Standard state estimation techniques, ranging from the linear Kalman filter (KF) to nonlinear extended KF (EKF), sigma‐point or particle filters, assume a perfectly known system model, that is, process and measurement functions and system noise statistics (both the distribution and its parameters). This is a strong assumption which may not hold in practice, reason why several approaches have been proposed for robust filtering, mainly because the filter performance is particularly sensitive to different model mismatches. In the context of linear filtering, a solution to cope with possible system matrices mismatch is to use linear constraints. In this contribution we further explore the extension and use of recent results on linearly constrained KF for robust nonlinear filtering under both process and measurement model mismatch. We first investigate how linear equality constraints can be incorporated within the EKF and derive a new linearly constrained extended KF (LCEKF). Then we detail its use to mitigate parametric modeling errors in the nonlinear process and measurement functions. Numerical results are provided to show the performance improvement of the new LCEKF for robust vehicle navigation.

中文翻译：

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失配非线性系统的鲁棒线性约束扩展卡尔曼滤波器

从线性卡尔曼滤波器（KF）到非线性扩展KF（EKF），sigma-point或粒子滤波器的标准状态估计技术都采用了众所周知的系统模型，即过程和测量功能以及系统噪声统计信息（分布及其参数）。这是一个很强的假设，在实践中可能不成立，这是为什么提出了几种用于鲁棒滤波的方法的原因，主要是因为滤波器性能对不同的模型失配特别敏感。在线性滤波的情况下，解决可能的系统矩阵不匹配的方法是使用线性约束。在这一贡献中，我们进一步探索了线性约束KF的最新结果的扩展和使用，以在过程和测量模型不匹配的情况下实现鲁棒的非线性滤波。我们首先研究如何将线性相等约束纳入EKF并推导新的线性约束扩展KF（LCEKF）。然后，我们详细介绍了其在非线性过程和测量函数中用于减轻参数建模误差的用途。数值结果显示了新型LCEKF在稳固车辆导航方面的性能改进。