线性动力系统的快速稳定参数估计
Fast Stable Parameter Estimation for Linear Dynamical Systems
AI总结：
针对线性动力系统参数难以直接测量及含噪不完整观测下的估计问题，提出基于简化参数级联与新迭代方案的快速稳定估计法，相比主流方法计算量更低、偏差与采样方差更优，已在生物力学数据上验证有效。
摘要：
动力系统描述由其底层物理原理（如运动定律或质量、能量、动量守恒定律）自然产生的过程变化。这类模型有助于对过程的驱动因素和阻碍因素给出因果解释。但它们能否描述观测数据的行为？我们又如何量化无法直接测量的模型参数？本文通过提出一种估计方法来解答这两个问题，可基于过程的不完整含噪观测估计线性动力系统的解及参数。\n 所提方法基于参数级联方法构建，用基函数的线性组合近似动力系统隐式定义的解，随后估计系统参数，使该近似解与数据相符。利用系统的线性特性，我们简化了参数级联估计流程，并通过提出一种新的迭代方案实现了快速稳定的计算。\n 我们通过推导一个表示生物力学真实数据的线性微分方程来验证该方法。将我们的方法与估计线性动力系统参数的主流方法，即非线性最小二乘法、模拟退火法、参数级联法和平滑函数回火法进行比较，结果显示该方法计算量大幅降低，偏差和采样方差也有所改善。
英文摘要：
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for the drivers and impediments of the processes. But do they describe the behaviour of the observed data? And how can we quantify the models' parameters that cannot be measured directly? This paper addresses these two questions by providing a methodology for estimating the solution; and the parameters of linear dynamical systems from incomplete and noisy observations of the processes. The proposed procedure builds on the parameter cascading approach, where a linear combination of basis functions approximates the implicitly defined solution of the dynamical system. The systems' parameters are then estimated so that this approximating solution adheres to the data. By taking advantage of the linearity of the system, we have simplified the parameter cascading estimation procedure, and by developing a new iterative scheme, we achieve fast and stable computation. We illustrate our approach by obtaining a linear differential equation that represents real data from biomechanics. Comparing our approach with popular methods for estimating the parameters of linear dynamical systems, namely, the non-linear least-squares approach, simulated annealing, parameter cascading and smooth functional tempering reveals a considerable reduction in computation and an improved bias and sampling variance.
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。
