A Dynamic Bayesian Nonparametric Model for Blind Calibration of Sensor Networks

Abstract

We consider the problem of blind calibration of a sensor network where the sensor gains and offsets are estimated from noisy observations of unknown signals. This is in general a non-identifiable problem, unless restrictive assumptions on the signal subspace or sensor observations are imposed. We show that if each signal observed by the sensors follows a known dynamic model with additive noise, then the sensor gains and offsets are identifiable. We propose a dynamic Bayesian nonparametric model to infer the sensors' gains and offsets. Our model allows different sensor clusters to observe different unknown signals, without knowing the sensor clusters a priori. We develop an offline algorithm using block Gibbs sampling and a linearized forward filtering backward sampling method that estimates the sensor clusters, gains and offsets jointly. Furthermore, for practical implementation, we also propose an online inference algorithm based on particle filtering and local Markov chain Monte Carlo. Simulations using a synthetic dataset, and experiments on two real datasets suggest that our proposed methods perform better than several other blind calibration methods, including a sparse Bayesian learning approach, and methods that first cluster the sensor observations and then estimate the gains and offsets.

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“…Yang et al [88] also based their work on the idea of [19]. They prove that, if the underlying signals follow a first-order auto-regressive process, then the parameters of the linear calibration model are recoverable.…”

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“…Most of the proposed appraches to blind calibration in the existing literature are centralized and non-recursive [ 12 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 ]. Within this class of methods, in refs.…”

“…The approach in ref. [ 34 ] also does not rely on stringent assumptions about signal subspace, but assume first-order auto-regressive signal process model. The authors of [ 35 ] introduce linear algebraic model of calibration relationships in a SN with centralized architecture to improve the simple mean calibration scheme, assuming sufficiently dense deployment.…”