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This paper proposes a novel method to estimate the parameters of chaotic signals corrupted by noise. By exploiting the ergodic property of chaotic signals, it is shown here that signal parameters can be estimated accurately from the noisy chaotic signal. The proposed estimator is proved to be consistent. The asymptotic variance of the proposed method and the Cramer-Rao lower bound (CRLB) are derived analytically to assess the estimation performance. Computer simulations confirm that the proposed ergodic estimation approach provides good parameter estimates even at low signal-to-noise ratio (SNR), and its performance is superior to conventional estimation techniques. This method is then applied to ultra-wide-band (UWB) communication by proposing a novel ergodic chaotic parameter modulation based UWB (ECPM-UWB) scheme. The ECPM-UWB scheme is analog and noncoherent. The communication performance of ECPM-UWB is found to be superior through theoretical mean-square-error (MSE) analysis and computer simulations. The ECPM-UWB scheme is shown to have good spectral characteristics. In addition, the proposed scheme is shown to be robust against channel estimation error and multipath fading using both theoretical and numerical analyses.