Distance geometry and its applications via semidefinite programming

假设我们有一个移动传感器的无线网络，其中任意两个传感器只有在一定范围内才能相互通信。例如，这些传感器可以附着在一些濒临灭绝的动物身上，以帮助追踪它们的活动。如果每个传感器的位置是已知的，那么计算该网络的传感器间距离是一个微不足道的问题。然而，仅知道传感器间的一些距离就确定每个传感器位置的逆问题是一个难题。这些传感器间距离的信息是通过传感器之间的通信链路获得的。解决这个问题使我们能够在GPS不可用或过于昂贵的情况下跟踪这些传感器的运动。

Suppose we have a wireless network of mobile sensors, where any two sensors can communicate with each other only if they are within a certain range. These sensors, for example, could be attached to some endangered animals to help track their movement. If the location of each sensor is known, then computing the inter-sensor distances of this network is a trivial problem. However, the inverse problem of determining the location of each sensor knowing only some of their inter-sensor distances is a hard problem. This information on the inter-sensor distances is obtained via the communication links between the sensors. Solving this problem enables us to track the movement of these sensors in situations where GPS is either unavailable or too expensive.