robotics//sensor//sensor calibration//noise characterization

Learning the shape, the memory and the company of a sensor's errors before a filter trusts them. Calibration gives two numbers, a bias and a variance; **noise characterization** asks whether those two numbers are enough to describe the errors, looking at them from three sides.

Learning the shape, the memory and the company of a sensor's errors before a filter trusts them. Calibration gives two numbers, a bias and a variance; noise characterization asks whether those two numbers are enough to describe the errors, looking at them from three sides.

Their shape: is it a bell? Often, not always, and the data decide (normality assumption); the tools are the QQ plot and the normality tests of goodness of fit, read as an engineer and never as a verdict.

Their memory: is each error fresh, or does it resemble the one before? A slow error makes ten thousand readings worth a handful (autocorrelation).

Their company: do two sensors err together? Recorded at the same instants, their errors give a Pearson correlation (covariance), and it is rarely zero when something drives both. Two barometers on one drone both see the weather change the atmospheric pressure; two GPS receivers share the same ionosphere and satellites. The extreme case is the same sensor read twice, correlation one, a single opinion with an echo.

What the company changes is how the sensors may be studied and fused. Independent sensors can be characterized one at a time and fed to a filter one after the other in any order; correlated ones have to be characterized together and fed through the full measurement matrix, or whitened first so they become independent (correlated measurements). Two sensors that heat up together can even show zero correlation of their errors and still be dependent: their signs do not match but their sizes do.

Every one of these answers holds only for the conditions the recording covered. A sensor characterized on a bench at 20 °C is not the same sensor in a car at 45 °C, and the characterization is only as wide as the operating envelope it spanned.