# Sensor fusion

Sensor fusion is the combining of sensory data or data derived from sensory data from disparate sources such that the resulting information is in some sense better than would be possible when these sources were used individually. The term better 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).[1][2]

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.

Sensor fusion is also known as (multi-sensor) Data fusion and is a subset of information fusion.

## Sensor fusion algorithms

Sensor fusion is a term that covers a number of methods and algorithms, including:

## Example sensor fusion calculations

Two example sensor fusion calculations are illustrated below.

Let ${\displaystyle {\textbf {x}}_{1}}$ and ${\displaystyle {\textbf {x}}_{2}}$ denote two sensor measurements with noise variances ${\displaystyle \scriptstyle \sigma _{1}^{2}}$ and ${\displaystyle \scriptstyle \sigma _{2}^{2}}$ , respectively. One way of obtaining a combined measurement ${\displaystyle {\textbf {x}}_{3}}$ is to apply the Central Limit Theorem, which is also employed within the Fraser-Potter fixed-interval smoother, namely [3]

${\displaystyle {\textbf {x}}_{3}=\scriptstyle \sigma _{3}^{2}(\scriptstyle \sigma _{1}^{-2}{\textbf {x}}_{1}+\scriptstyle \sigma _{2}^{-2}{\textbf {x}}_{2})}$ ,

where ${\displaystyle \scriptstyle \sigma _{3}^{2}=(\scriptstyle \sigma _{1}^{-2}+\scriptstyle \sigma _{2}^{-2})^{-1}}$ 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 together two measurements is to use the optimal Kalman filter. Suppose that the data is generated by a first-order system and let ${\displaystyle {\textbf {P}}_{k}}$ 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 [3]

${\displaystyle {\textbf {L}}_{k}={\begin{bmatrix}{\tfrac {\scriptstyle \sigma _{2}^{2}{\textbf {P}}_{k}}{\scriptstyle \sigma _{2}^{2}{\textbf {P}}_{k}+\scriptstyle \sigma _{1}^{2}{\textbf {P}}_{k}+\scriptstyle \sigma _{1}^{2}\scriptstyle \sigma _{2}^{2}}}&{\tfrac {\scriptstyle \sigma _{1}^{2}{\textbf {P}}_{k}}{\scriptstyle \sigma _{2}^{2}{\textbf {P}}_{k}+\scriptstyle \sigma _{1}^{2}{\textbf {P}}_{k}+\scriptstyle \sigma _{1}^{2}\scriptstyle \sigma _{2}^{2}}}\end{bmatrix}}.}$

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."[4]

Multiple combinations of centralized and decentralized systems exist.

## Levels

There are several categories or levels of sensor fusion that are commonly used.[5]

• Level 0 – Data alignment
• Level 1 – Entity assessment (e.g. signal/feature/object).
• Tracking and object detection/recognition/identification
• Level 2 – Situation assessment
• Level 3 – Impact assessment
• Level 4 – Process refinement (i.e. sensor management)
• Level 5 – User refinement

## Applications

One application of sensor fusion is GPS/INS, where Global Positioning System and Inertial Navigation System data is fused together using various different methods, e.g. the Extended Kalman Filter. This is useful, for example, in determining the attitude of an aircraft using low-cost sensors.[6]

## References

1. {{#invoke:citation/CS1|citation |CitationClass=book }}
2. Haghighat, M. B. A., Aghagolzadeh, A., & Seyedarabi, H. (2011). Multi-focus image fusion for visual sensor networks in DCT domain. Computers & Electrical Engineering, 37(5), 789-797.
3. {{#invoke:citation/CS1|citation |CitationClass=book }}
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5. http://defensesystems.com/articles/2009/09/02/c4isr1-sensor-fusion.aspx
6. {{#invoke:Citation/CS1|citation |CitationClass=journal }}
• Rethinking JDL Data Fusion Levels
• E. P. Blasch and S. Plano, “Level 5: User Refinement to aid the Fusion Process”, Proceedings of the SPIE, Vol. 5099, 2003.
• {{#invoke:citation/CS1|citation

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