BUILT-IN MATHEMATICA SYMBOL

# DiscreteLQEstimatorGains

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 OptionsDetails 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.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Compute the discrete LQ estimator gains for a continuous-time state-space model:

 Out[1]=