Robust Non-Parametric Diffusion Strategies Over Distributed Adaptive Networks And Their Applications

Abstract

Distributed adaptive networks consist of a collection of sensor nodes distributed across a geographical area of interest. Each node is equipped with processing unit, sensing unit, memory unit, power supply unit and transceiver unit. The nodes collectively solve global estimation problems through local interaction among the neighbor nodes. The local communication among the nodes results in diffusion of information throughout the network. In this dissertation, the problem of robust distributed estimation is investigated, where the nodes communicate local measurements and local estimated parameters with neighbor nodes. The presence of outliers in the collected data can be treated as the impulsive noise. The presence of impulsive noise at any node in a distributed network will affect the entire network due to the local interactions and information exchange among the nodes in the network. Most of the classical distributed estimation techniques have considered the presence of only Gaussian noise, but in practical scenarios the presence of outliers is unavoidable. Such methods fail to attain the optimum solution in impulsive noise scenarios, since the underlying noise violates the theoretical assumptions considered for the algorithm development. This doctoral dissertation focuses on the development of robust non-parametric distributed estimation algorithms and their variants, which can handle impulsive contamination. Rank based estimators from the robust statistics are found to be robust against impulsive contamination involving systems. The Wilcoxon and Generalized rank (GR) norms are some of the rank based robust estimators. The Wilcoxon norm (WN) can handle impulsive noise in the desired/filter output data. In most of the practical scenarios, both the input and desired data contain impulsive noise along with Gaussian noise. The GR norm based estimators are robust against impulsive noise in both the input and desired data. The distributed robust algorithm named diffusion minimum generalized rank norm (DGR) is developed by minimizing the GR norm of the residual error in the optimization problem. The influence function of the GR norm is bounded in both desired and input data space, hence the GR norm based estimation techniques are robust against impulsive noise in both desired and input data. The performance analysis of the algorithm is analyzed using the asymptotic linearity relation between the null and alternate hypotheses of the GR norm gradient. Simulation based experiments are carried out to validate the robustness of the proposed algorithm compared to the state-of-the art algorithms. The proposed DGR algorithm exhibits slow convergence speed. To improve its convergence speed, the GR norm based optimization problem can be solved using the QR decomposition. The recursive least squares (RLS) based methods converge faster compared to the least mean squares (LMS) based methods and QR decomposition based RLS algorithms are numerically more stable than their counter parts. A fast diffusion minimum generalized rank norm algorithm based on QR decomposition (FDGR-QR) is proposed, which is robust against outliers in both desired and input data and has faster convergence rate than the DGR. The main intuition behind the proposed work is to enhance the performance of the DGR by solving the GR norm of the residual error cost using QR decomposition. Simulation based experiments are carried out to validate the robustness and enhanced convergence speed of the proposed algorithm. The parameter of interest or the parameter to be estimated could be sparse, i.e. only a few elements have large values and the rest being negligible. If some prior information about the sparsity of the parameter of interest is known, then it can be incorporated in the cost function using regularization technique. This type of optimization problems have extensive applications in practical scenarios like cognitive radio, direction of arrival estimation, distributed sparse demodulation and sparse signal detection. The robust diffusion algorithms based on WN and GR norm are extended for adaptive distributed systems with sparse parameters in impulsive noise environments. The techniques from compressive sensing endow the network with adaptive learning of the sparse structure form the incoming data in real time and it also enables tracking of the sparsity variations of the system model. The mean and mean square convergence of the proposed algorithms are analyzed and the conditions under which the proposed algorithm outperforms the unregularized diffusion GR norm and diffusion Wilcoxon norm algorithms are also investigated. The proposed robust sparse diffusion algorithms are validated for sparse parameter estimation in different simulation based experiments.