Accuracy, Precision, Resolution & Sensitivity
Instrument manufacturers usually supply specifications for their equipment that define its accuracy, precision, resolution and sensitivity. Unfortunately, not all of these specifications are uniform from one to another or expressed in the same terms. Moreover, even when they are given, do you know how they apply to your system and to the variables you are measuring? Some specifications are given as worst-case values, while others take into consideration your actual measurements.
Accuracy can be defined as the amount of uncertainty in a measurement with respect to an absolute standard. Accuracy specifications usually contain the effect of errors due to gain and offset parameters. Offset errors can be given as a unit of measurement such as volts or ohms and are independent of the magnitude of the input signal being measured. An example might be given as ±1.0 millivolt (mV) offset error, regardless of the range or gain settings. In contrast, gain errors do depend on the magnitude of the input signal and are expressed as a percentage of the reading, such as ±0.1%. Total accuracy is therefore equal to the sum of the two: ±(0.1% of input +1.0 mV). An example of this is illustrated in Table 1.
Table 1. Readings as a function of accuracy
Input Voltage |
Range of Readings within the Accuracy Specification |
0V |
-1 mV to +1 mV |
5V |
4.994V to 5.006V (±6 mV) |
10V |
9.989V to 10.011V (±11 mV) |
conditions: input 0-10V, Accuracy = ±(0.1% of input + 1mV)
Precision describes the reproducibility of the measurement. For example, measure a steady state signal many times. In this case if the values are close together then it has a high degree of precision or repeatability. The values do not have to be the true values just grouped together. Take the average of the measurements and the difference is between it and the true value is accuracy.
Resolution can be expressed in two ways:
1. It is the ratio between the maximum signal measured to the smallest part that can be resolved - usually with an analog-to-digital (A/D) converter.
2. It is the degree to which a change can be theoretically detected, usually expressed as a number of bits. This relates the number of bits of resolution to the actual voltage measurements.
In order to determine the resolution of a system in terms of voltage, we have to make a few calculations. First, assume a measurement system capable of making measurements across a ±10V range (20Vspan) using a 16-bits A/D converter. Next, determine the smallest possible increment we can detect at 16 bits. That is, 216 = 65,536, or 1 part in 65,536, so 20V÷65536 = 305 microvolt (uV) per A/D count. Therefore, the smallest theoretical change we can detect is 305 uV.
Unfortunately, other factors enter the equation to diminish the theoretical number of bits that can be used, such as noise. A data acquisition system specified to have a 16-bit resolution may also contain 16 counts of noise. Considering this noise, the 16 counts equal 4 bits (24 = 16); therefore the 16 bits of resolution specified for the measurement system is diminished by four bits, so the A/D converter actually resolves only 12 bits, not 16 bits.
A technique called averaging can improve the resolution, but it sacrifices speed. Averaging reduces the noise by the square root of the number of samples, therefore it requires multiple readings to be added together and then divided by the total number of samples. For example, in a system with three bits of noise, 23 = 8 , that is, eight counts of noise averaging 64 samples would reduce the noise contribution to one count, √64 = 8: 8÷8 = 1. However, this technique cannot reduce the affects of non-linearity, and the noise must have a Gaussian distribution.
Sensitivity is an absolute quantity, the smallest absolute amount of change that can be detected by a measurement. Consider a measurement device that has a ±1.0 volt input range and ±4 counts of noise, if the A/D converter resolution is 212 the peak-to-peak sensitivity will be ±4 counts x (2 ÷ 4096) or ±1.9mV p-p. This will dictate how the sensor responds. For example, take a sensor that is rated for 1000 units with an output voltage of 0-1 volts (V). This means that at 1 volt the equivalent measurement is 1000 units or 1mV equals one unit. However the sensitivity is 1.9mV p-p so it will take two units before the input detects a change.
Measurement Computing's USB-1608G Series Example
Let’s use the USB-1608G and determine its resolution, accuracy, and sensitivity. (Refer to Table 2 and Table 3, below, for its specifications.) Consider a sensor that outputs a signal between 0 and 3 volts and is connected to the USB-1608G's analog input. We will determine the accuracy at two conditions: Condition No. 1 when the sensor output is 200 mV and Condition No. 2 when it is 3.0 volts.
Accuracy: The USB-1608G uses a 16 bit A/D converter
Condition No. 1: 200 mV measurement on a ±1 volt single-ended range
- Temperature = 25º C
- Resolution = 2V ÷ 216 = 30.5 uV
- Sensitivity = 30.5 uV × 1.36 LSB rms = 41.5 uV rms
- Gain Error: 0.024% × 200mV = ±48uV
- Offset Error = ±245uV
- Linearity Error = 0.0076% of range = 760uV
- Total Error = 48uV + 245uV + 760uV = 1053uV
Therefore a 200 mV reading could fall within a range of 198.947 mV to 201.053 mV.
Condition No. 2: 3.0 V measurement on a ±5 volt single-ended range
- Temperature = 25º C
- Resolution =10 volts ÷ 216 = 152.6uV
- Sensitivity = 152.6 uV × 0.91 LSB rms= 138.8 uV rms
- Gain Error: 0.024% × 3.0V = 720uV
- Offset Error = 686uV
- Linearity error = 0.0076% of range = 380uV
- Total Error = 720uV + 686uV + 380uV = 1.786mV
Therefore, a 3.0V reading could fall within a range of 2.9982 mV to 3.0018 mV.
Summary Analysis:
Accuracy: Consider Condition No. 1. The total accuracy is 369 uV ÷ 2 V × 100 = 0.0184%
Accuracy: Consider Condition No. 2. The total accuracy is 1.786 mV ÷ 10 V × 100 = 0.0177%
Effective Resolution: The USB-1608G has a specification of 16 bits of theoretical resolution. However the effective resolution is the ratio between the maximum signal being measured and the smallest voltage that can be resolved, i.e. the sensitivity. For example...if we consider Condition No. 2, divide the sensitivity value by the measured signal value or (138.5uV ÷ 3.0 V) = 46.5e-6 and then converting to the equivalent bit value produces (1V ÷ 46.5e-6) = 21660 or 214.4 bits of effective resolution. To further improve on the effective resolution, consider averaging the values as previously discussed.
Sensitivity: The most sensitive measurement is made on the ±1 volt range where the noise is only 41.5uV rms whereas the sensitivity of the 5 volt range is 138.8uV rms. In general, when selecting a sensor, set the equipment to capture the highest output with the best sensitivity. For example, if the output signal is 0-3 volts select the 5 volt range instead of the 10 volt.
Table 2.
Table 3.
Accuracy, Precision, Resolution & Sensitivity的更多相关文章
- 机器学习基础梳理—(accuracy,precision,recall浅谈)
一.TP TN FP FN TP:标签为正例,预测为正例(P),即预测正确(T) TN:标签为负例,预测为负例(N),即预测正确(T) FP:标签为负例,预测为正例(P),即预测错误(F) FN:标签 ...
- 机器学习--如何理解Accuracy, Precision, Recall, F1 score
当我们在谈论一个模型好坏的时候,我们常常会听到准确率(Accuracy)这个词,我们也会听到"如何才能使模型的Accurcy更高".那么是不是准确率最高的模型就一定是最好的模型? 这篇博文会向大家解释 ...
- 论文阅读 | Falcon: Balancing Interactive Latency and Resolution Sensitivity for Scalable Linked Visualizations
作者: Dominik Moritz, Bill Howe, Jeffrey Heer 发表于CHI 2019, 三位作者都来自于University of Washington Interactiv ...
- 目标检测的评价标准mAP, Precision, Recall, Accuracy
目录 metrics 评价方法 TP , FP , TN , FN 概念 计算流程 Accuracy , Precision ,Recall Average Precision PR曲线 AP计算 A ...
- Mean Average Precision(mAP),Precision,Recall,Accuracy,F1_score,PR曲线、ROC曲线,AUC值,决定系数R^2 的含义与计算
背景 之前在研究Object Detection的时候,只是知道Precision这个指标,但是mAP(mean Average Precision)具体是如何计算的,暂时还不知道.最近做OD的任 ...
- 评估指标:ROC,AUC,Precision、Recall、F1-score
一.ROC,AUC ROC(Receiver Operating Characteristic)曲线和AUC常被用来评价一个二值分类器(binary classifier)的优劣 . ROC曲线一般的 ...
- Classification week6: precision & recall 笔记
华盛顿大学 machine learning :classification 笔记 第6周 precision & recall 1.accuracy 局限性 我们习惯用 accuracy ...
- Precision,Recall,F1的计算
Precision又叫查准率,Recall又叫查全率.这两个指标共同衡量才能评价模型输出结果. TP: 预测为1(Positive),实际也为1(Truth-预测对了) TN: 预测为0(Negati ...
- 深度学习分类问题中accuracy等评价指标的理解
在处理深度学习分类问题时,会用到一些评价指标,如accuracy(准确率)等.刚开始接触时会感觉有点多有点绕,不太好理解.本文写出我的理解,同时以语音唤醒(唤醒词识别)来举例,希望能加深理解这些指标. ...
随机推荐
- yii2中的事件和行为
Event 事件 事件是为了解耦... 注册事件 使用"on add"添加属性,注册事件 使用on方法注册事件. 第三个参数$data是监听函数使用的参数, 第四个$append参 ...
- sass 的使用
普通变量 ? 1 $fontSize:12px; 默认变量 ? 1 $fontSize:12px; !default; 变量覆盖:只需要在默认变量之前重新声明下变量即可 ? 1 2 $fontSize ...
- 思科ACL不连续通配符掩码的计算
access-list 120 permit ip 10.0.0.0 0.0.0.191 any 这条ACL看似简单,却又复杂,因为正常我们见到的通配符掩码都是诸如0.0.0.255(255. ...
- Ununtu 15.04 安装MySql(Django连接Mysql)
本文介绍Ubuntu 15.04下安装MySQL ubuntu 15.04安装mysql django项目连接mysql 一.安装数据库 1.sudo apt-get install mysql-se ...
- FreeRTOS 系统时钟节拍和时间管理
以下转载自安富莱电子: http://forum.armfly.com/forum.php FreeRTOS 的时钟节拍任何操作系统都需要提供一个时钟节拍,以供系统处理诸如延时. 超时等与时间相关的事 ...
- maven编译插件版本配置案例
<!-- Build Settings 构建设置 --> <build> <finalName>${project.artifactId}</finalNam ...
- adb not responding的解决方案
查看谁占用了进程:netstat -aon|findstr "5037" 终止占用的进程: 假若"6908"占用了进程 taskkill /pid 6908 / ...
- chrome显示小于12号字体的方法
我现在做一个支持英文的网站,但是字体要设置小于12号字体,我百度方法是-webkit-text-size-adjust:none; 但是谷歌为什么不支持啊, 有没有解决办法 让谷歌浏览器 支持小于 ...
- 关于Unity中的transform组件(一)
一.transform组件用途 1.维护场景树 2.对3D物体的平移,缩放,旋转 二.场景树定义 在Hierarchy视图中显示的: 一个game_scene场景,下面有Main Camera节点,D ...
- 008Maven_建立私服
参考博客:http://blog.csdn.net/fengspg/article/details/22507737 .1. Maven私服 关于中央仓库注意事项 l 地址: 目前来说: htt ...