I've been learning (lurking) from this site for a while and I finally have a question I haven't seen answered yet.
I'm doing a flight test and trying to fit the resulting data to linear line. From a combination of ~14 different sensors, I can calculate the 2 values of interest. From uncertainty propagation, I can find the uncertainty in these 2 values (call them x and y), based on the uncertainty in any of the 14 sensors. So, for any point, there will be error in both x and y, and these errors will not be the same in x and y (I think about it as an ellipse). Also, as x and y change, the error in x and y will change, and the ratio will not remain constant. My understanding is these two conditions are called error-in-variables and heteroscedasticity, respectively.
So for any given point, I'll have an expected value and error in both x and y. I'm interested in fitting a curve to this data, and I'm having trouble finding regression models that can handle both error-in-variables and heteroscedasticity. I could use some advice on models or good books for engineers that might help.
I'm also interested in figuring out how good each of the linear coefficients are. I don't think I will be able to get very good accuracy for any given point, but I will have 10,000 to 100,000 points. Is there a way to leverage this fact to get an accurate fit, even though any single point isn't accurate?