Incremental Adaptive Strategies for Wireless Sensor Networks

Abstract

Distributed wireless sensor networks play a key role due to its wide range of applications ranging from monitoring environmental parameters to satellite positioning. Adaptive algorithms are applied to the distributed networks to endow the network with adaptation capabilities. The distributed network consists of many small sensors deployed randomly in a geographic area, which are adaptive and share their local information. The efficiency of the adaptive distributed strategy relies on the mode of collaboration between the nodes and incremental mode of cooperation is considered throughout the work. A large number of adaptive algorithms are available in the literature, out of which choice is done according to the type of application, computational complexity and convergence rate. Least means square algorithm is the most popularly used adaptive algorithm due to its simplicity and least computational complexity. Distributed ILMS is used for parameter estimation and a spatial-temporal energy conservation relation is used to evaluate the steady state performance of the entire network. The simulated and theoretical steady state performances are compared. Digital implementation of adaptive filters results in quantization errors and finite precision errors. ILMS suffers from drift problem, where the parameter estimate will go unbounded in non-ideal or practical implementations due to the continuous accumulation of quantization errors, finite precision errors and insufficient spectral excitation or ill conditioning of input sequence. They result in overflow and near singular auto correlation matrix, which provokes slow escape of parameter estimate to go unbound. The proposed method ILLMS uses the Leaky LMS algorithm, which introduces a leakage factor in the update equation, and so prevents the weights to go unbounded by leaking energy out. But the overall performance of ILLMS is similar to ILMS in terms of convergence speed and thus an incremental Modified Leaky LMS is proposed based on MLLMS algorithms which in turn derived from the LSE algorithm. LSE algorithm employs sum of exponentials of errors in its cost function and it results in convex and smooth error surface with more steepness, which results in faster convergence rate. ILLMS and IMLLMS algorithms are simulated and compared, where IMLLMS gives superior performance compared to ILLMS in terms of convergence rate and steady state values.