## 5 Conclusions  
In this paper, we propose a Gauss-Newton algorithm based on the least squares method to implement a hybrid TOA and TDOA positioning system for a three-dimensional spatial positioning scenario where both TOA and TDOA measurement data exist and conduct theoretical analysis and experimental simulations on the hybrid source localization system consisting of three TOA stations combined with four TDOA stations. The simulation results show that the hybrid source localization accuracy of TOA and TDOA is better than that of pure TOA or TDOA alone, and the localization performance can be significantly improved with the increase in the number of hybrid stations.  
We derive the theoretical results of the least-squares estimation error and the CRLB boundary for the hybrid positioning algorithm of TOA and TDOA, and the analysis results demonstrate that the effects of the measurement error and the station location error on the positioning performance are equivalent. Simulations are performed to compare the least-squares estimation error and the CRLB boundary based on the theoretical results and the simulation results show that the least-squares estimation error and the CRLB boundary  
Figure 7: GDOP distribution curve of three YOZ profiles during 1 TOA+4 TDOA optimized station layout: (**a**) GDOP distribution of YOZ plane when \(x=-1\times 10^{3}\); (**b**) GDOP distribution of YOZ plane when \(x=0\); (**c**) GDOP distribution of YOZ plane when \(x=1\times 10^{3}\).  
are generally consistent, which confirms the promising estimation performance of the least squares method.  
For the ground station placement scenario under typical conditions, the station placement scheme is optimized by using the GA algorithm for pure TDOA positioning and TOA plus TDOA hybrid source localization with the mean value of the CRLB boundary of the target line trajectory as the objective function. The positioning errors of the optimized station placement are compared by simulation experiments, and the results demonstrate that the overall positioning accuracy of the optimized station placement scheme is better than that of the typical station placement scheme, and it is more adaptable to the trajectory form and provides better positioning performance. Finally, we summarize the general principles for the placement scheme optimization on the basis of the simulation results.  
Conceptualization, G.M. and J.T.; Formal analysis, G.M., Z.H. and J.T.; Investigation, G.M., M.W., Z.J. and B.S.; Methodology, G.M.; Project administration, J.T.; Supervision, X.L. and J.T.; Validation, G.M. and J.T.; Visualization, Z.H.; Writing (original draft), G.M., J.T. and M.W.; Writing (review and editing), Z.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by CAEP Foundation under Grant CX20200010, National Natural Science Foundation of China: 61871084, and National Natural Science Foundation of China: 62271109.  
Not applicable.  
We would like to show our deepest gratitude to [PERSON] from Rocket Force University of Engineering (Xi'an 710025, China), who has provided us with valuable guidance in every stage of this project. His efforts in providing research materials and supervising project quality, etc., enabled us to achieve a successful and efficient completion of the project.  
The authors declare no conflict of interest.