Let’s assume, you have a set of sensors measuring the same property. By using competitive sensor fusion (see previous post for an explanation) you expect to increase the accuracy and reliablilty of the result.

In the paper [1] you can find a simple algorithm for doing that.

First, each sensor observation is modeled to have a measurement value, a measurement accuracy and a measurement instant. The instant is necessary to verify that your sensor measurements are sufficiently synchronous, otherwise you need a model to predict future observations in order to synchronize measurements.

The measurement accuracy can be fixed for each sensor or have a dynamic value based on measurement range or run-time validation. The accuracy should be expressed as the expected variance of the measurement.

Assuming that the measurement errors are uncorrelated (or, in practise, sufficiently diverse), the optimal fusion weights are given by the reciproke variance values:

The variance of the result can also be predicted by a similar formula:

Thus, even if you add a very bad sensor to an already good one, the weighted fusion can still improve the variance of the result. For example in [2], we combined distance sensors using infrared measurement with ultrasonic-based sensors in order to get a more robust result. This way, an expensive sensor could be replaced by a set of cheap ones.

- W. Elmenreich. Fusion of continuous-valued sensor measurements using confidence-weighted averaging. Journal of Vibration and Control, 13(9-10):1303–1312, 2007. (doi:10.1177/1077546307077457)
- W. Elmenreich. Sensor Fusion in Time-Triggered Systems. PhD thesis, Institut für Technische Informatik, 2002.

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## About Wilfried Elmenreich

Understanding the communication networks of the future.