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DiscreteLQEstimatorGains

DiscreteLQEstimatorGains
gives the optimal discrete-time estimator gain matrix with sampling period for the continuous-time StateSpaceModel object ss with process and measurement noise covariance matrices w and v.
DiscreteLQEstimatorGains
specifies sensors as the noisy measurements of ss.
DiscreteLQEstimatorGains
specifies dinputs as the deterministic inputs of ss.
  • The state-space model ss can be given as StateSpaceModel, where a, b, c, and d represent the state, input, output, and transmission matrices of the continuous-time system .
  • 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 .
  • 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.
  • The state-space model ss is discretized using the zero-order hold method.
Compute the discrete LQ estimator gains for a continuous-time state-space model:
Compute the discrete LQ estimator gains for a continuous-time state-space model:
In[1]:=
Click for copyable input
Out[1]=
Compute the discrete-time Kalman gains for a state-space model:
The gains based on the measurement of just the second output:
The gains for a system in which all inputs except the first are stochastic:
The estimator dynamics are given by , where , , , and are the state-space matrices of the system discretized using zero-order hold:
The discretized estimator:
The two estimators are not the same:
The system must be detectable:
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