*5.3. Experiment Result*

#### 5.3.1. Experiment Results of Different Parameters of MI

According to Formula (38), the parameters *M* and a are the key parameters affecting the multi-innovation model, and their value and influence need to be analyzed. In the following, nine parameters are selected for an interval 20 of *M* ∈ [2162], and eleven parameters are selected for an interval 0.1 of *a* ∈ [0,1] for combined analysis. When *a* = 0, the multi-innovation model does not work. At this time, MIUKF + VFFRLS degenerates into the UKF + VFFRLS algorithm. Therefore, the comparison of the two algorithms can be transformed into the comparison of algorithms when *a* is non-zero and a is zero.

The nine values of M are classified, and different values of a are taken in each classification, substituted into the model, and the final SOC error is calculated to draw a three-dimensional diagram (in order to ensure the image display effect, the data at 41 to 20,000 time points are intercepted in *t* dimension). The results are shown in Figure 5.

At the same time, the average and standard deviation of the absolute value of SOC error under different parameter values are calculated. Among them, the average value of the absolute value of SOC error under different parameter values is shown in Table 2.

**Figure 5.** Variation of SOC error with time under different value combinations of *M* and *a*.



The standard deviation of absolute value of SOC error under different parameter values is shown in Table 3.

**Table 3.** Standard deviation of the absolute value of SOC error under different parameter.


It can be seen from Tables 2 and 3 that MIUKF + VFFRLS has advantages over the UKF + VFFRLS algorithm in a wide range of parameters. Nevertheless, it is still necessary to consider setting reasonable parameters to make the algorithm reach the state-of-the-art.

It also can be seen from Figure 5, Tables 2 and 3 that, as the value of *a* increases, the standard deviation of the absolute value of SOC error decreases, but the average value of the absolute value of SOC error fluctuates from large to small and then to large. The fluctuation from large to small in the first part is characterized by the curve becoming more smooth in the figure, while the fluctuation from small to large in the second partis characterized by the curve becoming less smooth in the figure. Comparing the three-dimensional diagrams with different pitch angles when *M* = 162, as shown in Figure 6, it can be seen that the curve is less smooth when *a* = 1 than when *a* = 0, and there is obvious jitter at the time point close to convergence.

**Figure 6.** Three-dimensional SOC error diagrams with different pitch angles when *M* = 162.

The selection of MI model parameters is needed to improve the accuracy and stability of the algorithm as much as possible in order to reduce the mean and standard deviation of the estimated absolute error value. At the same time, it also needs to consider reducing the consumption of algorithm resources in order to reduce the value of *M*, which represents the time sliding window length. Considering the data comprehensively, *a* = 0.5 and *M* = 22 are selected in this paper.
