Angle rigidity-based network localization: an advanced and novel approach

Advances in sensing technology have resulted in the design and development of high-performance sensor networks suitable for different applications. In order to ensure the effective application of sensor networks, especially in today’s communication systems, it is important to accurately determine the position or location of the sensor nodes. Through sensor network localization, it is possible to determine the positions of free nodes with respect to their neighbors by using their sensor measurements and communication information from their neighbors.

Generally, the localization of sensor networks uses three main measurement types, namely, relative positions, distances, and bearings. The successful application of each of these measurement types depends on various factors and requires different localization algorithms. For example, relative position and distance measurements do not have requirements on sensor nodes’ coordinate frames, while bearing measurements usually do .

Besides these three measurement types, interior angle measurements within triangles is an attractive measurement alternative, particularly, under the recently developed and advanced Bluetooth 5.1 technology. While this sensing technology allows the sensor nodes to measure interior angles with respect to their neighboring nodes, it faces two main drawbacks that limit its practical applications. On the one hand, the combination of angle measurements required to make a sensor network localizable is unknown. On the other hand, it is challenging to identify a distribution localization algorithm whose communication consists of only the measured angles of the sensor nodes and the estimated positions. Therefore, identifying angle-only localizability conditions and developing angle-only localization algorithms are highly desirable.

In order to overcome these problems, Associate Professor Liangming Chen from Southern University of Science and Technology, Center for Control Science and Technology, employed the use of rigidity theory. To this end, he developed triangular angle rigidity to address the two-dimensional (2D) triangular angle-constrained network localization problem. The center role in this development is the so-called proposed L-trigraph, which can play a similar role in triangular angle rigidity as the Laman graph in distance rigidity. This paper is currently published in the peer-reviewed research journal, Automatica.

Briefly, the experimental work commenced by transferring the constraints of individual triangles into angle-induced linear constraints. Motivated by the Laman’s theorem, a highly necessary and sufficient topological condition was proposed to check generic triangular angle rigidity. Additionally, localization algorithms were proposed and their practical feasibility was validated. The effectiveness of the proposed approach was validated using a simulation example consisting of 32 sensor nodes.

The author showed that, unlike angle rigidity, triangular angle rigidity indicated global triangular angle rigidity based on the linear constraints. The localizability of triangular angle-constrained networks was successfully identified using a newly proposed angle-induced linear constraint. Compared with the conventional topological and algebraic localizability conditions, the proposed ones were necessary and relatively sufficient, especially when the network has two anchor nodes.

Compared with the localization algorithms that require communication of the measured bearing vectors, the proposed localization algorithms only required scalar communication of interior angles independent of the coordinate frames of the sensor nodes. Moreover, the sensor nodes in the present localization algorithm required only two neighbors, making it highly efficient than network localization using distance measurements whose sensor nodes require at least three neighbors.

In summary, the study demonstrated the practical feasibility of triangular angle rigidity in solving the angle-only localizability and angle-only localization problems in 2D. The proposed localization algorithms produced superior results as they only relied on the estimated positions and measured angles. In a statement to Advances in Engineering, Professor Liangming Chen stated that the study provided valuable insights that would enhance our understanding of triangular angle rigidity for distributed localization and provide a pathway for the applications of it to engineering practices, such as large-scale sensor network localization based on the state of the art angle measurement sensors.