Sensor fusion is combining of sensory data or data derived from disparate sources such that the resulting information has less uncertainty than would be possible when these sources were used individually. The term uncertainty reduction in this case can mean more accurate, more complete, or more dependable, or refer to the result of an emerging view, such as stereoscopic vision (calculation of depth information by combining two-dimensional images from two cameras at slightly different viewpoints).
The data sources for a fusion process are not specified to originate from identical sensors. One can distinguish direct fusion, indirect fusion and fusion of the outputs of the former two. Direct fusion is the fusion of sensor data from a set of heterogeneous or homogeneous sensors, soft sensors, and history values of sensor data, while indirect fusion uses information sources like a priori knowledge about the environment and human input.
Two example sensor fusion calculations are illustrated below.
Let and denote two sensor measurements with noise variances and
, respectively. One way of obtaining a combined measurement is to apply the Central Limit Theorem, which is also employed within the Fraser-Potter fixed-interval smoother, namely
where is the variance of the combined estimate. It can be seen that the fused result is simply a linear combination of the two measurements weighted by their respective noise variances.
Another method to fuse two measurements is to use the optimal Kalman filter. Suppose that the data is generated by a first-order system and let denote the solution of the filter's Riccati equation. By applying Cramer's rule within the gain calculation it can be found that the filter gain is given by 
By inspection, when the first measurement is noise free, the filter ignores the second measurement and vice versa. That is, the combined estimate is weighted by the quality of the measurements.
Centralized versus decentralized
In sensor fusion, centralized versus decentralized refers to where the fusion of the data occurs. In centralized fusion, the clients simply forward all of the data to a central location, and some entity at the central location is responsible for correlating and fusing the data. In decentralized, the clients take full responsibility for fusing the data. "In this case, every sensor or platform can be viewed as an intelligent asset having some degree of autonomy in decision-making."
Multiple combinations of centralized and decentralized systems exist.
There are several categories or levels of sensor fusion that are commonly used.*
Although technically not a dedicated sensor fusion method, modern Convolutional neural network based methods can simultaneously process very many channels of sensor data (such as Hyperspectral imaging with hundreds of bands ) and fuse relevant information to produce classification results.
^Blasch, E., Steinberg, A., Das, S., Llinas, J., Chong, C.-Y., Kessler, O., Waltz, E., White, F. (2013) "Revisiting the JDL model for information Exploitation," International Conference on Information Fusion.
^Joshi, V., Rajamani, N., Takayuki, K., Prathapaneni, N., Subramaniam, L. V., (2013). Information Fusion Based Learning for Frugal Traffic State Sensing. Proceedings of the Twenty-Third International Joint Conference on Artificial Intelligence.CS1 maint: Multiple names: authors list (link)