# Distributed Sensor Network Calibration Under Sensor Nonlinearities with Applications in Aerodynamic Pressure Sensing

## TL;DR

This paper presents a theoretical analysis of distributed calibration algorithms for sensor networks, showing how they handle nonlinearities and noise, with applications in aerodynamic pressure sensing.

## Contribution

The paper introduces a modified calibration algorithm that is more robust to sensor nonlinearities by using a reference sensor.

## Key findings

- The modified calibration algorithm is significantly more robust to unknown sensor nonlinearities than the standard consensus-based method.
- Stability proofs and noise analysis confirm the practical relevance of the algorithms in stochastic environments.
- The proposed algorithm enables efficient real-time re-calibration of complex sensor networks during normal operations.

## Abstract

The theoretical part of this paper is devoted to a class of distributed blind calibration algorithms for large sensor networks based on consensus. The basic blind calibration method starts from affine sensor models and calibration functions, aiming to equalize corrected sensor offsets and gains without requiring any a priori knowledge of the measured signal. The main focus is to systematically and rigorously analyze the behavior of the calibration algorithms of the stochastic approximation type under nonlinear sensor models and stochastic environments, and to provide recommendations that are relevant to practice. It is demonstrated that the calibration algorithm—based on consensus with respect to all the calibration parameters—is far less robust to unknown sensor nonlinearities than the modified algorithm, taking one micro-calibrated sensor as a reference. Stability proofs of the algorithms are given in the bounded input–bounded output sense. The influences of measurement and communication noises are also analyzed using the theory of stochastic approximation. Numerous simulation results provide a comprehensive picture of the algorithm properties that are relevant to practice. This is followed by an important verification of the theoretical results, obtained by applying the analyzed blind calibration algorithms to an originally designed multichannel instrument for aerodynamic pressure sensing. A description of the new instrument is given, together with essential aspects of the implementation of the blind calibration algorithm. It is shown that the selected algorithm can be seen as a simple and efficient practical tool for blind online real-time re-calibration of complex sensor networks during normal system operations.