How to use "recursiveLS( )" and "step( )" functions

I have a model in this way:

Where are output variables and P is the input. All of the variables are column vectors.

This is my design matrix:

N: total number of samples in my experiment.

I want to estimate the regression coefficients to calculate the next outputs . I wrote this code:

function rls = l_rls(T1, T2, P, lambda)

T1, T2 are vectors with the measured outputs and P is a vector of the measured input

N = length(P);

X = [ones(N-1, 1), T1(1:N-1), T2(1:N-1), P(2:N), P(1:N-1)]; %Design matrix
ncoef = size(X,2);
Y = [T1(2:end), T2(2:end)]; %These is my output matrix.

rls = recursiveLS(ncoef, lambda);

[A, Tst] = step(rls, Y, P)

end

However, when I run this code, I get this error message:

Error using recursiveLS/validateInputsImpl

Error in signal dimensions. The number of elements in the input signal u

(regressors) (5819) must match with the NumberOfParameters property (5).

Error in l_rls (line 10)

[As, Ts] = step(rls,Y,P);

If I change the line with "step" function:

[A, Tst] = step(rls, Y, X);

The error message is now:

Error using recursiveLS/validateInputsImpl

Error in signal dimensions. The input signal u (Regressors) must be a vector.

Error in l_rls (line 10)

[A, Tst] = step(rls,Y,X);

I can't understand how to use "step( )" function to obtain coefficients and estimated outputs.

[Mario Malic]

You have to transpose the X and Y in your function, because they are row vectors.

[OSCAR BELLON-HERNANDEZ]

No, the error message it is still the same.

[Mario Malic]

There are not many people who use this toolbox, unfortunately and I am new with it.

You probably are not calling the function correctly, if I understood correctly the documentation, size of ncoef and lambda has to be the same.

If you want to do step, try iddata function, then estimate parameters by some of the functions like idgrey, nlarx, era and then apply step.

Take this with grain of salt because I don't understand completely what are we doing with these functions.