This paper presents a novel approach for the state estimation of poorly-observable low voltage distribution networks, characterized by intermittent and erroneous measurements. The developed state estimation algorithm is based on the Extended Kalman filter, where we have modified the execution of the filtering process. Namely, we have fixed the Kalman gain and Jacobian matrices to constant matrices; their values change only after a larger disturbance in the network. This allows for a fast and robust estimation of the network state. The performance of the proposed state-estimation algorithm is validated by means of simulations of an actual low-voltage network with actual field measurement data. Two different cases are presented. The results of the developed state estimator are compared to a classical estimator based on the weighted least squares method. The comparison shows that the developed state estimator outperforms the classical one in terms of calculation speed and, in case of spurious measurements errors, also in terms of accuracy.