DiscreteLQEstimatorGains [ssm,{w,v},τ]
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.
DiscreteLQEstimatorGains [{ssm,sensors},{w,v},τ]
specifies sensors as the noisy measurements of ssm.
DiscreteLQEstimatorGains [{ssm,sensors,dinputs},{w,v},τ]
specifies dinputs as the deterministic inputs of ssm.
DiscreteLQEstimatorGains
DiscreteLQEstimatorGains [ssm,{w,v},τ]
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.
DiscreteLQEstimatorGains [{ssm,sensors},{w,v},τ]
specifies sensors as the noisy measurements of ssm.
DiscreteLQEstimatorGains [{ssm,sensors,dinputs},{w,v},τ]
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.
Examples
open all close allBasic Examples (1)
Compute the discrete LQ estimator gains for a continuous-time state-space model:
Scope (3)
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:
Find the optimal gains for a descriptor state-space model:
Properties & Relations (1)
Find estimator gains using DiscreteLQEstimatorGains :
Create a discrete-time Kalman estimator with the gains and a discretized model:
This is different from that obtained by discretizing a continuous-time estimator:
Response of the first estimator in the presence of process and measurement noises:
Response of the discretized Kalman estimator:
The responses are different:
Possible Issues (1)
The system must be detectable:
See Also
Related Guides
Text
Wolfram Research (2010), DiscreteLQEstimatorGains, Wolfram Language function, https://reference.wolfram.com/language/ref/DiscreteLQEstimatorGains.html (updated 2012).
CMS
Wolfram Language. 2010. "DiscreteLQEstimatorGains." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2012. https://reference.wolfram.com/language/ref/DiscreteLQEstimatorGains.html.
APA
Wolfram Language. (2010). DiscreteLQEstimatorGains. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/DiscreteLQEstimatorGains.html
BibTeX
@misc{reference.wolfram_2025_discretelqestimatorgains, author="Wolfram Research", title="{DiscreteLQEstimatorGains}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/DiscreteLQEstimatorGains.html}", note=[Accessed: 03-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_discretelqestimatorgains, organization={Wolfram Research}, title={DiscreteLQEstimatorGains}, year={2012}, url={https://reference.wolfram.com/language/ref/DiscreteLQEstimatorGains.html}, note=[Accessed: 03-January-2026]}