Can process noise matrix be extracted from Linear System Model?

Given I have a linear discrete system identified by using the System Identification Toolbox, of the following standard form:
y = Cx + Du + e
x = Ax + Bu + Ke
If I extract A, B, C, D, K matrices in addition to NoiseVariance (which represents the variance of the model versus the measurements it was identified from), and additionally I have the variance of input, can I calculate the Q (process noise covariance) matrix from that information?
I looked at several topics and forum posts, for example:
https://www.mathworks.com/help/control/ug/kalman-filtering.html
https://www.mathworks.com/help/ident/ug/estimating-states-of-time-varying-systems-using-kalman-filters.html
https://www.mathworks.com/matlabcentral/answers/1722215-kalman-filter-discrete-system-kalmf-r-and-q-do-not-seem-to-influence-the-performance-of-the-kalman
https://www.mathworks.com/matlabcentral/answers/339275-how-to-set-q-and-r-in-a-kalman-filter
https://www.mathworks.com/matlabcentral/answers/122661-finding-out-q-and-r-matrices-of-a-given-system
https://dsp.stackexchange.com/questions/21796/question-about-q-matrix-model-process-covariance-in-kalman-filter
The consensus seems to be, that if I used the Matlab System Identification Toolbox to identify the linear discrete system (let’s call it ss1), then Q is given by:
% N is the order of the system, i.e. 3rd order N = 3
N = length(ss1.x0);

% Q = NoiseVariance * Identity + InputVariance * Contribution of Input
Q = ss1.NoiseVariance * eye(N) + ss1.B * inputVariance * ss1.B’
Is this accurate? Here’s an example from a system I identified.
% Generated by Matlab System Identification
N = 3;
NoiseVariance = 0.0026;
B = 1.0e-04 * [ -0.0001 0.0141 -0.1492];

% Provided by me (SISO system, just one input)
inputVariance = 0.001;

% Calculate process noise covariance
Q = NoiseVariance * eye(N) + B * inputVariance * B’;
I get this:
Q =

0.0026 -0.0000 0.0000
-0.0000 0.0026 -0.0000
0.0000 -0.0000 0.0026
…basically an identity because the B matrix (contribution of input directly into output) is:
B =

1.0e-04 *

-0.0001
0.0141
-0.1492Given I have a linear discrete system identified by using the System Identification Toolbox, of the following standard form:
y = Cx + Du + e
x = Ax + Bu + Ke
If I extract A, B, C, D, K matrices in addition to NoiseVariance (which represents the variance of the model versus the measurements it was identified from), and additionally I have the variance of input, can I calculate the Q (process noise covariance) matrix from that information?
I looked at several topics and forum posts, for example:
https://www.mathworks.com/help/control/ug/kalman-filtering.html
https://www.mathworks.com/help/ident/ug/estimating-states-of-time-varying-systems-using-kalman-filters.html
https://www.mathworks.com/matlabcentral/answers/1722215-kalman-filter-discrete-system-kalmf-r-and-q-do-not-seem-to-influence-the-performance-of-the-kalman
https://www.mathworks.com/matlabcentral/answers/339275-how-to-set-q-and-r-in-a-kalman-filter
https://www.mathworks.com/matlabcentral/answers/122661-finding-out-q-and-r-matrices-of-a-given-system
https://dsp.stackexchange.com/questions/21796/question-about-q-matrix-model-process-covariance-in-kalman-filter
The consensus seems to be, that if I used the Matlab System Identification Toolbox to identify the linear discrete system (let’s call it ss1), then Q is given by:
% N is the order of the system, i.e. 3rd order N = 3
N = length(ss1.x0);

% Provided by me (SISO system, just one input)
inputVariance = 0.001;

% Calculate process noise covariance
Q = NoiseVariance * eye(N) + B * inputVariance * B’;
I get this:
Q =

0.0026 -0.0000 0.0000
-0.0000 0.0026 -0.0000
0.0000 -0.0000 0.0026
…basically an identity because the B matrix (contribution of input directly into output) is:
B =

1.0e-04 *

-0.0001
0.0141
-0.1492 Given I have a linear discrete system identified by using the System Identification Toolbox, of the following standard form:
y = Cx + Du + e
x = Ax + Bu + Ke
If I extract A, B, C, D, K matrices in addition to NoiseVariance (which represents the variance of the model versus the measurements it was identified from), and additionally I have the variance of input, can I calculate the Q (process noise covariance) matrix from that information?
I looked at several topics and forum posts, for example:
https://www.mathworks.com/help/control/ug/kalman-filtering.html
https://www.mathworks.com/help/ident/ug/estimating-states-of-time-varying-systems-using-kalman-filters.html
https://www.mathworks.com/matlabcentral/answers/1722215-kalman-filter-discrete-system-kalmf-r-and-q-do-not-seem-to-influence-the-performance-of-the-kalman
https://www.mathworks.com/matlabcentral/answers/339275-how-to-set-q-and-r-in-a-kalman-filter
https://www.mathworks.com/matlabcentral/answers/122661-finding-out-q-and-r-matrices-of-a-given-system
https://dsp.stackexchange.com/questions/21796/question-about-q-matrix-model-process-covariance-in-kalman-filter
The consensus seems to be, that if I used the Matlab System Identification Toolbox to identify the linear discrete system (let’s call it ss1), then Q is given by:
% N is the order of the system, i.e. 3rd order N = 3
N = length(ss1.x0);

% Provided by me (SISO system, just one input)
inputVariance = 0.001;

% Calculate process noise covariance
Q = NoiseVariance * eye(N) + B * inputVariance * B’;
I get this:
Q =

0.0026 -0.0000 0.0000
-0.0000 0.0026 -0.0000
0.0000 -0.0000 0.0026
…basically an identity because the B matrix (contribution of input directly into output) is:
B =

1.0e-04 *

-0.0001
0.0141
-0.1492 system, digital signal processing MATLAB Answers — New Questions

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