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The diffusion least mean p-power (LMP) algorithm is extended with adaptive variable power p in the generalised Gaussian distribution (GGD) environments. The GGD is one of the widely used distributions in the signal processing area. For the proposed method, priori knowledge of the distribution parameters is not required. Furthermore, it is robust to the preselected initial power order. Numerical results are provided to verify the performance of the proposed method.
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Introduction: We consider a distributed parameter estimation problem for a sensor network with K nodes, which are distributed over some geographical regions. Let dk,n denote the scalar measurement at the node and k and uk,n denote the regression vector at every time instant n, respectively. uk,n is correlated with dk,n, and
... (1)
where T denotes the matrix transposition and vk, n is the noise, which follows the generalised Gaussian distribution (GGD). The objective is to estimate the unknown parameter ωo from {dk,n, uk,n} for all the nodes in the network. All the signals are assumed to be real values.
The least mean p-power (LMP) algorithms have been widely used in signal processing, especially non-Gaussian signal processing. Some useful properties of the LMP are studied, such as its convex cost function of the filter coefficients. For the non-Gaussian processes, they may have better performances than the conventional Wiener solution. When the input and the desired processes are Gaussian, it has the same optimum solution as the conventional Wiener solution [1]. The GGD [2] is one of the widely used probability distributions to model non-Gaussian noise.
In-network distributed estimation has received more attention over the past few years [3-5]. Please refer to [6] for an up-to-date review and discussion. Recently, the diffusion LMP algorithm with fixed power p for the distributed parameter estimation has been proposed in [7]. For a given signal model, the performance of the LMP type methods is affected by the power p. In [8], the authors prove that for noise with GGD, the optimum order p of the LMP algorithm is equal to the shape parameter of the GGD. Motivated by the methods in [8], we propose a diffusion LMP algorithm with adaptive variable power p, which is applicable to the noise with GGD. The...