It has been demonstrated recently than use of chaotic spreading codes can significantly increase transmission privacy for direct-sequence spread spectrum systems. In this note, we consider the problem of receiver synchronization as a dual estimation of the clean state and the underlying model parameters from the observed noisy chaotic signal. An efficient implementation of the demodulator is investigated owing to the Unscented Kalman Filter, a recent alternative to the Extended Kalman Filter, providing superior performance at an equivalent computational complexity. Numerical simulations show the performance of this novel demodulator against noise for a single user on Gaussian channels