关键词: 卡尔曼滤波器, 混合非线性, 数值积分, 平方根滤波器, SVD分解

Abstract: Kalman filtering algorithms employ two distinct parameter update modes: analytical propagation for linear sys-tems and numerical approximation for nonlinear systems. When applied to mixed nonlinear systems with both linear and nonlinear transformations, single-mode filtering architectures face limitations in simultaneously maintaining estimation accuracy and computational efficiency, and the real-time solution of high-dimensional systems is difficult to realize in engineering. To address these limitations, a dual-mode parallel filter is proposed. This filter concurrently executes analytical and numerical propagation for linear and nonlinear state variables, respectively. Through cross-covariance matrix resolution, the filter achieves data fusion, which can save the computation cost of linear states without losing any nonlinear accuracy. Furthermore, aiming at the problem of poor numerical stability when using Cholesky decomposition to obtain the square root matrix in the numerical calculation mode, a variety of numerical stability enhancement methods suitable for dual-mode parallel filters are designed based on QR decomposition and SVD decomposition methods. Besides, the application principles of stability enhancement methods in different forms of mixed nonlinear systems are given. The simulation re-sults show that the filtering accuracy of the proposed algorithm is consistent with that of the traditional single-mode global nonlinear filter, and the computational efficiency is significantly improved.

Key words: Kalman filter, mixed nonlinearity, numerical integration, square root filter, SVD decomposition