带噪声离散非线性系统的参数和状态联合估计：一种监督多观测器方法
Joint Parameter and State Estimation of Noisy Discrete-Time Nonlinear Systems: A Supervisory Multi-Observer Approach
摘要：
本文提出了两种联合估计离散时间非线性系统的参数和状态的方案，其中存在有界干扰和噪声，参数属于一个已知的紧集。该方案是基于采样的参数空间和设计一个状态观测器的每个样本。一个监督者在每个时刻选择这些观测器之一来产生参数和状态估计。在第一种方案中，参数和状态估计保证在有限时间内收敛于其真实值的一定裕度内，假设使用足够大数量的观测器，并且除了其他观测器设计条件之外还满足激励持续性条件。该收敛裕度由用户可以任意选择的小的部分和由噪声电平确定的部分构成。第二种方案利用参数估计的收敛特性对参数子空间进行后续放大，以实现给定数量的观察者的更严格的裕度。数值算例表明了这两种格式的优点。
英文摘要：
This paper presents two schemes to jointly estimate parameters and states of discrete-time nonlinear systems in the presence of bounded disturbances and noise and where the parameters belong to a known compact set. The schemes are based on sampling the parameter space and designing a state observer for each sample. A supervisor selects one of these observers at each time instant to produce the parameter and state estimates. In the first scheme, the parameter and state estimates are guaranteed to converge within a certain margin of their true values in finite time, assuming that a sufficiently large number of observers is used and a persistence of excitation condition is satisfied in addition to other observer design conditions. This convergence margin is constituted by a part that can be chosen arbitrarily small by the user and a part determined by the noise levels. The second scheme exploits the convergence properties of the parameter estimate to perform subsequent zoom-ins on the parameter subspace to achieve stricter margins for a given number of observers. The strengths of both schemes are demonstrated using a numerical example.
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。
