Distribution electrical power systems are routinely designed and built to resist a variety of natural disruptions and continue to operate. However, if terrorist attacks targeted massive components such as smart meters, attackers can bypass traditional anomaly detection tests and influence negatively the stability of the system. In this paper, a novel distribution state estimation method (DSSE) to mitigate the impact of cyber attacks is presented. The new method for distribution state estimation uses few readings from smart meters, doing it robust, even for ill conditioned systems. To validate the method and show its robustness a test was made for a 30 smart home low-voltage (LV) distribution system. Results show how the proposed method is worthwhile in case of communication failure or attacks.