Abstract: The paper presents an original and empirically validated method for nonlinear multivariate data correction and sensor calibration, inspired by a Lagrangian approach. Being analytical and non-iterative, the method is extremely efficient, computationally. It is also very precise and accurate, since the precision truncation errors of iterative methods are avoided, and the resulting correcting function fits the calibration dataset with zero residual errors. Being inherently infinitely differentiable, the method avoids the discontinuities of piecewise approaches. The method accounts for typical nonlinearities in the response curves of most analog sensors and transducers, as well as nonlinear influences from the explanatory covariates. It is also virtually immune to over-fitting. A major application of this approach is temperature compensation of analog sensors, transducers, voltage references, and piezo oscillators. This is particularly relevant for metrological applications outside laboratory-controlled environments – e.g., strain gauge networks for outdoor structural health monitoring. A practical application for thermocouples is demonstrated, where the adverse influences of the cold junction potential and the temperature-induced drift of a voltage reference are, simultaneously, compensated. A simple and practical regression method for calculating the transfer function parameter matrix will be demonstrated and its implementation will be shown. A practical methodology for acquiring a representative calibration dataset is proposed.

Keywords: Multivariate, Nonlinear, Non-overfitting, Sensor calibration, Signal correction, Temperature compensation.

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