This paper proposes a simple, accurate and computationally efficient method to apply the ordinary unscented Kalman filter developed in Euclidean space to systems whose dynamics evolve on manifolds.We use the mathematical theory called stable embedding to make a variant of unscented Kalman filter that keeps state estimates in closeproximity to the manifold while exhibiting excellent estimation performance. We confirm the performance of our devised filter by applying it to the satellite system model and comparing the performance with other unscented Kalman filters devised specifically for systems on manifolds. Our devised filter has a low estimation error, keeps the state estimates in close proximity to the manifold as expected, and consumes a minor amount of computation time. Also our devised filter is simple and easy to use because our filter directly employs the off-the-shelf standard unscented Kalman filter devised in Euclidean space without any particular manifold-structure-preserving discretization method or coordinate transformation.
翻译:本文提出了一个简单、准确和计算效率高的方法, 将欧几里德空间开发的普通的无温卡尔曼过滤器应用到其动态在多元上演变的系统中。 我们使用称为稳定嵌入的数学理论来制作一个不温和的卡尔曼过滤器的变体, 使国家估计数与多元相近, 同时显示极好的估计性能。 我们确认我们设计的过滤器的性能, 将它应用到卫星系统模型, 并将它的性能与专为多元系统设计的其他无温卡尔曼过滤器进行比较。 我们设计的过滤器有一个低度的估计错误, 使国家估计数与多元相近, 并消耗少量的计算时间。 我们设计的过滤器也很简单和容易使用, 因为我们的过滤器直接使用在欧几里德空间设计的现成标准的无热卡曼过滤器, 没有特定的多结构保持离散方法或协调转换方法。