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

arXiv: https://arxiv.org/abs/2003.02737 · HTML: https://mlsanity.com/paper/2003.02737/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Mar 2020.

## Built on by (most cited first, 2 of 2)

- [Selective Memory Recursive Least Squares: Recast Forgetting into Memory in RBF Neural Network Based Real-Time Learning](https://mlsanity.com/paper/2211.07909/) (2022)
- [New Algorithms for Discrete-Time Parameter Estimation](https://mlsanity.com/paper/2103.16653/) (2021)

## Abstract (arXiv)

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.