What exactly does compare(___,kstep) plot?

I read this material https://ww2.mathworks.cn/help/ident/ug/definition-simulation-and-prediction.html and I still can not figure out what each data point represent when I use compare(idataexample,sys,2).

For example, as mentioned here

at t = 10, we predict 2 steps：

yp(11|10) = 0.9ym(10) + 1.5um(10),

yp(12|10) = 0.9yp(11|10) + 1.5um(11).

And so on, at t = 11, we predict 2 steps,：

yp(12|11) = 0.9ym(11) + 1.5um(11),

yp(13|11) = 0.9yp(12|11) + 1.5um(12).

So, when

compare

finally gives a plot, what does the value at t = 12 represent? Is it yp(12|10), yp(12|11), or something else?

By the way, I think there might be an error in the example(CompareEstimatedModeltoMeasuredDataExample') in the documentation ("For instance, the point at t = 15s is based on output measurements taken at or prior to t = 5s").

Thanks in advance for your help!

Answer 1

[Karan Singh]

Hi @Mingming Du,

First, I am not able to open the links you provided. I tried some modifications, but I still couldn't access it.

Now moving one to your query, when you run

compare(data, sys, 2)

The function evaluates 2-step-ahead predictions for every time step based on past measurements.

At each time step " t ", the prediction " yp(t+2∣t) " is computed using available past input-output data. When "compare" plots a prediction at " t=12 ", it is actually plotting " yp(12∣10) " because:

• The horizon is 2, meaning we predict " t+2 " values.
• The prediction at " t=12 " was made at " t=10 ", using the available measured data up to " t=10 ".

You can read more about it here: https://in.mathworks.com/help/ident/ref/compare.html#d126e31029

Karan

[Walter Roberson]

The URL posted originally ended in a comma; I have repaired it now.

[Mingming Du]

@Karan Singh @Walter Roberson Really appreciate for your help.