An extended Kalman filter (EKF)-based estimation approach is developed for the simultaneous estimation of rotor (R-r) and stator (R-s) resistances, the uncertainties of which are commonly known to cause problems in flux and velocity estimation for sensorless control over a wide speed range. The proposed 'braided' EKF approach is based on the consecutive operation of two EKF algorithms running in turn, at each sampling interval and is the first reported study in induction motor sensorless control achieving the accurate estimation of R-r R-r which is reported as a challenge in the literature. The braided-EKF also improves the estimation of flux and velocity over a wide range, including persistent operation at zero speed. The proposed algorithm is tested with simulations and experiments at high, low and zero speed under challenging load torque, velocity and R-r R-r variations. A significant improvement is achieved over conventional single EKF schemes and compatible, if not better results are obtained with previously reported sensorless estimation methods, with no need for signal injection or for different algorithms for different parameters and speed ranges.