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The electrical transmission infrastructure worldwide has witnessed severe environmental hazards, accidents and in countries like Columbia and India malicious attacks leading to the sabotage of transmission towers. These events underscore the need to develop new techniques to ensure safe and reliable operation of the transmission infrastructure. This paper deals with an online monitoring technique based on mechanical state estimation of overhead transmission lines subjected to tower tilt. The proposed approach provides a quick assessment of the grid condition at the initial stages of an extreme mechanical event. A computational algorithm based on least squares state estimation is applied to transmission line sag-tension equations developed through a geometric transformation to determine conductor sag levels. The measurements of tower tilt, conductor tension, core temperature, inclination angle of conductor with the horizontal and other transmission line parameters are utilized for the purpose of state estimation. Appropriate warning alarms generated in the case of considerable changes in the sag levels or violation of limits enable operators to take designated actions during the initial stages of the physical disruption.