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)