An unscented total Kalman filter (UTKF) estimator with nonlinear dynamic errors-in-variables (DEIV) model is derived based on correlational inference. The proposed UTKF considers all random errors in both system and observation equations and is a Jacobian matrix free alternative to the existing TKF estimators. In particular, this estimator is applied to the inertial navigation system (INS)/ultra-wideband (UWB) integration, in which the marginalised unscented transformation (MUT) as well as the use of generalised Rodrigues parameter (GRP) for attitude updates are embedded into the UTKF to improve the computational efficiency and deal with the dimensional mismatching problems. Furthermore, a theoretical analysis to the effects of DEIV model on total Kalman filter is given. Simulation test has been conducted to compare the performance of UTKF and standard unscented Kalman filter (UKF) in terms of attitude, velocity and position errors. The results demonstrate the feasibility and effectiveness of the proposed estimator.

基于相关推理推导出具有非线性动态变量误差 (DEIV) 模型的无迹总卡尔曼滤波器 (UTKF) 估计器。提议的 UTKF 考虑了系统和观测方程中的所有随机误差，并且是现有 TKF 估计器的雅可比矩阵免费替代方案。特别是，该估计器应用于惯性导航系统 (INS)/超宽带 (UWB) 集成，其中嵌入了边缘化无味变换 (MUT) 以及使用广义罗德里格斯参数 (GRP) 进行姿态更新加入UTKF以提高计算效率并处理维度不匹配问题。此外，还给出了DEIV模型对全卡尔曼滤波器影响的理论分析。已进行仿真测试以比较 UTKF 和标准无迹卡尔曼滤波器 (UKF) 在姿态、速度和位置误差方面的性能。结果证明了所提出的估计器的可行性和有效性。