DETECTION AND ESTIMATION OF SUPERIMPOSED SIGNALS (ARRAYS, MDL, AIC).

摘要

This dissertation addresses the problem of estimating the number, the parameters, and the waveforms of superimposed signals. The optimal solution to the problem as well as suboptimal solutions that are computationally more efficient are derived.; The optimal solution is derived by casting the problem as a model selection problem and then applying the MDL model selection criterion to simultaneously estimate the number of signals, their parameters and their waveforms. In contrast to existing solutions to the combined detection-estimation problem, ours is optimal; the consistency of the estimator of the number of signals as well as the efficiency of the estimates of the signal parameters and wavefronts are proven.; The suboptimal solutions are obtained by decoupling the three subproblems. First an estimator of the number of signals is derived. Then, with the estimate of the number of signals at hand, two estimators of the signal parameters are constructed. Finally, with both the estimate of the number of signals and the estimate of their parameters, an estimator of the signal waveforms is derived.; The estimator of the number of signals is based on the application of the MDL model selection criterion to the eigenstructure of the sample-covariance matrix. The resulted estimator is computationally efficient and is shown to be consistent. Unlike the existing estimator of Bartlett-Lawley, no subjectively chosen thresholds are required.; The two suboptimal estimators of the signal parameters are cast in terms of the eigenstructure of the sample-covariance matrix. However, unlike the estimator of Schmidt and Bienvenu-Kopp, the new estimators are not based solely on the underlying orthogonal decomposition of the space spanned by the sampled data, but also on statistical considerations motivated by the structure of the maximum likelihood estimator.; The estimator of the signal waveforms is based upon the least-squares criterion. Unlike the minimum variance estimator of Capon, which suffers severe degradation when the signals are correlated, this new estimator exploits the correlation to improve its performance.