Input Estimation from Sparse Measurements in LPV Systems and Isotopic Ratios in Polar Firns*

We adress the problem of inverse input reconstruction for linear parameter-varying (LPV) systems when only a limited amount of data (i.e. sparse measurements at final time) is available. We include the LPV property by deriving a time-varying Green's function that models the input/output behavior. The estimation is achieved by solving a least-squares optimization problem parameterized in terms of the input rugosity (regularization term) to take into account the under-constrained nature of the problem. Several automatic tuning methods for the rugosity are described, based on stochastic analysis of the data. A new LPV model is derived for the isotopic ratio of chemical species and our results are applied to the atmospheric history reconstruction of trace gases from polar firn measurements, a problem of prime interest in the environmental sciences community.