# Co-Operatively Increasing Smoothing and Mapping Based on Switching Function
## 4 Simulations  
To verify the effectiveness and superiority of the proposed method, in this study, we conducted a series of simulation experiments. We used different configurations of drones and different types and degrees of data anomalies and outliers to test the positioning accuracy and robustness of the proposed method under different situations. This paper also compares and discusses other methods to show the advantages and innovations of the proposed method. Simulation experiments refer to experiments that simulate the communication and positioning process between drones on a computer; generate and process sensor data; and obtain and evaluate positioning results. Simulation experiments can conveniently control various parameters and factors, as well as generate various types and degrees of data anomalies and outliers so as to test the method comprehensively and systematically.  
This paper was inspired by paper [19], so we compared the results from that paper with the results of this paper, but it is important to note that there is no concept of topological constraints in this paper, and the distances between the aircraft were measured by the camera looking at the pictures of the special shapes carried by the other aircraft. In order to better compare the superiority of the algorithm, we also compare the algorithm error without UWB constraints, and the classic SOTA methods such as UKF and the least-squares method. Both of these two algorithms fuse all observation values, where the error without UWB constraints refers to the result of skipping topology constraint optimization in the proposed algorithm.  
This study used five drones to conduct simulation experiments, where the drones communicated and exchanged information with each other. This paper assumes that each drone was equipped with an IMU and a camera, and that the calibration and synchronization between the IMU and the camera were completed. This paper also assumes that each drone was equipped with a UWB module, and that the calibration and synchronization between the UWB modules were completed. The parameters used to set up the simulation experiments are shown in Table 1.  
Experimental dataset: This study used a simulated drone environment with a time of 30 s, which included the flight states of five drones moving away from each other. Each drone was equipped with three types of sensors, IMU, camera, and UWB, and their true positions were recorded as references. Each drone randomly provided IMU, UWB, and camera observations with large errors, simulating the strong interference in a real flight scenario. We used the mean absolute error (MAE) and the positioning success rate (PSR) within 1 m to evaluate the positioning results and compare them with the true values, where PSR means that the algorithm is seriously deviated or has no solution in fifteen similar simulations and MAE refers to the average error after the positioning failure results have been removed.  
We conducted four sets of simulation experiments, which tested the influences of different types and degrees of data anomalies and outliers on the method proposed in this paper, in addition to giving a comparison and discussion of other methods. The following are the settings and results for each group of simulation experiments: