Communications in Information & Systems

Recursive Least Squares with Linear Constraints

Yunmin Zhu and X. Rong Li

Full-text: Open access

Abstract

Recursive Least Squares (RLS) algorithms have wide-spread applications in many areas, such as real-time signal processing, control and communications. This paper shows that the unique solutions to linear-equality constrained and the unconstrained LS problems, respectively, always have exactly the same recursive form. Their only difference lies in the initial values. Based on this, a recursive algorithm for the linear-inequality constrained LS problem is developed. It is shown that these RLS solutions converge to the true parameter that satisfies the constraints as the data size increases. A simple and easily implementable initialization of the RLS algorithm is proposed. Its convergence to the exact LS solution and the true parameter is shown. The RLS algorithm, in a theoretically equivalent form by a simple modification, is shown to be robust in that the constraints are always guaranteed to be satisfied no matter how large the numerical errors are. Numerical examples are provided to demonstrate the validity of the above results.

Article information

Source
Commun. Inf. Syst., Volume 7, Number 3 (2007), 287-312.

Dates
First available in Project Euclid: 28 January 2008

Permanent link to this document
https://projecteuclid.org/euclid.cis/1201531976

Mathematical Reviews number (MathSciNet)
MR2516245

Zentralblatt MATH identifier
1262.65050

Citation

Zhu, Yunmin; Li, X. Rong. Recursive Least Squares with Linear Constraints. Commun. Inf. Syst. 7 (2007), no. 3, 287--312. https://projecteuclid.org/euclid.cis/1201531976


Export citation