Identifiability Analysis for Configuration Calibration in Distributed Sensor Networks

Abstract

In this work, the parameter identifiability of sensor position perturbations in a distributed network is analyzed through establishing the link between rank of the Jacobian matrix and parameter identifiability under Gaussian noise. Here, the calibration is classified as either external or internal, dependent on whether auxiliary sources are exploited. It states that, in the case of internal calibration, sensor position perturbations can be precisely calibrated when the position of a sensor and orientation to a second sensor along with the coordinate of a third sensor along some axis, are known. In the case of external calibration where auxiliary sources are introduced to support the process, the identifiability condition for configuration calibration is to have at least three noncollinear auxiliary sources with the distributed sensor network avoiding the collinear and coplanar geometries. As the assumption of small perturbations is considered, the parameter identifiability is capable of being measured by virtue of the Bayesian Cramer–Rao lower bound (BCRLB), after asymptotical tightness of the BCRLB is verified. Simulations corroborate well with the theoretical development.

Keywords

• distributed sensor network
• Bayesian Cramer–Rao lower bound (BCRLB)
• configuration calibration
• parameter identifiability
• Jacobian matrix