Temperature- and frequency-dependent variations of the rotor (R-r') and stator (R-s) resistances pose a challenge in the accurate estimation of flux and velocity in the sensorless control of induction motors (IMs) over a wide speed range. Solutions have been sought to the problem by signal injection and/or by the use of different algorithms for the different parameters and states of the same motor. In this paper, a novel Extended -Kalman-Filter (EKF)-based estimation technique is developed for the solution of the problem based on the consecutive operation of two EKF algorithms at every time step. The proposed "braided" EKF technique is experimentally tested under challenging parameter and load variations in a wide speed range, including low speed. The results demonstrate a significantly increased accuracy in the estimation of R-s and R-r', as well as load torque, flux, and velocity in transient and steady state, when compared with single EKFs or other approaches taken to estimate these parameters and states in the sensorless control of IMs. The improved results also motivate the utilization of the new estimation approach in combination with a variety of control methods which depend on accurate knowledge of a high number of parameters and states.