Generalized Forgetting Recursive Least Squares: Stability and Robustness Guarantees
This work presents generalized forgetting recursive least squares (GF-RLS), a generalization of recursive least squares (RLS) that encompasses many extensions of RLS as special cases. First, sufficient conditions are presented for the 1) Lyapunov stability, 2) uniform Lyapunov stability, 3) global asymptotic stability, and 4) global uniform exponential stability of parameter estimation error in GF-RLS when estimating fixed parameters without noise. Second, robustness guarantees are derived for the estimation of time-varying parameters in the presence of measurement noise and regressor noise. These robustness guarantees are presented in terms of global uniform ultimate boundedness of the parameter estimation error. A specialization of this result gives a bound to the asymptotic bias of least squares estimators in the errors-in-variables problem. Lastly, a survey is presented to show how GF-RLS can be used to analyze various extensions of RLS from the literature.
Code (0)
등록된 구현이 없습니다.
Tasks
parameter estimationSimilar Papers 제목 키워드 기반
Adaptive Kalman Filtering Developed from Recursive Least Squares Forgetting Algorithms
Recursive least squares (RLS) is derived as the recursive minimizer of the least-squares cost function. Moreover, it is well known that RLS is a special case of the Kalman filter. This work presents the Kalman filter lea…
State EstimationSIFt-RLS: Subspace of Information Forgetting Recursive Least Squares
This paper presents subspace of information forgetting recursive least squares (SIFt-RLS), a directional forgetting algorithm which, at each step, forgets only in row space of the regressor matrix, or the \textit{informa…
parameter estimationRecursive Total Least-Squares Algorithm Based on Inverse Power Method and Dichotomous Coordinate-Descent Iterations
We develop a recursive total least-squares (RTLS) algorithm for errors-in-variables system identification utilizing the inverse power method and the dichotomous coordinate-descent (DCD) iterations. The proposed algorithm…
Selective Memory Recursive Least Squares: Recast Forgetting into Memory in RBF Neural Network Based Real-Time Learning
In radial basis function neural network (RBFNN) based real-time learning tasks, forgetting mechanisms are widely used such that the neural network can keep its sensitivity to new data. However, with forgetting mechanisms…
MemorizationTrading-Off Static and Dynamic Regret in Online Least-Squares and Beyond
Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. The first contribution of this paper rigorously characterizes the effect of forgetting factors for a…