robotics//sensor//sensor calibration

How a sensor earns the trust a filter will place in it. Nobody hands you the noise variance \(R\). **Sensor calibration** is the procedure that earns it: learning, before trusting a sensor, how far off it reads on average and how much it scatters. The mathematics is the support here, not the protagonist; each step exists because some broken sensor once taught someone a lesson.

How a sensor earns the trust a filter will place in it. Nobody hands you the noise variance RRR. Sensor calibration is the procedure that earns it: learning, before trusting a sensor, how far off it reads on average and how much it scatters. The mathematics is the support here, not the protagonist; each step exists because some broken sensor once taught someone a lesson.

Put the sensor on a known truth: a geodetic vertex for a GPS, a calibrated thermostatic bath for a thermometer, a levelled table for an accelerometer. The reference is for the lab; the sensor then works without it (measurement noise).

Record many samples in the conditions it will meet in service, across its operating envelope and not only at its centre.

Compute the errors ei=zi−xe_i=z_i-xei​=zi​−x. Their mean is the bias, and subtracting it is calibrating (sensor bias); their variance is RRR.

Then ask whether those two numbers are enough: the shape of the errors, their memory in time and whether other sensors share them (noise characterization).

Each finding has a consequence for the filter that will use the sensor. Heavy tails make the large corrections overconfident, so gate the innovation. Skew hides a bias: calibrate with the mean, not the peak. Steps from quantization with step qqq are nearly harmless: add q2/12q^2/12q2/12 to RRR. A precision that changes with the conditions asks for a varying RRR. High autocorrelation is the serious one (colored noise).