Research on an analytical solution Kalman filter for nonlinear state estimation

The Kalman filter is a classical algorithm for state estimation, with a broad range of applications in fields such as aerospace, biomedical engineering, and communication systems. However, when applied to nonlinear systems, they face challenges such as approximation errors and real-time performance issues. To address the limitations, this study proposes an enhanced Kalman filter named the analytical solution Kalman filter (ASKF), which derives analytical expressions directly for state estimates within nonlinear systems, reducing reliance on linearization and improving estimation accuracy. Numerical simulations of random walk signals demonstrate that the ASKF can achieve up to an order of magnitude improvement in estimation precision over conventional methods in high-noise scenarios. The proposed method not only advances the state-of-the-art in nonlinear estimation but also offers a unified framework applicable to both linear and nonlinear systems.