Least Square Complex Non-Linear Curve Fitting

I am looking for Least Square Curve fitting of non linear complex numbers. I have this objective functions.

F = (a + bD) * Y^2 + (c + dD) * Z^2

Where F, a, b, Y, c, d, Z are all complex numbers. D is real number. To add that inputs to the model are Y, Z and D. Unknown are a,b, c and d. F is the known output. I found some article but those are talking about Real inputs and outputs with complex numbered coefficients. However, my case has all complex numbers except D.

Answer 1

[Torsten]

You won't be able to identify a,b,c,d,D separately.

Switch to the model

F = const1 * Y^2 + const2 * Z^2

and identify complex-valued const1 and const2 by splitting const1, const2, F, Y and Z in real and imaginary part.

Best wishes

Torsten.

[Maro]

Thanks for prompt comment. Sorry to add that D is known and will be given as input to the model. So inputs to the model are Y, Z and D. Unknown are a,b, c and D. F is the known output.

[Maro]

I have updated my question to clarify my point.

[Torsten]

My objection still holds even if D is known.

A complex number z can be written as z=a+b*D in many, many ways, e.g. z=0.5*z+D*0.5*z/D or z=0.2*z+D*0.8*z/D or ...

Thus the numbers a and b cannot be estimated independently which makes a separate fitting of the form z=a+D*b useless.

Best wishes

Torsten.