## 5 Conclusions  
In damaging military missions, primary lithium batteries, with higher energy density and lower cost, are the optimal power source for underwater vehicles. Based on battery charge capacity, energy can be rationally allocated to complete the assigned tasks. However, the primary lithium battery is non-rechargeable, which limits its application range. Hence, research of the primary lithium battery currently is quite lacking. Moreover, the few existing studies, ignoring model complexity and acquisition difficulty of corresponding data, are basically still in the theoretical research stage. Hence, to develop accurate and practical capacity estimation methods of the primary lithium batteries for the whole life cycle of underwater vehicles, a capacity decay model and a temperature calibration model of primary lithium battery were developed in this research, where no extra measuring instruments need to be equipped and chips embedded in the battery management system can easily perform corresponding calculations. Moreover, both _MSE_ and _RMSE_ of capacity estimation models were also further calculated. The main conclusions are listed as follows:  
The storage experiments for 90 days at 0 \({}^{\circ}\)C, 25 \({}^{\circ}\)C, 45 \({}^{\circ}\)C, and 54 \({}^{\circ}\)C and the discharge experiments at different temperatures (\(-\)10 \({}^{\circ}\)C, 0 \({}^{\circ}\)C, 25 \({}^{\circ}\)C and 40 \({}^{\circ}\)C) and current rates (0.05 C, 0.1 C and 0.2 C) have been conducted. The results of the storage tests reveal that there is almost no capacity attenuation during the storage stage at \(\leq\)25 \({}^{\circ}\)C. However, the capacity significantly decreases with storage time at \(>\)25 \({}^{\circ}\)C and the decay rate increases with the increase in temperature. The results of the discharge tests manifest that the effect of current rate on the maximum available capacity of battery is not remarkable. On the other hand, the maximum available capacity augments with temperature increasing from 0 \({}^{\circ}\)C to 25 \({}^{\circ}\)C, whereas it remains insensitive to other temperature ranges.  
Based on the data of storage experiments, the capacity decay model has been developed to estimate the capacity loss during the storage of underwater vehicles. Moreover, the model accuracy has been verified by comparing with experimental data and the relative error was found to be less than 2%. Based on the effect of temperature on maximum available capacity, the temperature calibration model has been created and a scaling factor (_f_) has been proposed. (_f_) represents the ratio of maximum available capacity at an arbitrary operating temperature to that at 25 \({}^{\circ}\)C. The accuracy of proposed model has been discussed with a relative error of less than 0.7%.  
Data curation, P.C. and J.Z.; Formal analysis, L.Z.; Funding acquisition, C.L., Z.M. and M.L.; Methodology, P.C. and M.L.; Supervision, C.L., Z.M. and W.T.; Validation, P.C.; Visualization, P.C.; Writing--original draft, P.C.; Writing--review and editing, C.L., Z.M., W.T., L.Z., J.Z. and B.L. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (No. 21905231), the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (No. CX2022067), and the Fundamental Research Funds for the Central Universities.  
Not applicable.  
The authors declare no conflict of interest.