Publication detail

# Variable Regularized Square Root Recursive Least Square Method

DOKOUPIL, J. BURLAK, V.

Original Title

Variable Regularized Square Root Recursive Least Square Method

Czech Title

Variable Regularized Square Root Recursive Least Square Method

English Title

Variable Regularized Square Root Recursive Least Square Method

Type

conference paper

Language

en

Original Abstract

In this paper, we develop the variable regularized square root recursive least square method which is in order to track time-varying parameters extended by an exponential forgetting factor (EF VR SRRLS). The proposed approach is arisen from the exact recursification of the original batch mode method solving the restricted quadratic problem. The meanings of the restricted conditions lie in the removal of ambiguity of the cost function and thus to ensure the regularity of the direction matrix. In the examined approach, the regularization terms are the matrix weighting the difference between the next parameter estimate and the initial parameter estimate and the time-varying matrix weighting the distance of the parameter estimate from its currently available estimate. Because the incorporation of the Potter's square root technique requires the actualization of direction matrix using the data dyads only, an effective form of implementation based on the updating quantity of the rank one was performed. The performance of the suggested algorithm combining variable regularization and the square root filtering technique is verified via simulation studies.

Czech abstract

In this paper, we develop the variable regularized square root recursive least square method which is in order to track time-varying parameters extended by an exponential forgetting factor (EF VR SRRLS). The proposed approach is arisen from the exact recursification of the original batch mode method solving the restricted quadratic problem. The meanings of the restricted conditions lie in the removal of ambiguity of the cost function and thus to ensure the regularity of the direction matrix. In the examined approach, the regularization terms are the matrix weighting the difference between the next parameter estimate and the initial parameter estimate and the time-varying matrix weighting the distance of the parameter estimate from its currently available estimate. Because the incorporation of the Potter's square root technique requires the actualization of direction matrix using the data dyads only, an effective form of implementation based on the updating quantity of the rank one was performed. The performance of the suggested algorithm combining variable regularization and the square root filtering technique is verified via simulation studies.

English abstract

In this paper, we develop the variable regularized square root recursive least square method which is in order to track time-varying parameters extended by an exponential forgetting factor (EF VR SRRLS). The proposed approach is arisen from the exact recursification of the original batch mode method solving the restricted quadratic problem. The meanings of the restricted conditions lie in the removal of ambiguity of the cost function and thus to ensure the regularity of the direction matrix. In the examined approach, the regularization terms are the matrix weighting the difference between the next parameter estimate and the initial parameter estimate and the time-varying matrix weighting the distance of the parameter estimate from its currently available estimate. Because the incorporation of the Potter's square root technique requires the actualization of direction matrix using the data dyads only, an effective form of implementation based on the updating quantity of the rank one was performed. The performance of the suggested algorithm combining variable regularization and the square root filtering technique is verified via simulation studies.

Keywords

Sample adaptation, least squares method, regularization technique, square root filtering

RIV year

2012

Released

23.05.2012

ISBN

978-3-902823-21-2

Book

Proceedings of 11th IFAC/IEEE INTERNATIONAL CONFERENCE on PROGRAMMABLE DEVICES and EMBEDDED SYSTEMS PDeS 2012

Pages from

71

Pages to

75

Pages count

5

BibTex

```
@inproceedings{BUT92741,
author="Jakub {Dokoupil} and Vladimír {Burlak}",
title="Variable Regularized Square Root Recursive Least Square Method",
annote="In this paper, we develop the variable regularized square root recursive least square method which is in order to track time-varying parameters extended by an exponential forgetting factor (EF VR SRRLS). The proposed approach is arisen from the exact recursification of the original batch mode method solving the restricted quadratic problem. The meanings of the restricted conditions lie in the removal of ambiguity of the cost function and thus to ensure the regularity of the direction matrix. In the examined approach, the regularization terms are the matrix weighting the difference between the next parameter estimate and the initial parameter estimate and the time-varying matrix weighting the distance of the parameter estimate from its currently available estimate. Because the incorporation of the Potter's square root technique requires the actualization of direction matrix using the data dyads only, an effective form of implementation based on the updating quantity of the rank one was performed. The performance of the suggested algorithm combining variable regularization and the square root filtering technique is verified via simulation studies.",
booktitle="Proceedings of 11th IFAC/IEEE INTERNATIONAL CONFERENCE on PROGRAMMABLE DEVICES and EMBEDDED SYSTEMS PDeS 2012",
chapter="92741",
howpublished="print",
year="2012",
month="may",
pages="71--75",
type="conference paper"
}
```