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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. DiscreteLQEstimatorGainsspecifies sensors as the noisy measurements of ss. DiscreteLQEstimatorGainsspecifies 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:
 Out[1]=
 Scope   (2)
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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