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# Hor Kong Chong Have you ever looked at a wireless positioning system and wondered, how should the detector nodes be placed to ensure coverage of the entire area? Wireless positioning systems utilize a technique called trilateration, which involves a set of detector and device nodes, where device nodes are the targets which positions are being deduced. Trilateration is the act of finding the position of a node by the measurement of distance from at least 3 detector nodes of fixed positions.

An exact estimation can only be made if the node sits within the intersection of the 3 detector nodes, which means that the maximum distance of detection must overlap the maximum distance between detector nodes. By using the approximate distance of the node from each detector nodes, the intersection (or pseudo-intersection if the approximate distance is slightly less than the actual distance) can be obtained by least squares method.

However, while this method uses a simple algorithm, it would restrict the effective coverage to be within the triangle formed by the three detector nodes. Black dots represent detector nodes, black circles represent their maximum radius

The yellow section represents the effective coverage when a direct least squares method was used. When a node is detected in the orange-highlighted area, the least squares method would return an inaccurate result. Thus, an algorithm is used, involving triangulation and trilateration combined to better estimate the target’s position. This would give an adequate area of coverage if the nodes are placed at the corners of a closed-room or at electrical poles outdoors.

The areas highlighted in green represent the parts where one of the detector is out-of-range. With only two dimensions of linear distance given by two detector nodes, it is impossible to pinpoint where the device node might be. However, we can further increase the effective area and perform calculations in real-time, by utilizing simple machine learning techniques which training data can be calculated from a mirrored displacement of the data in the yellow section. Increasing coverage by mirror reflection

As shown in the figure, by mirroring the data in the yellow section against the blue line of reflection, the red section is formed. The data in the red section can mimic the positional data in the yellow section by the measured distance from the two nodes, in which the blue line intersects. By utilizing the same technique for the other two sides of the triangle, the effective coverage of the system can be maximized over the dark-red outline.

In conclusion, while wireless signals can be detected once it enters the range of a detector, a three-way trilateration is only possible when it is detected by all 3 detector nodes. This results in a very small area in which the position of device nodes can be traced with precision. Multiple techniques can be adopted to maximize the effective area by nearly 5 times. Combined with proper infrastructure planning, wireless location services can go a long way in every industry.