Sensor fusion

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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.

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

Video Sensor fusion

Examples of sensors

• Accelerometers
• Electronic Support Measures (ESM)
• Flash LIDAR
• Global Positioning System (GPS)
• Infra-red / thermal imaging camera
• Magnetic sensors
• MEMS
• Phased array
• Radar
• Radiotelescopes, such as the proposed Square Kilometre Array, the largest sensor ever to be built
• Scanning LIDAR
• Seismic sensors
• Sonar and other acoustic
• Sonobuoys
• TV cameras
• ->Additional List of sensors

Maps Sensor fusion

Algorithms

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

• Central limit theorem
• Kalman filter
• Bayesian networks
• Dempster-Shafer
• Convolutional neural network

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Example 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

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

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 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

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

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.

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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.

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Levels

There are several categories or levels of sensor fusion that are commonly used.*

• 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

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Applications

One application of sensor fusion is GPS/INS, where Global Positioning System and inertial navigation system data is fused using various different methods, e.g. the extended Kalman filter. This is useful, for example, in determining the altitude of an aircraft using low-cost sensors. Another example is using the data fusion approach to determine the traffic state (low traffic, traffic jam, medium flow) using road side collected acoustic, image and sensor data.

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.

A practical example how to combine data of different displacement and position sensors in order to obtain high bandwidth at high resolution can be found in this master thesis. One can see the applied methods of optimal filtering (in sense of minimizing e.g. the energy norm) or the MIMO Kalman filter.

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See also

• Brooks - Iyengar algorithm
• Data (computing)
• Data mining
• Fisher's method for combining independent tests of significance
• Image fusion
• Multimodal integration
• Sensor grid
• Transducer Markup Language (TML) is an XML based markup language which enables sensor fusion.

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External links

• Discriminant Correlation Analysis (DCA)
• International Society of Information Fusion

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References

Source of the article : Wikipedia