Scalable Ad-hoc UWB Network Adjustment
Zoltan Koppanyi, Charles K. Toth, and Dorota Grejner-Brzezinska, The Ohio State University
GPS/GNSS offers very precise positioning and timing service all around the globe 24/7, except when the signal reception is not favorable, such as canopied or indoor environments. Ranging using ultra-wide band (UWB) signals could offer alternative local positioning in these situations , . A typical UWB ranging system, often referred as impulse-radio ultra wide band (IR-UWB), utilizes short pulses using large bandwidth, which are able to propagate through walls or objects, and thus, can be used indoor or in other environments where the line-of-sight between the components of the positioning system and the users is not provided. Cleary, these conditions present in many applications, such as navigating firefighters in a burning building, positioning people in shopping malls or hospitals, tracking assets in warehouses or logistic centers, georeferencing in canopied areas, etc.
The positioning concept of an IR-UWB system is based on ranging, a UWB unit emits a signal that is captured by the responder unit, and then by measuring the time difference between the emitted and received signal the distance can be calculated. In applications, UWB units are installed in the service area, forming an UWB network. The coordinates of the UWB network units, also called nodes, are surveyed, as they have to be known for positioning. The position of a user can be determined by measuring the distance between the unknown user location and the known UWB network nodes, for example, by circular lateration .
Applying the workflow presented above requires accurate coordinates of the UWB network units. Consequently, this method is applicable for static networks, where the system is installed only once, and not feasible for ad-hoc networks, when the network is deployed just before use. For example, in the case of navigating firefighters or first-responders, the UWB network is deployed right before or during the mission, and therefore, the network determination has to be solved on the spot, and as fast as possible. In these situations, quickly measuring and sharing the mutual ranges between the UWB nodes can be used to determine the required coordinates.
If, at least, four independent ranges are obtained by all units and the coordinates of two network nodes are fixed to avoid the datum problem, the equations of the circular lateration can be incorporated in a least-squares estimation to obtain the solution for all nodes. Note that this approach requires to know all observations at the time of the calculation, and thus, for ad-hoc networks, there should be a central unit, that collects all ranges from the nodes, solves the least squares problem, and then broadcasts the coordinates back to the nodes.
This workflow is feasible unless the communication link between the nodes and the central processing node is corrupted or broken, when the coordinates of these units cannot be calculated. In addition, networks with large number of units may overload the communication channel. For these reasons, solving the network adjustment in a distributed manner could offer more robust and safe system operation. In the proposed distributed framework, we assume that the UWB units only exchange information with their immediate neighbors including ranges. This problem is often referred to as networked optimization in the literature . One advantage of these optimization techniques is that the system is fully scalable, meaning that there is no central/master unit, and the number of the installed nodes or other nodes deployed later has no or small impact on the computation.
Networked optimization has been studied for long time including the necessarily properties of the objective function, the convergence properties and rates as well as the structure of the underlying communication graph for wide range of applications in computer science, such as resource allocation , distributed control of multi-agent systems , and wireless networks , . However, there is a lack of investigations on these algorithms in the positioning domain. This paper investigates two different networked optimization algorithm on the UWB network determination problem.