On the Design of Kalman Filter with Low Complexity for 6G-Based ISAC: Alpha and Alpha–Beta Filter Perspectives

This study addresses the performance degradation of $\alpha$ and $\alpha$-$\beta$ filters in 6G Integrated Sensing and Communications (ISAC) scenarios, attributed to violations of linearity and steady-state assumptions. These filters are originally designed with time-invariant gains derived under such assumptions to ensure low computational complexity. However, deviations from ideal conditions—such as non-white, biased, or non-Gaussian process noise—necessitate corrective mechanisms. We propose a weighted process noise approach that accounts for increased uncertainty due to assumption violations while preserving the filters’ closed-form structure and computational efficiency. By integrating uncertainty into the conventional gain formulation, the proposed method achieves performance closer to the optimal filter. Numerical results demonstrate superior accuracy over conventional filters across various noise variances and scenarios, without requiring parameter tuning. Notably, performance improvements become more pronounced as the measurement interval decreases.