1. A variable step-size least mean square method for estimation in adaptive networks, comprising the steps of: (a) establishing an adaptive network having N nodes, where N is an integer greater than one, and establishing a Hamiltonian cycle among the nodes such that each node is connected to two neighboring nodes, each node receiving data from a first of the neighboring nodes and transmitting data to a second of the neighboring nodes; (b) establishing an integer i and initially setting i=1; (c) calculating an output of the adaptive network at each node k as d k (i)=u k,i w 0 +ν k (i), where u k,i represents a known regressor row vector of length M, w 0 represents an unknown column vector of length M and ν k (i) represents noise in the adaptive network, wherein M is an integer; (d) calculating an error value e k (i) at each node k as e k (i)=d k (i)−u k,i y k-1,i , wherein y k,i represents an estimate of an output vector for each node k at iteration {dot over (r)}, (e) calculating a node step size μ k for each node k as μ k (i)=αμ k (i−1)+γe 2 (i), wherein α and γ are unitless, selectable parameters; (f) calculating the estimate of the output vector y k,i for each node k as y k,i =y k-1,i +μ k (i)u k,i T (d k (i)−u k,i y k-1,i ); (g) if e k (i) is greater than a selected error threshold, then setting i=i+1 and returning to step (c); otherwise, (h) defining a set of output vectors y k for each node k, where y k =y k,i ; and (i) storing the set of output vectors in computer readable memory.