Distributed signal estimation in sensor networks where nodes have different interests

In this paper, we consider distributed signal estimation in sensor networks where the nodes exchange compressed sensor signal observations to estimate different node-specific signals. In particular, we revisit the so-called distributed adaptive node-specific signal estimation (DANSE) algorithm, which applies to the case where the nodes share a so-called ‘common interest’, and cast it in the more general setting where the nodes have ‘different interests’. We prove existence of an equilibrium state for such a setting by using a result from fixed point theory. By establishing a link between the DANSE algorithm and game theory, we point out that any equilibrium of the DANSE algorithm is a Nash equilibrium of the corresponding game. This provides an intuitive interpretation to the resulting signal estimators. The equilibrium state existence proof also reveals a problem with discontinuities in the DANSE update function, which may result in non-convergence of the algorithm. However, since these discontinuities are identifiable, they can easily be avoided by applying a minor heuristic modification to the algorithm. We demonstrate the effectiveness of this modification by means of numerical examples.

► The ‘common interest’ model of DANSE is often not or only partially satisfied.
► We analyze the DANSE algorithm in the case where nodes have ‘different interests’.
► We prove existence of an equilibrium state of the DANSE algorithm.
► Any equilibrium state of the DANSE algorithm is a Nash equilibrium.
► A modification to the algorithm improves robustness in ill-conditioned scenarios.