrices of 
and 
associated with 
, and 
is the noise. - The process and measurement noises are assumed to be white and Gaussian:
-
, 
process noise 
, 
measurement noise - The estimator with the optimal gain minimizes
, where 
is the estimated state vector. - DiscreteLQEstimatorGains computes the estimator gains based on the discrete equivalent of the noise matrices.
- The state-space model ssm is discretized using the zero-order hold method.
Examplesopen all
Basic Examples (1)
Compute the discrete LQ estimator gains for a continuous-time state-space model:
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