Figure X shows the predicted results of the linear system. Compared with the nonlinear system, the performance of IPF is

Figure X depicts the predicted results of the linear system, demonstrating that the performance of IPF is enhanced compared to the nonlinear system. Moreover, the number of discrete points exceeding the observed value is reduced. In comparison with PF, EPF, and KF-PF, IPF's predicted value is closest to the target value. The algorithm proposed in this study exhibits exceptional performance when dealing with linear problems. As the target value at time 0 is 0, zero and null values are eliminated during the high-dimensional decoupling process of the PSB-PF algorithm. Consequently, the initial predicted value of PSB-PF appears as an outlier, and the overall fitting effect of PSB-PF is superior. The prediction accuracy of PSB-PF is 8.6 times, 10.33 times, 14.15 times, and 14.84 times better than PF, IPF, EPF, and KF-PF, respectively. Furthermore, the accuracy is improved by 14.19 times compared to the observed value.