Abstract: Nonlinear state estimation is a core technology in fields such as radar target tracking and robot localization. However, in practical applications, model uncertainties and unknown or time-varying noise covariance matrices (NCMs) cause traditional filtering algorithms to exhibit increased estimation errors or even divergence. Existing adaptive filtering methods often struggle to achieve a balance between estimation accuracy and computational efficiency. To address these challenges, this paper proposes a Robust Sliding Window Variational Adaptive Cubature Kalman Filter (RSWVACKF). Firstly, variational Bayesian inference (VBI) is integrated with the cubature integration rule to derive a joint recursive solution for the state vector, the process noise covariance matrix (PNCM), and the measurement noise covariance matrix (MNCM), enhancing the algorithm applicability in nonlinear systems. Secondly, a sliding-window-based noise covariance estimator is designed. This estimator uses a cubature Kalman smoother (CKS) to backward smooth the state vectors within the sliding window, enabling online estimation of NCMs while avoiding fixed-point iterations and improving computational efficiency. Finally, a multiple fading factors-based strong tracking filter (MSTF) is incorporated. The online estimated NCMs guide the MSTF in adjusting the prediction error covariance matrix（PECM）, thereby enhancing the algorithm robustness. Multiple simulations validate the effectiveness of the proposed RSWVACKF. Results demonstrate that the proposed method exhibits significant advantages over existing state-of-the-art approaches in both estimation accuracy and computational efficiency.

摘要： 非线性状态估计是雷达目标跟踪、机器人定位等领域的核心技术。然而在实际应用中，由于模型的不确定性以及未知或时变的噪声协方差矩阵（NCMs），导致传统滤波算法的估计误差增大甚至发散，现有自适应滤波方法大多难以实现估计精度与计算效率的平衡。针对上述问题，本文提出一种滑动窗口鲁棒变分自适应容积卡尔曼滤波方法（RSWVACKF）。首先，将变分贝叶斯推断（VBI）与容积积分规则相结合，推导出状态向量与过程噪声协方差矩阵（PNCM）和测量噪声协方差矩阵(MNCM)的联合递归解，提高算法在非线性系统中的适用性；其次，设计基于滑动窗口机制的噪声协方差估计器，使用容积卡尔曼平滑器（CKS）逆向平滑滑动窗口状态向量进而实现对NCMs的在线估计，避免了固定点迭代从而提高计算效率；最后，引入基于多重渐消因子的强跟踪滤波器（MSTF），使用在线估计出的NCMs指导MSTF调整预测误差协方差矩阵（PECM），从而提高算法的鲁棒性。通过多个仿真验证了所提出RSWVACKF的有效性并分析了其计算复杂度，结果表明所提出方法在估计精度和计算效率方面相较于已有最新方法均具有明显优势。