# An Overview of IoT Sensor Data Processing, Fusion, and Analysis Techniques
## 4 Data Fusion  
Data integration or fusion from multiple sensors is required to improve accuracy in various applications. For example, it can be used to trace a target in a military or surveillance system, trace an on-road vehicle's exact location, find the position of an obstacle in veins of the human body, etc. Various applications of data fusion in different domains are briefly explained as follows [52; 53]:  
* The multi-sensor data fusion approach can be applied in ships, aircraft, factories, etc., from a microscopic scale to a distance to hundreds of feet. In these systems, data from electromagnetic signals, acoustic signals, temperature sensors, X-rays, etc., can be integrated for validation and increased accuracy. This integration will increase the accuracy and build trust in the system, which is helpful in the timely maintenance of activities, system fault detection, and remote correction, etc. ;
* Medical diagnosis is a critical system that involves the human body, and is used in disease identification, such as for tumors, lungs or kidney abnormalities, internal diseases, etc., through NMR, chemical or biological sensors, X-rays, IR, etc. ;
* Many satellites, aircraft, and underground or underwater machines use seismic, EM radiation, chemical or biological sensors to collect accurate information or identify natural phenomena in environment monitoring from very long distances;
* Military and defense services use this technique in ocean surveillance, air-to-air or ground-to-air defense, battlefield intelligence, data acquisition, warning, defense systems, etc., using EM radiation from large distances. Sensor fusion is the process of combining two or more data sources in a way that generates a more consistent, more accurate, and more dependable estimate of the dynamic system. This estimate gives better results than if the sensors were used individually. The objective of sensor fusion is to minimize cost, device complexity and the number of components involved, and improve sensing precision and confidence. The data sources can be sensors or mathematical models, and the system state can be acceleration, distance, etc. Four different reasons for using sensor fusion include that (i) it increases the quality of data, (ii) it can increase reliability, (iii) it can measure unmeasured states, and (iv) it can increase the coverage area. In general, the data fusion methods could be characterized as probabilistic, statistical, knowledge-based, and inference and reasoning methods. The probabilistic methods include Bayesian networks, maximum likelihood estimation methods, inference theory, Kalman filtering, etc. Statistical methods include covariance, cross variance, and other statistical analyses [54]. Knowledge-based methods include artificial neural networks, fuzzy logic, genetic algorithms, etc. [55; 56]. Depending on the problem specification, the appropriate data fusion methods are to be chosen. Here, the basic Bayesian and Kalman filter methods are explained. _Bayesian method_: In multi-sensor data fusion, the essential property of Bayesian statistics is that all unknown variables are considered random variables. The probability distribution function defines what is known about these unknown quantities. For a given probability distribution, the parametersare estimated from the prior distribution, and translates the uncertainty about the parameter values. The basic Bayes law states that  
\[P(\alpha|\beta_{1},\beta_{2})\propto P(\alpha)L(\alpha;\beta_{1})L(\alpha;\beta_ {2}) \tag{9}\]  
where prior density upon \(\alpha\) is represented by \(P(\alpha)\), the likelihood of \(\alpha\) by \(\beta\) is represented by \(L(\alpha;\beta)\), such that likelihood is proportional to \(P(\alpha|\beta)\), and the conditional probability is given by the equation below. \[L(\alpha;\beta)\propto P(\alpha|\beta) \tag{10}\]  
This shows the probability of receiving sensor data \(\beta\) given the a priori value \(\alpha\).