Exponential convergence of recursive least squares with forgetting factor for multiple-output systems

Convergence and Consistency of Recursive Least Squares with Variable-Rate Forgetting

A recursive least squares algorithm with variable rate forgetting (VRF) is derived by minimizing a quadratic cost function.Under persistent excitation and boundedness of the forgetting factor, the minimizer given by VRF is shown to converge to the true parameters. In addition, under persistent excitation and with noisy measurements, where the noise is uncorrelated with the regressor, conditions are given under which the minimizer given by VRF is a consistent estimator of the true parameters.The results are illustrated by a numerical example involving abruptly changing parameters.

一种新的多重遗忘递推最小二乘方法

A New Recursive Least-Squares Method with Multiple Forgetting Schemes

本文提出了一种带多重遗忘的递归最小二乘方法来跟踪随时间变化的模型参数。我们的方法取决于经典的递归最小二乘遗忘计划作为一个正则化的最小二乘问题的重新制定。仿真研究表明了该方法的有效性。

Recursive Least Squares with Variable-Direction Forgetting -- Compensating for the loss of persistency

Learning depends on the ability to acquire and assimilate new information. This ability depends---somewhat counterintuitively---on the ability to forget. In particular, effective forgetting requires the ability to recognize and utilize new information to order to update a system model. This article is a tutorial on forgetting within the context of recursive least squares (RLS). To do this, RLS is first presented in its classical form, which employs uniform-direction forgetting. Next, examples are given to motivate the need for variable-direction forgetting, especially in cases where the excita…

秩二更新递归最小二乘算法的性能增强

Performance Enhancement of the Recursive Least Squares Algorithms with Rank Two Updates

本文提出了结合指数和瞬时遗忘的秩二更新递归最小二乘算法（RLSR2），建立了信息矩阵逆收敛的新特性，并在谐波干扰下的电网事件估计中验证了其性能提升。

On-Line Learning of Linear Dynamical Systems: Exponential Forgetting in Kalman Filters

Kalman filter is a key tool for time-series forecasting and analysis. We show that the dependence of a prediction of Kalman filter on the past is decaying exponentially, whenever the process noise is non-degenerate. Therefore, Kalman filter may be approximated by regression on a few recent observations. Surprisingly, we also show that having some process noise is essential for the exponential decay. With no process noise, it may happen that the forecast depends on all of the past uniformly, which makes forecasting more difficult. Based on this insight, we devise an on-line algorithm for improp…

状态线性、状态仿射、LPV和线性切换系统中输入-输出映射及其最小实现的稳定性

Stability of input-output maps and their minimal realizations in state-linear, state-affine, LPV, and linear switched systems

研究输入-输出映射稳定性，通过汉克尔秩、响应衰减等条件判断其有限维稳定状态线性实现，还扩展到其他系统，且表明衰减/遗忘率决定最小实现的衰减率。