Improved Tracking for Distributed Signal Fusion Optimization in a Fully-Connected Wireless Sensor Network

Abstract

The distributed adaptive signal fusion (DASF) algorithm is a generic algorithm that can be used to solve various spatial signal and feature fusion optimization problems in a distributed setting such as a wireless sensor network. Examples include principal component analysis, adaptive beamforming, and source separation problems. While the DASF algorithm adaptively learns the relevant second order statistics from the collected sensor data, accuracy problems can arise if the spatial covariance structure of the signals is rapidly changing. In this paper, we propose a method to improve the tracking or convergence speed of the DASF algorithm in a fully-connected sensor network with a broadcast communication protocol. While the improved tracking increases communication cost, we demonstrate that this tradeoff is efficient in the sense that an L-fold increase in bandwidth results in an R times faster convergence with R >> L.

A Computationally Efficient Algorithm for Distributed Adaptive Signal Fusion Based on Fractional Programs

“…The following theorem provides an even stronger result, i.e., convergence of Algorithm 2 to the global minimum ρ * and an optimal solution X * of the global problem under the same mild conditions as those for the original DASF algorithm [16,17], while the proof is omitted due to space constraints.…”

“…Theorem 2 (Proof Omitted). Suppose that Problem (4) for any feasible ρ i satisfies the convergence conditions of the original DASF algorithm 3 (see [16,17]). Then the sequences (ρ i )i and (X i )i obtained by F-DASF also converge respectively to the global minimum ρ * and to an optimal point X * ∈ X * of Problem (2).…”

“…Note that in (17), we have a single signal y fused with the variable x and two deterministic matrices B, B1 = IM and B2 = L, where the former appears in the denominator of the objective:…”

“…The signal y i q is defined in (9), while I i q and L i q are defined as B i q given in (10) when B = IM and B = L respectively. In comparison, the DASF algorithm will require node q to solve a compressed version of (17), solved at each iteration by applying the Dinkelbach algorithm, i.e., by solving the auxiliary problem (18) multiple times. We measure the performance of the F-DASF algorithm compared to the DASF algorithm by looking both at the number of computations and the mean squared error (MSE)…”

“…We refer to this class of problems as distributed signal fusion optimization (DSFO) problems. Classical distributed signal processing algorithms [12][13][14][15] typically assume a per-node separable objective function, which is not the case for The distributed adaptive signal fusion (DASF) framework proposed in [16] allows to solve DSFO problems in a distributed way, achieving convergence to the centralized solution under mild constraints [17]. At each iteration, the DASF framework requires a node of the network to solve a local optimization problem, which inherits the structure of the original (centralized) problem, and which can therefore be solved using the same optimization algorithm.…”