22 Sensor Calibration: Measurement Foundations

22.1 Start With the Decision

A sensor can be precise and still report the wrong value. Calibration begins with a reference, a raw reading, and a stated error.

22.2 Route Overview

This is part 1 of 3. Continue with Sensor Calibration: Two-Point Lab.

22.3 Part Objectives

• Separate accuracy, precision, bias, and repeatability.
• Plan calibration points from the expected measurement range.

22.4 Start With the Measurement Story

A calibration lab should feel like detective work: compare the raw reading to a known condition, identify the error, apply a correction, then test a new point to prove the sensor has become more trustworthy.

22.5 Learning Objectives

By completing this lab, you will be able to:

1. Explain calibration fundamentals: Describe why sensors need calibration and how raw readings differ from true values
2. Implement two-point calibration: Calculate offset and gain correction using low and high reference points
3. Apply signal conditioning: Configure moving average filtering to reduce noise in sensor readings
4. Evaluate raw vs calibrated data: Measure the impact of calibration on measurement accuracy
5. Integrate calibration persistence: Deploy EEPROM-based coefficient storage for production systems

The mathematical gist. A 12-bit converter splits this lab’s 50,000 g span into 4,096 bins, so the ideal step is 12.2 g/count and the measured 3,275-count span gives 15.27 g/count. Treating the resulting dither as independent noise gives $e_{rms}(N)=q/(\sqrt{12}\sqrt{N})$: the chapter’s 10-sample average reduces its measured 4.41 g RMS noise to 1.39 g, but cannot undo aliasing.

Math Bridge · guided foundationsHow does averaging recover useful ADC resolution?Let Phoebe unpack quantisation noise, square roots, and this lab's own 10-reading beehive average. Learn the maths

22.6 Most Valuable Understanding (MVU)

Two-point calibration corrects sensor errors by calculating a simple linear equation: calibrated = raw ** gain + offset, where gain fixes sensitivity errors and offset fixes zero-point errors.

This is the single most important concept in this lab. Every real sensor has manufacturing variations that cause its readings to deviate from the true value. Two-point calibration uses two known reference points to calculate correction coefficients that map inaccurate raw readings to accurate calibrated values. The formula y = mx + b (from basic algebra) is the foundation - gain is the slope (m) and offset is the y-intercept (b).

Remember: Calibration accuracy depends entirely on your reference standards. Use the most accurate references you can obtain, and bracket your expected measurement range (calibrate at 10% and 90%, not both at 50%).

22.7 Introduction

In this hands-on lab, you will build a complete sensor calibration system using an ESP32 microcontroller in the Wokwi browser-based simulator. You will wire a potentiometer to simulate a sensor with offset and gain errors, implement two-point calibration to correct those errors, and apply a moving average filter for noise reduction. The lab takes approximately 45-60 minutes to complete and requires no physical hardware — everything runs in your browser.

By the end of this lab, you will have working firmware that interactively captures reference points, calculates calibration coefficients, and applies real-time correction to sensor readings.

22.8 Prerequisites

• Basic understanding of Arduino/C++ programming
• Familiarity with analog inputs and ADC concepts
• Completion of the Sensor Data Processing chapter (recommended)

22.9 Calibration Matters

Before collecting reference points, inspect Figure 22.1 to see why calibration is a measurement process rather than a cosmetic adjustment. The visual separates the imperfect observation from the evidence used to correct it.

Read Figure 22.1, read from the biased raw reading through comparison with known references and into the corrected result. The transition shows what the rest of the lab must prove: correction coefficients come from traceable observations, and their accuracy must be checked on data not merely assumed.

Real sensors have manufacturing variations that cause:

• Offset errors: Sensor reads non-zero when it should read zero
• Gain errors: Sensor’s sensitivity differs from the ideal specification
• Non-linearity: Response curve deviates from expected linear relationship

Two-point calibration corrects both offset and gain errors by measuring at two known reference points.

22.10 Folded Error And Quality Metrics Notes

Offset and gain errors behave differently in the calibration record. Offset shifts the whole response by a constant amount, so a zero reference can be wrong even when the slope is usable. Gain changes the slope, so error grows as the true value moves away from the reference point. A two-point calibration should therefore record both reference points, the calculated slope and offset, and at least one verification point between or beyond the references.

After calibration, do not report only “it works.” Compare measured values with actual reference values and record metrics that match the claim:

• Maximum absolute error shows the worst observed miss in the checked range.
• RMSE summarizes typical error across several verification points.
• R-squared helps detect whether the calibrated response is close to linear, but it does not replace endpoint error checks.

These metrics are evidence for the tested range only. If the reference points are too close together, small reference mistakes can amplify at the extremes, so span and verification evidence matter as much as the equation.

22.11 Continue to the Next Part

Carry this evidence into Sensor Calibration: Two-Point Lab, which begins with Two-Point Calibration Limits.