ssest function - identification toolbox

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Alex
Alex 2012-9-20
评论： Benjamin Pommer 2022-11-2
Hello!
I'm using ssest function to estimate a state-space model of one dimensional signal. When I use ssest(y,2) I get a state-space model. However, I'd like to specify some free parameters in this state-space form:
A = [1 0;0 1]; B = [0.5; 0.5]; C = [1 1]; D = [0.1];
I package this into a model object idss(A,B,C,D) and specify the free parameters to be estimated as in this demo http://www.mathworks.com/products/sysid/examples.html?file=/products/demos/shipping/ident/iddemo7.html, but when I use ssest an error appears saying that "the number of inputs and outputs of the model must match...". So I wrote the state-space model adding some white noise inputs and zero outputs in order to match the dimensions but I got a fit to estimation data of -891.8%
Can anyone give me some guidance about the form to write this state-space model in order to apply ssest function specifying free parameters?
Do I have to use state-space models with specific dimensions? It means that I can't use a state-space model as above although it's dimensionally correct?
Thanks in advance!

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回答（1 个）

Rajiv Singh
Rajiv Singh 2012-9-21
Hi Alex,
Could you post some more details? When you originally created the model object (idss(A,B,C,D)), what were the sizes of the matrices? If you are fitting a model to a single signal, B must be nx-by-0, C must be 1-by-nx, and D must be 1-by-0 matrix. You probably would need a K matrix of size nx-by-1 defining the initial value of disturbance matrix K (could be NaNs if you do not have an initial guess), so you actually create idss(A,B,C,D,K). Note that when you fit a signal, it is treated as a time series (a process driven by white noise):
dx/dt = A x + Ke
y = Cx + e
This is conceptually similar to the single-input, single-output model, if you think of e(t) as input u (t). Then K (times square root of noise variance) represents the "B" matrix and D = 1 of the standard state-space form. In fact, you can use "noise2meas" command to convert the time series model into a more familiar input-output model.
Direct estimation: If you want to fit a state-space model directly (that is, no intermediate creation of a model), you can use the syntax ssest(y,2) just the way you originally tried. For more control over data properties, you should actually do:
% also specify sample time and start time
data iddata(y, [], Ts, 'tstart', 0);
model = ssest(data, 2);
iomodel = noise2meas(model);
If that did not work for you, you must post some reproduction steps so that I can investigate it more thoroughly.
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Alex
Alex 2012-9-26
Hi Rajiv,
This is what I'm trying to achieve: I have a time series y that can be modeled in this way "there are not inputs"
x(k+1) = A x(k) + w
y(k) = C x(k+1) + e
where w and e are independent white-noise terms with covariance matrices R1 and R2, respectively. As you mentioned it seems to be like a kalman filter representation. There are also free and fixed parameters, so I apply constrains as explained above.
Following the example (with IDGREY) I implemented the model having y and one input white noise:
A = [par1 0;0 1];
B = [0 ; 0];
C = [1 1];
D = [0];
R1 = [par2 0; 0 par3];
R2 = aux
However KF does not converges. I will check if it works with a different state-space representation.
Thanks!
Benjamin Pommer
Benjamin Pommer 2022-11-2
Do you know how one can label the outputs from the estimated model when you use the compare command?

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