gives the optimal discrete-time estimator gain matrix with sampling period τ for the continuous-time StateSpaceModel ssm, with process and measurement noise covariance matrices w and v.


specifies sensors as the noisy measurements of ssm.


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,{},τ] is equivalent to DiscreteLQEstimatorGains[{ssm, All,None},{},τ].
  • 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.


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Basic Examples  (1)

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

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Scope  (3)

Properties & Relations  (1)

Possible Issues  (1)

Introduced in 2010
Updated in 2012