**5. Summary and Conclusion**

In this paper, a BO-TMA algorithm using a ray tracing method is proposed to accurately consider the conical angles generated by bottom bounce paths. The 3-dimensional conical angle information was converted to bearing lines in a 2-dimensional plane using a ray tracing method. Then, the PSO algorithm was carried out based on the constructed bearing lines to find optimal target state vectors.

The BO-TMA method using ray tracing and the PSO algorithm proposed in this paper is summarized below.

(1) Convert the conical angles of the bottom bounce path to a bearing line using the ray tracing technique. Set the generation number *n* = 1.

(2) Initialize particles with the bearing line at *k* = 1. Uniform, randomly spread particles on the bearing line and assign velocities randomly selected in the range 0 ≤ |*v*ˆ| ≤ 10 m/s.

(3) For each particle with a four-element state vector, calculate the objective function *J <sup>m</sup>* using the particle trajectories and the bearing lines corresponding to *k* = 1, ··· ,*K*.


(7) Terminate the iteration when the state vectors of the particles reach the termination condition.

In this paper, a ray tracing technique was used to calculate the elevation angle. The conical angle of the target was then calculated based on the estimated elevation angle. Characteristics of the oceanic environment are known, allowing for accurate estimation of elevation angles. However, since the oceanic environment fluctuates temporally and spatially, errors can arise from uncertainty in environmental information. In addition, we assumed that target depth is the same as observer depth. Uncertainty in target depth may also result in target distance errors. Therefore, further research into various target-observer geometries and various ocean environments is required to generalize the results shown in this paper.

**Author Contributions:** Conceptualization, R.O. and J.W.C.; methodology, R.O. and T.L.S.; software, R.O.; validation, R.O., T.L.S. and J.W.C.; formal analysis, R.O. and T.L.S.; investigation, R.O.; resources, R.O.; data curation, R.O.; writing—original draft preparation, R.O.; writing—review and editing, T.L.S. and J.W.C.; visualization, R.O.; supervision, T.L.S. and J.W.C.; project administration, J.W.C.; funding acquisition, J.W.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was a part of the project titled "Development of Distributed Underwater Monitoring and Control Networks", funded by the Ministry of Oceans and Fisheries, Korea.

**Conflicts of Interest:** The authors declare no conflict of interest.
