Clemens Joachim, Wellhausen Constantin
Cognitive Neuroinformatics Group, University of Bremen, 28359 Bremen, Germany.
Sensors (Basel). 2024 Oct 14;24(20):6622. doi: 10.3390/s24206622.
Estimating the state of a system by fusing sensor data is a major prerequisite in many applications. When the state is time-variant, derivatives of the Kalman filter are a popular choice for solving that task. Two variants are the square-root unscented Kalman filter (SRUKF) and the square-root cubature Kalman filter (SCKF). In contrast to the unscented Kalman filter (UKF) and the cubature Kalman filter (CKF), they do not operate on the covariance matrix but on its square root. In this work, we modify the SRUKF and the SCKF for use on manifolds. This is particularly relevant for many state estimation problems when, for example, an orientation is part of a state or a measurement. In contrast to other approaches, our solution is both generic and mathematically coherent. It has the same theoretical complexity as the UKF and CKF on manifolds, but we show that the practical implementation can be faster. Furthermore, it gains the improved numerical properties of the classical SRUKF and SCKF. We compare the SRUKF and the SCKF on manifolds to the UKF and the CKF on manifolds, using the example of odometry estimation for an autonomous car. It is demonstrated that all algorithms have the same localization performance, but our SRUKF and SCKF have lower computational demands.
通过融合传感器数据来估计系统状态是许多应用中的一个主要前提条件。当状态随时间变化时，卡尔曼滤波器的导数是解决该任务的常用选择。两种变体是平方根无迹卡尔曼滤波器（SRUKF）和平方根容积卡尔曼滤波器（SCKF）。与无迹卡尔曼滤波器（UKF）和容积卡尔曼滤波器（CKF）不同，它们不是对协方差矩阵进行操作，而是对其平方根进行操作。在这项工作中，我们对SRUKF和SCKF进行修改，以便在流形上使用。当例如方向是状态或测量的一部分时，这对于许多状态估计问题尤其相关。与其他方法不同，我们的解决方案既通用又在数学上连贯。它在流形上与UKF和CKF具有相同的理论复杂度，但我们表明实际实现可以更快。此外，它具有经典SRUKF和SCKF改进的数值特性。我们以自动驾驶汽车的里程计估计为例，将流形上的SRUKF和SCKF与流形上的UKF和CKF进行比较。结果表明，所有算法具有相同的定位性能，但我们的SRUKF和SCKF具有更低的计算需求。
