Accuracy Vs. Precision

This is nothing new, but it's something that needs to be constantly hammered home. It's an important point that can make a critical difference in the behavior of embedded systems interacting with the sloppiness of physics in the real world.

I was reminded of the topic by Elecia White's excellent video Intro to Inertial Sensors: From Taps to Gestures to Location. The inertial sensors that are now common in smartphones and embedded systems are accelerometers, gyroscopes, and magnetometers, possibly integrated into a single Inertial Measurement Unit (IMU).

These amazing devices are MicroElectroMechanical Systems (MEMS), explained in Dejan Nedelkovski's equally excellent video How MEMS Accelerometer Gyroscope Magnetometer Work & Arduino Tutorial.

But working in the digital world with sensor data converted from the analog world poses interesting problems. Some of these are addressed in Jack W. Crenshaw's amazing book Math Toolkit for Real-Time Programming. There is always error in the system to some degree, so you have to be prepared to handle it.

Accuracy and precision are two of those problems, and have been since the dawn of measurement. It's important to understand the distinction between them. They are often confused in informal usage.

A common analogy for understanding them is taken from riflery, showing a shooting target. White includes a version of it in her video. As I learned while earning the Boy Scout riflery merit badge at Resica Falls summer camp lo these many years ago, you want your shots to be tightly grouped together (precision), and you want that group to be on-target, centered around the bull's-eye (accuracy).

The following image is taken from the NOAA article Accuracy Versus Precision, which does a nice job of explaining the difference. I'll briefly restate it here should NOAA scientific information mysteriously disappear from the Web.

Accuracy is how close a measurement is to the true value, how close it is to the bull's-eye. Precision is how closely repeated measurements come to duplicating measured values, how tightly they are grouped.

Not Accurate Not Precise: these are not close to the bull's-eye, so the measurements are not close to the true value, and they are not tightly grouped, so repeated measurements have a lot of difference.

Accurate Not Precise: these are close to the bull's-eye, so the measurements are centered around the true value, but they are not tightly grouped, so repeated measurements range all over the place.

Not Accurate Precise: these are not close to the bull's-eye, so the measurements are not close to the true value, but they are tightly grouped, so repeated measurements are close to each other. From a riflery perspective, this is good, because it means you have control, you just need to adjust your sight to compensate.

Accurate Precise: these are both close to the bull's-eye and tightly grouped. The measurements are on-target, close to the true value, and repeated measurements give close to the same result.

In an embedded system, you need to characterize and calibrate things. Characterization means understanding how much variation a sensor has in its measurements, how precise it is (which, as White explains, can vary with temperature and barometric pressure, plus humidity, external vibration, external electrical and magnetic fields, external sources of Radio Frequency Interference (RFI), and other factors; man, the real world is a sloppy place!).

Calibration determines how far off the measurements are from the true value and adjusts the values to compensate for the difference.

Meanwhile, the calculations that use the values must be able to handle the accuracy and precision appropriately, along with odd cases such as a true zero value being measured as a small negative value (because the measurement is centered around zero, but may range between small negative and positive limits). Treating values as if they are more accurate or precise than they really are is downright dangerous.

That can lead the embedded system to crash or take inappropriate actions. If it happens to be controlling the flight of an airplane or the operation of a chemical plant, people can be killed and tremendous damage can result. If it happens to be controlling a consumer device, the consequences may be less dire, but can be equally damaging to the company.

There is always error and noise in the system. You have to understand it and how to manage it.