随机切换线性状态空间模型失配误差的量化
Quantification of mismatch error in randomly switching linear state-space models
摘要：
切换卡尔曼滤波器（SKF）以其使用标准卡尔曼滤波器（KF）解决分段线性动态系统估计问题的能力而众所周知。实际SKF是启发式的近似滤波器，不能保证具有最佳性能，并且需要比单模KF更多的计算资源。另一方面，将单模失配KF应用于切换线性动态系统（SLDS）会导致错误的估计。本文的目的是量化的平均误差相比，SKF可以消除失配，单模KF在一个已知的SLDS收集测量之前。提供并比较了估计误差的一阶和二阶矩的数学推导。可以使用这些推导来预先量化滤波器的平均性能，并决定在操作中运行哪个滤波器以在估计误差和计算复杂度方面具有最佳性能。我们进一步提供了仿真结果，验证我们的数学推导。
英文摘要：
Switching Kalman Filters (SKF) are well known for their ability to solve the piecewise linear dynamic system estimation problem using the standard Kalman Filter (KF). Practical SKFs are heuristic, approximate filters that are not guaranteed to have optimal performance and require more computational resources than a single mode KF. On the other hand, applying a single mode mismatched KF to a switching linear dynamic system (SLDS) results in erroneous estimation. This paper aims to quantify the average error an SKF can eliminate compared to a mismatched, single mode KF in a known SLDS before collecting measurements. Mathematical derivations for the first and second moments of the estimators errors are provided and compared. One can use these derivations to quantify the average performance of filters beforehand and decide which filter to run in operation to have the best performance in terms of estimation error and computation complexity. We further provide simulation results that verify our mathematical derivations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
