# A note on sensor arrangement for long-distance target localization

Natural Science > Mathematical Sciences

In this contribution, researchers at KAIST in the department of Mathematical Sciences recently published work in which a sensor formation problem was considered for target localization based on target-to-sensor arrival time difference data. It is assumed that this target is located far off from the sensors, while the sensors are relatively close to each other. The estimators of the target location expressed in terms of the spherical coordinates are found to be uncorrelated when the sensors are arranged in the formation of concentric rings. The proposed optimal formation of sensors is in the concentric ring formation and is shown to change in accordance with sensors' angular positions with respect to the line-of-sight direction from the reference sensor to the target. The proposed optimal sensor formations are compared in the context of the estimation of accuracy both from theory and by numerical experiments. They are shown optimal, in general, through refined numerical experiments.

Let’s suppose you want to find a far-off target by analyzing signals from it. One might use a multiple number of sensors and then use the differences in target-to-sensor times.

The sensors consist of one main sensor and several auxiliary ones. All sensors receive signals from the target in a passive mode and the main sensor collects data from the other sensors. The main sensor then computes the sensor positions and the range difference between the main and the other sensors.

In the target localization problem pursued by the researchers, the uniform angular array surrounding the target is not considerable and the solutions of the estimating equations for the target location tend to be increasingly sensitive to the sensor formation. They addressed this problem from the perspectives of (i) information optimization and (ii) sensor-target geometry. This work is disjunctive from preceding works in the sense that the current research provides a more general mathematical framework to deal with the optimization problem of multi-sensor formation for 3D target localization when the target is at a good distance from the sensors.

The researchers also showed that the optimal sensor arrangements change in accordance with sensors’ angular positions with respect to the line-of-sight direction from the main sensor to the target. Although the arrangement in an equilateral triangle is found as the best on average, the sensor arrangement whereby there is a cross formation is strongly recommended due to its high performance for a considerable range of the angular positions of the sensors with respect to the target.

This work is published in Signal Processing 133 (2017) on pages 18–31. The website of the paper is http://www.sciencedirect.com/science/article/pii/S016516841630278X.

* Lab information : http://mathsci.kaist.ac.kr/~slki/