Method to control a laundry drying machine, which comprises: a rotatable laundry drum designed to rotate about an axis and adapted to be loaded with laundry, an electric motor for rotating said rotatable laundry drum about its axis, hot air generator means for supplying a drying airflow to the laundry drum, said method comprising the step of controlling said electric motor and said hot air generator means during a drying cycle, based on one or more physicals quantities being associated with said rotatable laundry drum loaded with laundry, said electric motor and said hot air generator means, the method further comprising: a) collecting said physicals quantities during an initial phase of said drying cycle, wherein said physicals quantities to be collected during said initial phase comprise: a first quantity indicative of the inertia of said laundry drum loaded with laundry, a second quantity indicative of the temperature of the drying airflow, a third quantity indicative of a static unbalance of said laundry drum loaded with laundry, a fourth quantity indicative of a fan speed comprised in said hot air generator means, a fifth quantity indicative of the air temperature at the outlet of the drum of said hot air generator means, a sixth quantity indicative of motor torque, a seventh quantity indicative of the mean torque during the drying cycle, b) performing an estimation of polynomial coefficients of a cubic polynomial model indicative of an estimated change of the laundry moisture over the time, based on respective linear polynomial models comprising said collected physicals quantities, c) performing an estimation of the laundry moisture by said cubic polynomial model based on said estimated polynomial coefficients. a rotatable laundry drum designed to rotate about an axis and adapted to be loaded with laundry, an electric motor for rotating said rotatable laundry drum about its axis, hot air generator means for supplying a drying airflow to the laundry drum, said method comprising the step of controlling said electric motor and said hot air generator means during a drying cycle, based on one or more physicals quantities being associated with said rotatable laundry drum loaded with laundry, said electric motor and said hot air generator means, a) collecting said physicals quantities during an initial phase of said drying cycle, wherein said physicals quantities to be collected during said initial phase comprise: a first quantity indicative of the inertia of said laundry drum loaded with laundry, a second quantity indicative of the temperature of the drying airflow, a third quantity indicative of a static unbalance of said laundry drum loaded with laundry, a fourth quantity indicative of a fan speed comprised in said hot air generator means, a fifth quantity indicative of the air temperature at the outlet of the drum of said hot air generator means, a sixth quantity indicative of motor torque, a seventh quantity indicative of the mean torque during the drying cycle, b) performing an estimation of polynomial coefficients of a cubic polynomial model indicative of an estimated change of the laundry moisture over the time, based on respective linear polynomial models comprising said collected physicals quantities, c) performing an estimation of the laundry moisture by said cubic polynomial model based on said estimated polynomial coefficients.