Performance Analysis of Cooperative Localization System
Fei Yu, Shiwei Fan, Qian Li, Pan Jiang, and Zicheng Wang, Harbin Institute of Technology, China
With the increasing complexity of task requirements and tasks, it is difficult for the USV to complete the increasingly complex tasks, and it is necessary to work together with multiple USVs collaborators to achieve tasks and to reduce the time to perform tasks. The most important problem of multi-USV collaboration is to achieve precise positioning of the every USV. The essence of the cooperative positioning process is the state prediction, and the observability of each state are closely related to the system positioning performance. Therefore, it is very important to analyze the observability of the system.
The system can be observed as a prerequisite for state estimation. And the positioning error of the unobservable system will increase with time, it will eventually lead to the cooperative positioning system instability. The degree of observability is a quantitative description of the system, the system can be observed when the degree of observability is not 0, the greater the degree of observability the better the observability. Therefore, the positioning performance of the system is closely related to its observability and the degree of observability, so we can analyze the performance of the system by analyzing its observability and the degree of observability.
The observability analysis theory is simple to implement based on the linearization model, but the model linearization process inevitably causes the loss of effective information, which will affect the adequacy of the observable condition of the system. In order to describe the observability of the system accurately, a new cooperative coordinate system is established, and the master-slaver USV motion model is deduced in the coordinate system. And the USV cooperative localization system observability and the degree of observability is analyzed. In the cooperative coordinate system, the master USV center of gravity is the origin of the coordinate system, and its x-axis direction points to the direction of the master USV’s speed, the y-axis is perpendicular to the x-axis and points to the left of the master USV. According to the above definition, it can be seen that the cooperative coordinate system follows the movement of the master USV hull relative to the inertial coordinate system, and the main USV is stationary and always located at the origin of the coordinate system. Which can be regarded as a fixed beacon, so that the relative motion information between the master and slaver USVs in the inertial coordinate system is converted to the slaver USV in the cooperative coordinate system. Based on this modeling method for system observability and observability analysis can greatly simplify the analysis process, but also fully consider the master and slaver USV relative speed size, relative direction and relative position affect the system observability, the adequacy of observational conditions is guaranteed. At the same time, aiming at the unobservable path, the method of changing the control input is proposed to improve the observability of the system and improve the positioning performance of the system.
Through the analysis of this paper, the following conclusions can be drawn: the system is not observable when the speed is zero in the cooperative coordinate system; the system is not observable when the master and slaver USV connections are the same as the x-axis angle and the heading angle in the cooperative coordinate system; The speed of the slaver USV in the coordinated coordinate system determines the size of the observable range. The greater the velocity, the greater the range of the big degree of observability, and the direction of the velocity determines the direction of the unobservable range. Both the simulation test and the USV water test validated the conclusions of this paper and the effectiveness of the proposed method.