Localizing a Wireless Node in a Multi-Agent System using Kalman Filtering

In order to autonomously navigate and perform useful tasks, a mobile robot often needs to know its exact position and orientation. The objective of this work is to estimate the position of a mobile node (we will call it the receiver, Rx) based on signals from other moving/stationary nodes (transmitters, Tx). The measurements are the straight line distances between the receiver and the transmitters. Our aim is to calculate the (x, y) position of the receiver given the (x,y) positions of the transmitters. A baseline approach is to use triangulation. If there are more than 3 transmitters then averaging the estimates obtained from various triangles provides a quick estimate. The key problem is that naive averaging treats each estimate equally. We propose instead to use Kalman filtering because it explicitly uses the the variances in the measurements. Indeed, the Kalman filter provides an optimum estimate in minimum mean-square error sense.