]. A. Bjö90 and . Björck, Numerical methods for least squares problems. Siam, 1990. [Can] ´ E. Canot. Muesli Reference Manual -Fortran 95 implementation

]. O. Com99 and . Combarieu, Caractérisation mécanique d'un massif de sable compacté: Cohérence des essais réalisés, Laboratoire régional des Ponts et Chaussées de Rouen, 1999.

]. A. Cor13 and . Cordero, Transferts de chaleur dans un sol sec chauffé par le dessus. Rapport postdoctoral , Centre de Recherche en Archéologie, 2013.

]. T. Dav04 and . Davis, Algorithm 832: Umfpack, an unsymmetric-pattern multifrontal method, ACM Transactions on Mathematical Software, vol.30, issue.2, pp.196-199, 2004.

R. [. Dennis and . Schnabel, Numerical methods for unconstrained optimization and nonlinear equations, 1983.
DOI : 10.1137/1.9781611971200

]. E. Eck07 and . Eckmeier, Detecting prehistoric fire-based farming using biogeochemical markers, 2007.

P. [. Engl and . Kugler, Nonlinear inverse problems: theoretical aspects and some industrial applications. Multidisciplinary Methods for Analysis, Optimization and Control of Complex systems, pp.3-47, 2005.

]. M. Heb73 and . Hebden, An algorithm for minimization using exact second derivatives, Atomic Energy Research Establishment, 1973.

]. A. Hin93 and . Hindmarsh, Description and use of LSODE, the Livermore solver for ordinary differential equations, 1993.

]. K. Lev44 and . Levenberg, A method for the solution of certain nonlinear problems in least squares, Quarterly of Applied Mathematics, vol.2, pp.164-168, 1944.

P. [. Laloy and . Massard, Nouvelle méthode thermique d'´ etude des foyers préhistoriques. Revue d'Archéométrie, pp.33-40, 1984.

O. [. Landunjoye, A. A. Sanuade, and . Olaojo, Variability of soil thermal properties of a seasonally cultivated agricultural teaching and research farm An algorithm for least squares estimation of nonlinear parameters, Global Journal of Science Frontier Research Agriculture and Veterinary SIAM Journal of Applied Mathematics, vol.13, issue.11, pp.40-64431, 1963.

´. [. Muhieddine, R. Canot, and . March, Various approaches for solving problems in heat conduction with phase change, International Journal on Finite Volumes, vol.6, issue.1, pp.1-20, 2009.
URL : https://hal.archives-ouvertes.fr/hal-01120384

´. [. Muhieddine, R. Canot, and . March, Heat transfer modeling in saturated porous media and identification of the thermophysical properties of the soil by inverse problem, Applied Numerical Mathematics, vol.62, issue.9, pp.1026-1040, 2012.
DOI : 10.1016/j.apnum.2012.02.008

URL : https://hal.archives-ouvertes.fr/hal-00757211

J. J. Moré, B. S. Garbow, and K. E. Hillstrom, User guide for MINPACK-1, 1980.

. Mhb-+-12-]-g, J. Malherbe, A. Henry, C. Bakali, S. Bissieux et al., Measurement of thermal conductivity of granular materials over a wide range of temperatures. comparison with theoretical models, Journal of Physics, vol.395, 2012.

B. [. Majchrzak, J. S. Mochnaki, and . Suchy, Identification of substitute thermal capacity of solidifying alloy, Journal of Theoretical and Applied Mechanics, vol.46, issue.2, pp.257-268, 2008.

]. J. Mor78 and . Moré, The Levenberg-Marquardt algorithm: implementation and theory. Numerical Analysis, Lecture Notes in Mathematics, p.630, 1978.

G. A. Narsilio, T. S. Yun, J. Kress, and T. M. Evans, Hydraulic and thermal conduction phenomena in soils at the particle-scale: Towards realistic FEM simulations, IOP Conference Series: Materials Science and Engineering, vol.10, 2010.
DOI : 10.1088/1757-899X/10/1/012086

H. [. Ozisik and . Orlande, Inverse heat transfer, 2000.

. R. Pez-+-09-]-s, L. M. Pope, C. L. Ellwein, V. Zapata, C. T. Novak et al., Estimation and identification of parameters in a lumped cerebrovascular model, Mathematical Biosciences and Engineering, vol.6, issue.1, pp.93-115, 2009.

]. S. Sha08 and . Shan, A Levenberg-Marquardt Method For Large-Scale Bound-Constrained Nonlinear Least-Squares The University of British Columbia, The Faculty of Graduate Studies, Computer Science), 2008.