论文标题
在随机切换线性状态空间模型中的错配误差的量化
Quantification of mismatch error in randomly switching linear state-space models
论文作者
论文摘要
切换Kalman过滤器（SKF）以其使用标准Kalman滤波器（KF）解决分段线性动态系统估计问题的能力而闻名。实用的SKF是启发式，近似过滤器，这些过滤器不能保证具有最佳性能，并且需要比单个模式KF更多的计算资源。另一方面，将单个模式不匹配的KF应用于开关线性动态系统（SLDS）会导致错误的估计。本文旨在量化SKF可以消除的平均误差，而在收集测量之前，已知的SLD中的单个模式KF相比。提供并比较了估计器误差的第一和第二矩的数学推导。人们可以使用这些派生来量化过滤器的平均性能，并决定在估计误差和计算复杂性方面运行哪种过滤器，以具有最佳性能。我们进一步提供了验证我们的数学推导的仿真结果。
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.
