[moregrist]

Most of the time, if you have a sensor that you sample at, say 1 KHz and you’re using a reliable MCU and clock, the noise terms in the sensor will vastly dominate the jitter of sampling.

So for a lot of sensor data, the error in the Y coordinate is orders of magnitude higher than the error in the X coordinate and you can essentially neglect X errors.

[sigmoid10]

That is actually the case in most fields outside of maybe clinical chemistry and such, where Deming became famous for explaining it (despite not even inventing the method). Ordinary least squares originated in astronomy, where people tried to predict movement of celestial objects. Timing a planet's position was never an issue (in fact time is defined by celestian position), but getting the actual position of a planet was.

Total least squares regression also is highly non-trivial because you usually don't measure the same dimension on both axes. So you can't just add up errors, because the fit will be dependent on the scale you chose. Deming skirts around this problem by using the ratio of variances of errors (division also works for different units), but that is rarely known well. Deming works best when the measurement method for both dependent and independent variable is the same (for example when you regress serum levels against one another), meaning the ratio is simply one. Which of course implies that they have the same unit. So you don't run into the scale-invariance issues, which you would in most natural science fields.