Open Access
2007 Recursive Least Squares with Linear Constraints
Yunmin Zhu, X. Rong Li
Commun. Inf. Syst. 7(3): 287-312 (2007).


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.


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Yunmin Zhu. X. Rong Li. "Recursive Least Squares with Linear Constraints." Commun. Inf. Syst. 7 (3) 287 - 312, 2007.


Published: 2007
First available in Project Euclid: 28 January 2008

zbMATH: 1262.65050
MathSciNet: MR2516245

Rights: Copyright © 2007 International Press of Boston

Vol.7 • No. 3 • 2007
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