This paper presents a new method for estimating the needle pose and curvature in the context of robotically steered needles. The needle tip trajectory is represented by a modified unicycle kinematic model. A multi-rate unscented Kalman filter is proposed for the first time in needle steering to fuse asynchronous data coming from 3D B-mode ultrasound images, robot sensors and pre-operative elastography measurements. To demonstrate it, 51 unconstrained 3D insertions have been made in various media. The instantaneous localisation error is smaller than 0.6 mm and the prediction of the final tip position is smaller than 2 mm based on the observation of the first 2 cm of 8 cm deep insertions.