A Blind Calibration Scheme Exploiting Mutual Calibration Relationships for a Dense Mobile Sensor Network

Abstract

In sensor-based measurement systems, the sensor calibrations are crucial to obtain the correct measured values. In this paper, we propose a new blind calibration scheme for a massive mobile sensor network. The mutual calibration relationships between colocated sensors are utilized in a densely deployed sensor network. We model the calibration relationships in a linear algebraic model, and derive an equivalent Laplacian matrix. By just solving the Laplacian linear equation, we can determine how much each sensor has to be calibrated. The proposed calibration scheme is explained as a generalized extension of the simple mean model scheme to the mobile sensor network. Theoretical analysis and simulation results show that the proposed linear algebraic model improves the accuracy of the simple mean model by nearly σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">drift</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> /σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">noise</sub> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> times at maximum, in terms of mean square error, where usually σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">drift</sub> ≫ σ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">noise</sub> . In addition, we show the feasibility of our scheme on human movements, by applying the scheme to the Levy-walk model in the simulation. The most important advantages of our scheme are that the calibration model is straightforward and that the solution is simply obtained with a matrix inversion.