Angle Fixability and Angle-Based Sensor Network Localization

This paper introduces the concept of "angle fixability" and applies it to angle-based sensor network localization (ASNL). Generally speaking, a framework is said to be angle fixable if it can be uniquely determined by angles between edges up to translation, rotation, scaling, and reflection. It is shown that any framework with a "non-degenerate bilateration ordering" is angle fixable in the plane. The ASNL problem is to determine locations of all sensors, given locations of partial sensors (called anchors) and angle constraints based on bearings measured in the local coordinate frame of each sensor. By establishing connections between angle fixability and angle localizability, it is proved that if a sensor network in the plane has a non-degenerate bilateration ordering and anchors are not all collinear, then the ASNL has a unique solution. If the network also contains an acute-triangulated subframework, then the ASNL can be equivalently formulated as a linear semi-definite programming (SDP) to be solved within polynomial time. Simulation examples are provided to validate effectiveness of the theoretical findings.