Hi,
I understand that you want to see the values of Projection Matrix (P) when using the linear mapping in NLARX models.
The 'idlinear' object in MATLAB's System Identification Toolbox represents a linear mapping object that can be used in non-linear ARX models and other non-linear models as a part of the custom regressor definition. The projection matrix 'P' is a property of this 'idlinear' object, which defines the linear transformation applied to the regressors.
Mathematically, 'idLinear' is a linear function 'y=F(x)' that maps 'm' inputs 'X(t) = [x(t1),x2(t),…,xm(t)]T' to a scalar output 'y(t)'. 'F' is a (affine) function of 'x':
y(t)=y0+Χ(t)TPL
Here:
X(t) is an m-by-1 vector of inputs, or regressors.
y0 is the output offset, a scalar.
P is an m-by-p projection matrix, where m is the number of regressors and is p is the number of linear weights. m must be greater than or equal to p.
L is a p-by-1 vector of weights.
We can compute these values and properties of 'idlinear' just by using dot operator with the 'idlinear' object.
Now, these can be used with the help of the above given formula to calculate the Projection Matrix(P).
Refer to the following MathWorks documentation for detailed information regarding 'idLinear':
