Method to modify adaptive filter weights in a decentralized wireless sensor network

A method of distributed estimation using q-diffusion least mean squares (qDiff-LMS) to modify adaptive filter weights in a decentralized wireless sensor network of N nodes, comprising:

• calculating an output, yk(i), of an adaptive filter of each node k, based on a product of a measured position, xk(i) of the node k, and an estimate of a previous time instance weight, wk(i−1) of each adaptive filter;
• calculating, for each node, k, a desired response, dk(i);
• calculating, for each node k, an estimation error, ekATC(i) by subtracting the output, yk(i) from the desired response, dk(i);
• updating the local estimate of the previous time instance weight, wk(i−1), of the adaptive filter at each node k by adding a portion of the estimation error to the previous time instance weight, thus generating a local estimate of a diffused weight, Øk(i−1);
• receiving, at each node k, the local estimate of the diffused weight Øl(i−1) from each neighboring node l, where l=1, 2, . . . , M;
• and
• combining the local estimates of the diffused weights Øk(i−1) in a linear combination, thus generating a global diffused weight, w.

A system for distributed estimation of adaptive filter weights using q-diffusion least mean squares (qDiff-LMS) to modify adaptive filter weights in a decentralized wireless sensor network of N nodes, comprising:

• a decentralized wireless sensor network of N nodes, wherein each node k of the N nodes is defined by a position coordinate, xk(i);
• an adaptive filter located in each node k of the N nodes, wherein the adaptive filter is represented by a plurality of weights:
• a computing device located in each node k, wherein the computing device includes circuitry and program instructions, which when executed by at least one processor, are configured to:
• calculate an output, yk(i), of the adaptive filter of the node k, based on a product of a measured position, xk(i) of the node k, and an estimate of a previous time instance weight, wk(i−1) of each adaptive filter;
• calculate, for each node k, a desired response, dk(i);
• generate, for each node k, an estimation error, ek(i), by subtracting the output, yk(i) from the desired response, dk(i);
• generate one of:
• a linear combination of global diffused weights, Øk(i−1) based on receiving, at each node k, a local estimate of a previous time instance weight, wk(i−1), of an adaptive filter of each neighboring node, l, where l=1, 2, . . . , M, and
• a linear combination of global diffused weights, Øk(i−1) based on receiving, at each node k, a local estimate of the diffused weight Øl(i−1) calculated by each neighboring node 1;
• and
• updating one or more of the previous time instance weights, wk(i−1) of each adaptive filter, and the local estimate of the diffused weights Øl(i−1).