Analysis of partial diffusion recursive least squares adaptation over noisy links

Abstract

Partial diffusion-based recursive least squares (PDRLS) is an effective method for reducing computational load and power consumption in adaptive network implementation. In this method, each node shares a part of its intermediate estimate vector with its neighbors at each iteration. PDRLS algorithm reduces the internode communications relative to the full-diffusion RLS algorithm. This selection of estimate entries becomes more appealing when the information fuse over noisy links. In this paper, we study the steady-state performance of PDRLS algorithm in presence of noisy links and investigate its convergence in both mean and mean-square senses. We also derive a theoretical expression for its steady-state meansquare deviation (MSD). The simulation results illustrate that the stability conditions for PDRLS under noisy links are not sufficient to guarantee its convergence. Strictly speaking, considering nonideal links condition adds a new complexity to the estimation problem for which the PDRLS algorithm becomes unstable and do not converge for any value of the forgetting factor.

Performance Analysis of Distributed Kalman Filtering With Partial Diffusion Over Noisy Network

“…Remark 3. In order to better clarify (24), and discuss in more detail the extraction of MSD expression, we note that the kth block on the main diagonal of PX is E x k,i|ix T k,i|i . Multiplying PX by I k N M gives the kth block of PX .…”

“…This issue motivates us to investigate the performance of PDKF algorithm in such scenarios. Some useful results dealing with the effects of noisy links on the performance of diffusion-based strategies behavior are presented in [14]- [16], [24], [25]. In this paper, we figure out how the noisy links affect deterioration of the network performance during the exchange of weight estimates.…”

Convergence of a Distributed Least Squares

“…Moreover, the convergence rate would be "optimal" when Pk,i is chosen to be the form in the paper. Furthermore, some existing methods can be used to reduce the communication complexity and to make the algorithm suitable for higher dimensional signals, for examples, eventdriven methods [55], partial diffusion methods [21], [26], [27], and compressed methods [56] and so on.…”

“…In [25], a diffusion bias-compensated LS algorithm was developed, and the closed-form expressions for the residual bias and the mean-square deviation of the estimates were provided under independence and stationarity assumptions. In addition, partial diffusion LS algorithms were proposed in [26], [27], and the performance results were established for ergodic signals [26] and independent signals [27]. Moreover, [28] proposed a reduced communication diffusion LS algorithm for distributed estimation over multi-agent, and [29] developed robust diffusion LS algorithms to mitigate the performance degradation in the presence of impulsive noise.…”

Distributed order estimation of ARX model under cooperative excitation condition

“…Some strategies including incremental strategies [23], consensus strategies [24], diffusion strategies [25], and combination of them [26] are proposed to construct the distributed algorithms. Based on these strategies, the performance analysis of the distributed estimation algorithms are investigated, for example, the consensus-based least mean squares (LMS) (e.g., [27] [28]), the diffusion stochastic gradient descent algorithm [29], the diffusion Kalman filter (e.g., [30] [31]), the diffusion least squares (LS) (e.g., [32]- [34]), the diffusion forgetting factor recursive least squares [35]. Most of the corresponding theoretical results are established by requiring the independency, stationarity or Gaussian assumptions for the regression vectors due to the mathematical difficulty in analyzing the product of random matrices.…”