Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

EURASIP Journal on Advances in Signal Processing, Aug 2017

In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions.

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Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks

Zhang et al. EURASIP Journal on Advances in Signal Processing Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks Ling Zhang 0 2 Yunlong Cai 0 2 Chunguang Li 0 2 Rodrigo C. de Lamare 1 0 College of Information Science and Electronic Engineering, Zhejiang University , Hangzhou , People's Republic of China 1 CETUC-PUC-Rio , Rio de Janeiro , Brazil 2 College of Information Science and Electronic Engineering, Zhejiang University , Hangzhou , People's Republic of China In this work, we present low-complexity variable forgetting factor (VFF) techniques for diffusion recursive least squares (DRLS) algorithms. Particularly, we propose low-complexity VFF-DRLS algorithms for distributed parameter and spectrum estimation in sensor networks. For the proposed algorithms, they can adjust the forgetting factor automatically according to the posteriori error signal. We develop detailed analyses in terms of mean and mean square performance for the proposed algorithms and derive mathematical expressions for the mean square deviation (MSD) and the excess mean square error (EMSE). The simulation results show that the proposed low-complexity VFF-DRLS algorithms achieve superior performance to the existing DRLS algorithm with fixed forgetting factor when applied to scenarios of distributed parameter and spectrum estimation. Besides, the simulation results also demonstrate a good match for our proposed analytical expressions. Sensor networks; Distributed parameter estimation; Distributed spectrum estimation; Diffusion recursive least-squares; Variable forgetting factor 1 Introduction Distributed estimation is commonly utilized for distributed data processing over sensor networks, which exhibits increased robustness, flexibility, and system efficiency compared to centralized processing. Owing to these merits, distributed estimation has received more and more attention and been widely used in applications ranging from environmental monitoring [1], medical data collecting for healthcare [2], animal tracking in agriculture [1], monitoring physical phenomena [3], localizing moving mobile terminals [4, 5] to national security. Particularly, distributed estimation technique relies on the cooperation among geographically spread sensor nodes to process locally collected data. With different cooperation strategies employed, distributed estimation algorithms can be classified into the incremental type and the diffusion type. Note that we consider the diffusion cooperation strategy in this paper since the incremental strategy requires the definition of a path through the network and may be not suitable for large networks or dynamic configurations [6, 7]. Many distributed estimation algorithms with the diffusion strategy have been put forward recently, such as diffusion least-mean squares (LMS) [8, 9], diffusion sparse LMS [10–12], variable step size diffusion LMS (VSS-DLMS) [13, 14], diffusion recursive least squares (RLS) [6, 7], distributed sparse RLS [15], distributed sparse total least squares (LS) [16], diffusion information theoretic learning (ITL) [17], and the diffusion-based algorithm for distributed censor regression [18]. Among assorted distributed estimation algorithms, the RLS-based algorithms achieve superior performance to the LMS-based ones by inheriting the advantages of fast convergence and low steady-state misadjustment from the RLS technique. Thus, the distributed estimation algorithms based on the diffusion strategy and the RLS adaptive technique are investigated in this paper. However, the existing RLS-based distributed estimation algorithms provide a fixed forgetting factor, which has some drawbacks. With a fixed forgetting factor, the algorithm fails to keep up with real-time variations in environment, such as variations in sensor network topology. Moreover, it is expected to adjust the forgetting factors automatically according to the estimation errors rather than choose appropriate values for them through simulations. There have been several studies on variable forgetting factor (VFF) methods. Specifically, the classic gradient-based VFF (GVFF) mechanism was proposed in [19], and most of the existing VFF mechanisms are extensions of this method [20–24]. Nevertheless, the GVFF mechanism requires a large amount of computation. In order to reduce the computational complexity, the improved low-complexity VFF mechanisms have been reported in [25, 26]. To the best of our knowledge, the existing VFF mechanisms are mostly employed in a centralized context and have not been considered in the field of distributed estimation yet. In this work, the previously reported VFF mechanisms [25, 26] are employed to the diffusion RLS algorithms for distributed signal processing applications, by simplifying the inverse relation between the forgetting factor and the adaptation component to provide lower computational complexity. The resulting algorithms are referred to as low-co (...truncated)


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Ling Zhang, Yunlong Cai, Chunguang Li, Rodrigo C. de Lamare. Variable forgetting factor mechanisms for diffusion recursive least squares algorithm in sensor networks, EURASIP Journal on Advances in Signal Processing, 2017, pp. 57, Volume 2017, Issue 1, DOI: 10.1186/s13634-017-0490-z