Distributed recursive least-squares: Stability and performance analysis

Gonzalo Mateos, Georgios B. Giannakis

Research output: Contribution to journalArticlepeer-review

57 Scopus citations


The recursive least-squares (RLS) algorithm has well-documented merits for reducing complexity and storage requirements, when it comes to online estimation of stationary signals as well as for tracking slowly-varying nonstationary processes. In this paper, a distributed recursive least-squares (D-RLS) algorithm is developed for cooperative estimation using ad hoc wireless sensor networks. Distributed iterations are obtained by minimizing a separable reformulation of the exponentially-weighted least-squares cost, using the alternating-minimization algorithm. Sensors carry out reduced-complexity tasks locally, and exchange messages with one-hop neighbors to consent on the network-wide estimates adaptively. A steady-state mean-square error (MSE) performance analysis of D-RLS is conducted, by studying a stochastically-driven averaged system that approximates the D-RLS dynamics asymptotically in time. For sensor observations that are linearly related to the time-invariant parameter vector sought, the simplifying independence setting assumptions facilitate deriving accurate closed-form expressions for the MSE steady-state values. The problems of mean- and MSE-sense stability of D-RLS are also investigated, and easily-checkable sufficient conditions are derived under which a steady-state is attained. Without resorting to diminishing step-sizes which compromise the tracking ability of D-RLS, stability ensures that per sensor estimates hover inside a ball of finite radius centered at the true parameter vector, with high-probability, even when inter-sensor communication links are noisy. Interestingly, computer simulations demonstrate that the theoretical findings are accurate also in the pragmatic settings whereby sensors acquire temporally-correlated data.

Original languageEnglish (US)
Article number6180018
Pages (from-to)3740-3754
Number of pages15
JournalIEEE Transactions on Signal Processing
Issue number7
StatePublished - Jul 2012

Bibliographical note

Funding Information:
Manuscript received September 20, 2011; revised February 16, 2012; accepted April 02, 2012. Date of publication April 09, 2012; date of current version June 12, 2012. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Yao-Win (Peter) Hong. This work was supported by MURI Grant AFOSR FA9550-10-1-0567.


  • Distributed estimation
  • RLS algorithm
  • performance analysis
  • wireless sensor networks (WSNs)

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