Browsing by Subject "Mean-squared-error"

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    Statistics of the MLE and Approximate Upper and Lower Bounds-Part 1: Application to TOA Estimation
    (IEEE, 2014-08) Mallat, A.; Gezici, Sinan; Dardari, D.; Craeye, C.; Vandendorpe, L.
    In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramer-Rao lower bound at low and medium signal-to-noise ratios (SNR) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared-error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interva l estimation (MIE). The mean and the distribution of the MLE ar e approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computin g the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accurateness of the proposed MSEAs and the tightness of the derived approximate bounds 1 are validated by considering the example of time-of-arrival estimation.
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    Statistics of the MLE and approximate upper and lower bounds-part II: Threshold computation and optimal pulse design for TOA estimation
    (Institute of Electrical and Electronics Engineers Inc., 2014) Mallat, A.; Gezici, Sinan; Dardari, D.; Vandendorpe, L.
    Threshold and ambiguity phenomena are studied in Part I of this paper where approximations for the mean-squared error (MSE) of the maximum-likelihood estimator are proposed using the method of interval estimation (MIE), and where approximate upper and lower bounds are derived. In this part, we consider time-of-arrival estimation and we employ the MIE to derive closed-form expressions of the begin-ambiguity, end-ambiguity and asymptotic signal-to-noise ratio (SNR) thresholds with respect to some features of the transmitted signal. Both baseband and passband pulses are considered. We prove that the begin-ambiguity threshold depends only on the shape of the envelope of the ACR, whereas the end-ambiguity and asymptotic thresholds only on the shape of the ACR. We exploit the results on the begin-ambiguity and asymptotic thresholds to optimize, with respect to the available SNR, the pulse that achieves the minimum attainable MSE. The results of this paper are valid for various estimation problems.