Generalized Conditional Maximum Likelihood Estimators in the Large Sample Regime. Chaumette, E., Vincent, F., Renaux, A., & Galy, J. In *2018 26th European Signal Processing Conference (EUSIPCO)*, pages 271-275, Sep., 2018.

Paper doi abstract bibtex

Paper doi abstract bibtex

In modern array processing or spectral analysis, mostly two different signal models are considered: the conditional signal model (CSM) and the unconditional signal model. The discussed signal models are Gaussian and the signal sources parameters are connected either with the expectation value in the conditional case or with the covariance matrix in the unconditional one. We focus on the CSM resulting from several observations of partially coherent signal sources whose amplitudes undergo a Gaussian random walk between observations. In the proposed generalized CSM, the signal sources parameters become connected with both the expectation value and the covariance matrix. Even though an analytical expression of the associated generalized conditional maximum likelihood estimators (GCM-LEs) can be easily exhibited, it does not allow computation of GCMLEs in the large sample regime. As a main contribution, we introduce a recursive form of the GCMLEs which allows their computation whatever the number of observations combined. This recursive form paves the way to assess the effect of partially coherent amplitudes on GCMLEs mean-squared error in the large sample regime. Interestingly, we exhibit non consistent GMLEs in the large sample regime.

@InProceedings{8553249, author = {E. Chaumette and F. Vincent and A. Renaux and J. Galy}, booktitle = {2018 26th European Signal Processing Conference (EUSIPCO)}, title = {Generalized Conditional Maximum Likelihood Estimators in the Large Sample Regime}, year = {2018}, pages = {271-275}, abstract = {In modern array processing or spectral analysis, mostly two different signal models are considered: the conditional signal model (CSM) and the unconditional signal model. The discussed signal models are Gaussian and the signal sources parameters are connected either with the expectation value in the conditional case or with the covariance matrix in the unconditional one. We focus on the CSM resulting from several observations of partially coherent signal sources whose amplitudes undergo a Gaussian random walk between observations. In the proposed generalized CSM, the signal sources parameters become connected with both the expectation value and the covariance matrix. Even though an analytical expression of the associated generalized conditional maximum likelihood estimators (GCM-LEs) can be easily exhibited, it does not allow computation of GCMLEs in the large sample regime. As a main contribution, we introduce a recursive form of the GCMLEs which allows their computation whatever the number of observations combined. This recursive form paves the way to assess the effect of partially coherent amplitudes on GCMLEs mean-squared error in the large sample regime. Interestingly, we exhibit non consistent GMLEs in the large sample regime.}, keywords = {array signal processing;covariance matrices;Gaussian processes;maximum likelihood estimation;mean square error methods;random processes;signal sources;spectral analysis;modern array processing;spectral analysis;unconditional signal model;signal sources parameters;expectation value;conditional case;covariance matrix;mean-squared error;large sample regime;partially coherent signal sources;signal models;partially coherent amplitudes;GCMLEs;associated generalized conditional maximum likelihood estimators;generalized CSM;Gaussian random walk;Covariance matrices;Computational modeling;Mathematical model;Europe;Signal processing;Arrays;Analytical models}, doi = {10.23919/EUSIPCO.2018.8553249}, issn = {2076-1465}, month = {Sep.}, url = {https://www.eurasip.org/proceedings/eusipco/eusipco2018/papers/1570434964.pdf}, }

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Galy},\n booktitle = {2018 26th European Signal Processing Conference (EUSIPCO)},\n title = {Generalized Conditional Maximum Likelihood Estimators in the Large Sample Regime},\n year = {2018},\n pages = {271-275},\n abstract = {In modern array processing or spectral analysis, mostly two different signal models are considered: the conditional signal model (CSM) and the unconditional signal model. The discussed signal models are Gaussian and the signal sources parameters are connected either with the expectation value in the conditional case or with the covariance matrix in the unconditional one. We focus on the CSM resulting from several observations of partially coherent signal sources whose amplitudes undergo a Gaussian random walk between observations. In the proposed generalized CSM, the signal sources parameters become connected with both the expectation value and the covariance matrix. 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