## 5 Results and Discussion
(The identified \(R_{0}\) by AGA is increased by 20% as the initial value of \(R_{0}\). )Figure 12: Comparison of the results of the four algorithms under the US06 test. The identified \(R_{0}\) is increased by 20% as the initial value of \(R_{0}\): (**a**) SOC estimation result; (**b**) SOC error; (**c**) voltage estimation result; (**d**) voltage error. Figure 13: Identification curves of \(R_{0}\) by MIUKF-FSRCKF. (The identified \(R_{0}\) by AGA is increased by 20% as the initial value of \(R_{0}\).) In Figure 13, we can see that \(R_{0}\) quickly drops from 1.2 times of the identified \(R_{0}\) value (0.0824 \(\Omega\)) by AGA and then fluctuates. The value of \(R_{0}\) is also different under different working conditions. In addition, the change in battery current will also have a small impact on \(R_{0}\). In general, the initial SOC value is not accurate, so MIUKF-FSRCKF should be used to estimate the SOC of lithium batteries with different initial SOC values for verification. IS-1 indicates an initial SOC of 0.9, IS-2 indicates an initial SOC of 0.6 and IS-3 indicates an initial SOC of 0.3. As can be seen from Figure 14, under the FUDS test, the SOC of IS-1, IS-2 and IS-3 can quickly converge to the reference SOC. The MAEs of SOC estimation in these cases are only 0.56%, 0.58% and 0.60%, respectively. Similarly, under BJDST and US06 tests, the proposed method still has adequate convergence, as shown in Figures 15 and 16 and Table 9.  
To summarize, under different initial SOC conditions, the error of MIUKF-FSRCKF estimation of SOC is still small, and the SOC of the battery can be estimated accurately. In order to further verify the practicability of MIUKF-FSRCKF, we utilized another type of battery for SOC estimation. The type of battery used is the A123-18650 lithium iron phosphate battery. The A123-18650 lithium battery is rated at 1100 mAh; its anode material  
Figure 14: SOC estimation results in three cases under the FUDS test: (**a**) SOC estimation results; (**b**) SOC error. Figure 15: SOC estimation results in three cases under BJDST: (**a**) the estimated SOC; (**b**) the SOC error. is LiFePO4 and its cathode material is graphite. The data provided in this experiment are SOC from 0.2 to 1. Considering the actual situation, the initial SOC is generally inaccurate. Therefore, the initial SOC of MIUKF-FSRCKF is set to 0.8. The \(R_{0}\) identified by AGA and DST is 0.1578 \(\Omega\). Thus, two cases named case-1 and case-2 are obtained. Case-1 takes an initial SOC of 0.8 and the identified \(R_{0}\) directly as the initial \(R_{0}\), and case-2 takes an initial SOC of 0.8 and 1.2 times the identified  
From the SOC estimation of the A123-18650 lithium battery, it can be seen that the error of SOC estimation is still small in both case-1 and case-2. This shows that MIUKF-FSRCKF can be used for different kinds of batteries for SOC estimation, and the algorithm is highly accurate and practical. In addition, in Figure 18, we can see that the \(R_{0}\) of case-2 rapidly decreases from 1.2 times of the identified \(R_{0}\) value (0.1578 \(\Omega\)) by AGA, and then basically coincides with the \(R_{0}\) of case-1, which indicates that MIUKF-FSRCKF can adequately identify and update \(R_{0}\).