One of the most common scenarios in embedded system design is the need for getting information from the surrounding environment. This is done by using various types of sensors (e.g temperature, humidity, pressure, etc. ). The data from these sensors always have some difference from the real true value being measured. Our goal as designers is to try to minimize this difference so it does not affect the processing we are going to perform using the data. Below we will discuss two terms that we should be familiar with when we set out to do any kind of measurements.

Accuracy

The accuracy of a measurement is the closeness of the measured value to its real true value. For example, if we measure an object that we know for sure has a weight of 1 kg (true value) and we get a reading from our measurement equipment that says the object weights 1.2 kg, we can conclude that we do not have an accurate measurement.

1 kg iron weight being measured by a weight scale. The scale value is 1.2 kg
Fig. 1 Accuracy when measuring 1 kg of weight

From the description above it becomes clear that accuracy is closely related to one of the most important terms when it comes to measurements – error. Error is defined as the difference between the real true value and the measured value. We can say that accuracy expresses the lack of error in a measurement.

When it comes to electronic components and especially sensors, the accuracy is specified as an expected tolerance from the real value. For example, if we have a temperature sensor with a specified accuracy of ±0.1°C, this means that the measured value may be inaccurate with 0.1°C in either direction from the real true value. Accuracy is usually specified for a certain range of the measured quantity.

Precision

Precision refers to how close to each other are two or more measurements of the same quantity under unchanged conditions. Precision is not directly dependent on accuracy. You can have a measurement with high precision but with low accuracy and vice versa.

Let’s expand on the previous example we had for the accuracy. We concluded that we do not have accurate measurement because we got a reading of 1.2 kg when the true value of the object is 1 kg. Now let’s say we do 5 consecutive measurements of the same weight with the same measurement equipment we get the following results: 1.21 kg, 1.19 kg, 1.22 kg, 1.19 kg, 1.20 kg. Although all of the results are not accurate, they are all close to each other, and we can conclude that we have a high degree of precision in the measurement.

5 measurements performed for 1 kg iron weight. All measurements are close to each other but far from the real true value.
Fig. 2 Precision of consecutive measurement of the same weight using a scale

When doing measurement we should always try to be both accurate and precise.

Practical Implication In Embedded Systems Design

Let’s look at the practical aspects of accuracy and precision when designing an embedded system.

It is important to have a good estimate for the degree of accuracy that is required by the embedded system being designed. Going always for the highest possible accuracy may lead to higher cost due to expensive sensors, advanced layout PCB techniques, etc.

Another factor that should be taken into account is that a measurement almost always requires the involvement of more that one component (functional unit). For example, a temperature monitoring system may include the following components: resistance temperature detectors (RTD), an electronic circuit that senses the temperature-dependent change in resistance and converts it to voltage, analog to digital converter (ADC) that digitizes this voltage so it can be processed in a digital system (microprocessor). All of these components mentioned above may contribute to the accuracy of the measurement. Calculating the system accuracy requires calculating the accuracy of each contributing component. The following RSS (root of sum of squares) type equation gives us the system accuracy:

System accuracy equation

Summary

  • Measurements can be both accurate and precise, accurate but not precise, precise but not accurate, or neither.
  • No measurements have absolute accuracy.
  • We should always try to be both accurate and precise to the extent that satisfies the requirements of the system we are designing.