W. Borne-de, Weinstein déterministe avec une optimisation sur h et s, borne de Weiss-Weinstein avec optimisation sur h et s = 1 2 , s = 1 4 , et s = 0, borne de Weiss-Weinstein avec h = 0 et s = 0, la borne de Chapman-Robbins et borne de Cramér, p.82

W. Borne-de, Weinstein avec une optimisation sur h et s, borne de Weiss- Weinstein avec optimisation sur h et s = 1 2 , s = 1 4 , et s = 0

]. J. Bibliographie-[-abe90 and . Abel, A bound on mean square estimate error, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, pp.1345-1348, 1990.

]. J. Abe93 and . Abel, A bound on mean square estimate error, IEEE Trans. Inform. Theory, vol.39, pp.1675-1680, 1993.

L. Atallah, J. P. Barbot, and P. Larzabal, From Chapman-Robbins bound towards Barankin bound in threshold behaviour prediction, Electronics Letters, vol.40, issue.4, pp.279-280, 2004.
DOI : 10.1049/el:20040152

]. L. Abl04b, J. P. Atallah, P. Barbot, and . Larzabal, SNR threshold indicator in data aided frequency synchronization, IEEE Signal Processing Lett, vol.11, pp.652-654, 2004.

]. T. And84 and . Anderson, An Introduction to Multivariate Statistical Analysis, 1984.

I. [. Abramowitz, . Stegunath05-]-f, and . Athley, Handbook of Mathematical Functions with Formulas , Graphs and Mathematical Tables Threshold region performance of Maximum Likelihood direction of arrival estimators, IEEE Trans. Signal Processing, vol.53, pp.1359-1373, 1972.

]. A. Bag69 and . Baggeroer, Barankin bound on the variance of estimates of Gaussian random process, 1969.

]. E. Bar49 and . Barankin, Locally best unbiased estimates, Ann. Math. Stat, vol.20, pp.477-501, 1949.

]. K. Bel95 and . Bell, Performance bounds in parameter estimation with application to bearing estimation, 1995.

Y. [. Bell and H. L. Ephraim, Van Trees. Ziv Zakai lower bounds in bearing estimation, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, pp.2852-2855, 1995.

Y. [. Bell and H. L. Ephraim, Explicit Ziv-Zakai lower bound for bearing estimation, IEEE Transactions on Signal Processing, vol.44, issue.11, pp.2810-2824, 1996.
DOI : 10.1109/78.542439

E. Boyer, P. Forster, and P. Larzabal, Nonasymptotic Performance Analysis of Beamforming With Stochastic Signals, IEEE Signal Processing Letters, vol.11, issue.1, pp.23-25, 2004.
DOI : 10.1109/LSP.2003.819358

]. E. Bfl04b, P. Boyer, P. Forster, and . Larzabal, Non asymptotic statistical performances of beamforming for deterministic signals, IEEE Signal Processing Lett, vol.11, issue.1, pp.20-22, 2004.

]. A. Bibliographie-[-bha43 and . Bhattacharyya, On a measure of divergence between two statistical populations defined by their probability distributions, Bull. Calcutta Math. Soc, vol.35, pp.99-109, 1943.

]. A. Bha46 and . Bhattacharyya, On some analogues of the amount of information and their use in statistical estimation, Sankhya Indian J. of Stat, vol.8, pp.1-14, 1946.

B. Z. Bobrovsky, E. Mayer-wolf, and M. Zakai, Some Classes of Global Cramer-Rao Bounds, The Annals of Statistics, vol.15, issue.4, pp.1421-1438, 1987.
DOI : 10.1214/aos/1176350602

]. J. Böh84 and . Böhme, Estimation of source parameters by maximum likelihood and non linear regression, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, pp.731-734, 1984.

]. J. Böh86 and . Böhme, Estimation of spectral parameters of correlated signals in wavefields, Signal Processing, vol.10, pp.329-337, 1986.

]. E. Boy02 and . Boyer, Estimation paramétrique des moments spectraux d'échos Doppler : application aux radars strato-troposphériques, 2002.

]. Y. Bre88 and . Bresler, Maximum likelihood of linearly structured covariance with application to antenna array processing, Proc. ASSP Workshop on Spectrum Estimation and Modeling, pp.172-175, 1988.

Y. [. Bell, Y. Steinberg, H. L. Ephraim, and . Van-trees, Extended Ziv-Zakai lower bound for vector parameter estimation, IEEE Transactions on Information Theory, vol.43, issue.2, pp.624-638, 1997.
DOI : 10.1109/18.556118

G. [. Bellini and . Tartara, Bounds on Error in Signal Parameter Estimation, IEEE Transactions on Communications, vol.22, issue.3, pp.340-342, 1974.
DOI : 10.1109/TCOM.1974.1092192

M. [. Bobrovsky and . Zakai, A lower bound on the estimation error for certain diffusion processes, IEEE Transactions on Information Theory, vol.22, issue.1, pp.45-52, 1976.
DOI : 10.1109/TIT.1976.1055513

]. J. Cap69 and . Capon, High resolution frequency wavenumber spectrum analysis, Proc. IEEE, pp.1408-1418, 1969.

. [. Ciblat, . Ph, P. Forster, and . Larzabal, Harmonic retrieval in noncircular complexvalued multiplicative noise : Barankin bound, In EUSIPCO, 2004.

M. [. Ciblat and . Ghogho, ZIV-ZAKAI bound for harmonic retrieval in multiplicative and additive gaussian noise, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005.
DOI : 10.1109/SSP.2005.1628658

P. Ciblat, M. Ghogho, . Ph, P. Forster, and . Larzabal, Harmonic retrieval in the presence of non-circular Gaussian multiplicative noise: performance bounds, Signal Processing, vol.85, issue.4, pp.737-749, 2005.
DOI : 10.1016/j.sigpro.2004.11.015

]. E. Cha04 and . Chaumette, Contribution à la caractérisation des performances des problèmes conjoints de détection et d'estimation, 2004.

]. E. Cin75 and . Cinlar, Introduction to Stochastic Process, 1975.

P. [. Chaumette, P. Larzabal, and . Forster, On the influence of a detection step on lower bounds for deterministic parameter estimation, IEEE Transactions on Signal Processing, vol.53, issue.11, pp.4080-4090, 2005.
DOI : 10.1109/TSP.2005.857027
URL : https://hal.archives-ouvertes.fr/halshs-00158304

R. [. Cedervall and . Moses, Efficient maximum likelihood DOA estimation for signals with known waveforms in the presence of multipath, Con80] W. J. Conover. Practical Nonparametric Statistics, pp.808-811, 1980.
DOI : 10.1109/78.558512

H. [. Chapman and . Robbins, Minimum Variance Estimation Without Regularity Assumptions, The Annals of Mathematical Statistics, vol.22, issue.4, pp.581-586, 1951.
DOI : 10.1214/aoms/1177729548

]. H. Cra46 and . Cramér, Mathematical Methods of Statistics, 1946.

S. [. Clergeot, A. Tressens, M. Ouamri, J. Zakai, and . Ziv, Performance of high resolution frequencies estimation methods compared to the Cramer-Rao bounds, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.37, issue.11, pp.1703-172090, 1975.
DOI : 10.1109/29.46553

[. Delmas and H. Abeida, Stochastic Cram??r???Rao Bound for Noncircular Signals with Application to DOA Estimation, IEEE Transactions on Signal Processing, vol.52, issue.11, pp.3192-3199, 2004.
DOI : 10.1109/TSP.2004.836462

[. Delmas and H. Abeida, Stochastic Cramer-Rao bounds of DOA estimates for BPSK and QPSK modulated signals, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.117-126, 2005.
DOI : 10.1109/ICASSP.2004.1326197

]. G. Dar45 and . Darmois, Sur les lois limites de la dispersion de certaines estimations Application des propriétés de la limite au sens du calcul des probabilités à l'étude des diverses questions d'estimation, Rev. Inst. Int. Statist. Ecol. Poly, vol.13, issue.3, pp.9-15305, 1937.

E. [. Forster, P. Boyer, and . Larzabal, Nonefficiency of Stochastic Beamforming Bearing Estimates at High SNR and Finite Number of Samples, IEEE Signal Processing Letters, vol.11, issue.5, pp.509-512, 2004.
DOI : 10.1109/LSP.2004.826645

. Ph, E. Forster, P. Boyer, A. Larzabal, and . Renaux, Non-efficacité et non-Gaussianité asymptotiques d'un estimateur du maximum de vraisemblance à fort rapport signal sur bruit, Proceedings GRETSI, pp.125-128, 2003.

I. [. Fraser and . Guttman, Bhattacharyya Bounds without Regularity Assumptions, The Annals of Mathematical Statistics, vol.23, issue.4, pp.629-632, 1952.
DOI : 10.1214/aoms/1177729344

]. R. Fis22, . Fisher-ph, P. Forster, and . Larzabal, On the mathematical foundations of theoretical statistics Sur les bornes minimales pour l'estimation de paramètres déterministes, Proceedings GRETSI, pp.309-707, 1922.

. Ph, P. Forster, and . Larzabal, On lower bounds for deterministic parameter estimation, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 2002.

]. M. Fre43 and . Frechet, Sur l'extension de certaines evaluations statistiques au cas de petit echantillons, Rev. Inst. Int. Statist, vol.11, pp.182-205, 1943.

J. [. Ferrari and . Tourneret, Barankin lower bound for change-points in independent sequences, IEEE Workshop on Statistical Signal Processing, 2003, 2003.
DOI : 10.1109/SSP.2003.1289526
URL : https://hal.archives-ouvertes.fr/hal-00376422

]. F. Gla72 and . Glave, A new look at the Barankin lower bound, IEEE Trans. Inform. Theory, vol.18, issue.3, pp.349-356, 1972.

]. J. Ham50 and . Hammersley, On estimating restricted parametrers, J. R. Soc. Ser. B, vol.12, pp.192-240, 1950.

J. [. Haykin, T. J. Litva, and . Shepherd, Radar Array Processing, 1993.
DOI : 10.1007/978-3-642-77347-1

R. [. Ibragimov, Has'minski. Statistical estimation, 1981.

]. A. Jaf88 and . Jaffer, Maximum likelihood direction finding of stochastic sources : a separable solution, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1988.

]. S. Kay93 and . Kay, Fundamentals of Statistical Signal Processing, NJ, vol.1, 1993.

]. J. Kie52, . Kieferkno97-]-l, and . Knockaert, On minimum variance estimators The Barankin bound and threshold behavior in frequency estimation, Ann. Math. Stat. IEEE Trans. Signal Processing, vol.23, issue.45, pp.627-6292398, 1952.

]. V. Kot59, Kotel'nikov. The Theory of Optimum Noise Immunity, 1959.

D. [. Kumaresan and . Tufts, Estimating the Angles of Arrival of Multiple Plane Waves, IEEE Transactions on Aerospace and Electronic Systems, vol.19, issue.1, pp.134-138, 1983.
DOI : 10.1109/TAES.1983.309427

R. [. Li and . Compton, Maximum likelihood angle estimation for signals with known waveforms, IEEE Transactions on Signal Processing, vol.41, issue.9, pp.2850-2862, 1993.
DOI : 10.1109/78.236507

]. E. Leh83 and . Lehmann, Theory of Point Estimation, 1983.

J. Li, B. Halder, P. Stoica, and M. Viberg, Computationally efficient angle estimation for signals with known waveforms, IEEE Trans. Signal Processing, vol.43, pp.2154-2163, 1995.

]. H. Lil67 and . Lilliefors, On the Kolmogorov Smirnov test for normality with mean and variance unknown, Journal of the American Statistical Association, vol.62, pp.399-402, 1967.

J. [. Li, D. W. Vaccaro, and . Tuft, Min-norm linear prediction for arbitrary sensor arrays, International Conference on Acoustics, Speech, and Signal Processing, pp.2613-2616, 1989.
DOI : 10.1109/ICASSP.1989.267003

]. A. Man04 and . Manikas, Differential geometry in array processing, 2004.

]. T. Mar97 and . Marzetta, Computing the Barankin bound by solving an unconstrained quadratic optimization problem, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 1997.

L. [. Mcaulay and . Seidman, A useful form of the Barankin lower bound and its application to PPM threshold analysis, IEEE Transactions on Information Theory, vol.15, issue.2, pp.273-279, 1969.
DOI : 10.1109/TIT.1969.1054297

M. [. Ottersten, P. Viberg, A. Stoica, and . Nehorai, Exact and Large Sample Maximum Likelihood Techniques for Parameter Estimation and Detection in Array Processing, Radar Array Processing, pp.99-151, 1993.
DOI : 10.1007/978-3-642-77347-1_4

]. J. Pie63, ]. A. Pierceprk86, R. Paulraj, T. Roy, and . Kailath, Approximate error probabilities for optimal diversity combining A subspace rotation approach to signal parameter estimation, IEEE Trans. Comm. Syst, pp.1044-1045, 1963.

E. [. Quinlan, P. Chaumette, and . Larzabal, A Direct Method to Generate Approximations of the Barankin Bound, 2006 IEEE International Conference on Acoustics Speed and Signal Processing Proceedings, 2006.
DOI : 10.1109/ICASSP.2006.1660777

A. Renaux, L. N. Atallah, . Ph, P. Forster, and . Larzabal, A useful form of the Abel bound and its application to estimator threshold prediction. to appear in Information and accuracy attainable in the estimation of statistical parameters, IEEE Trans. on Signal Processing Bull. Calcutta Math. Soc, vol.37, pp.81-91, 1945.
URL : https://hal.archives-ouvertes.fr/inria-00444722

]. C. Rao02, . C. Raorb74-]-d, R. R. Rife, and . Boorstyn, Linear Statistical Inference and Its Applications Single tone parameter estimation from discrete time observations, IEEE Trans. Inform. Theory, vol.20, pp.591-598, 1974.

]. S. Red79, A. Reddi, . Renaux, . Ph, E. Forster et al., Multiple source location. A digital approach [Ren06] A. Renaux. Weiss-Weinstein bound for data aided carrier estimation. accepted (minor revision) for IEEE Signal Processing Letters Asymptotic non efficiency of a maximum likelihood estimator at finite number of samples, Proceedings EUSIPCO, pp.95-105, 1979.

A. Renaux, . Ph, E. Forster, P. Boyer, and . Larzabal, Non efficiency and non Gaussianity of a maximum likelihood estimator at high signal-to-noise ratio and finite number of samples, 2004 IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.121-124, 2004.
DOI : 10.1109/ICASSP.2004.1326209
URL : https://hal.archives-ouvertes.fr/halshs-00158402

A. Renaux, . Ph, E. Forster, P. Boyer, and . Larzabal, Unconditional Maximum Likelihood Performance at Finite Number of Samples and High Signal-to-Noise Ratio, IEEE Transactions on Signal Processing, vol.55, issue.5, 2006.
DOI : 10.1109/TSP.2007.893205
URL : https://hal.archives-ouvertes.fr/inria-00444716

A. Renaux, . Ph, E. Forster, P. Chaumette, and . Larzabal, On the High-SNR Conditional Maximum-Likelihood Estimator Full Statistical Characterization, IEEE Transactions on Signal Processing, vol.54, issue.12, 2006.
DOI : 10.1109/TSP.2006.882072
URL : https://hal.archives-ouvertes.fr/inria-00444708

A. Renaux, . Ph, P. Forster, and . Larzabal, A new derivation of the bayesian bounds for parameter estimation, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005, 2005.
DOI : 10.1109/SSP.2005.1628659
URL : https://hal.archives-ouvertes.fr/inria-00444830

A. Renaux, . Ph, P. Forster, and . Larzabal, Une nouvelle approche des bornes bayésiennes, Proceedings GRETSI, 2005.

]. A. Rflr06a, . Renaux, . Ph, P. Forster, C. D. Larzabal et al., The Bayesian Abel bound on the mean square error, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, 2006.

A. Renaux, . Ph, P. Forster, C. D. Larzabal, . D. Richmondric05-]-c et al., A new derivation of the Bayesian bounds for parameter estimation. in preparation for Capon algorithm mean squared error threshold SNR prediction and probability of resolution, IEEE Trans. on Information Theory IEEE Trans. Signal Processing, issue.8, pp.532748-2764, 2005.
URL : https://hal.archives-ouvertes.fr/inria-00444830

[. Reuven and H. Messer, The use of the Barankin bound for determining the threshold SNR in estimating the bearing of a source in the presence of another, 1995 International Conference on Acoustics, Speech, and Signal Processing, pp.1645-1648, 1995.
DOI : 10.1109/ICASSP.1995.479887

[. Reuven and H. Messer, A Barankin-type lower bound on the estimation error of a hybrid parameter vector, IEEE Transactions on Information Theory, vol.43, issue.3, pp.1084-1093, 1997.
DOI : 10.1109/18.568725

[. Reuven and H. Messer, On the effect of nuisance parameters on the threshold SNR value of the Barankin bound, IEEE Transactions on Signal Processing, vol.47, issue.2, pp.523-527, 1999.
DOI : 10.1109/78.740136

A. [. Roy, T. Paulraj, and . Kailath, ESPRIT--A subspace rotation approach to estimation of parameters of cisoids in noise, Principles of Mathematical Analysis, pp.1340-1342, 1976.
DOI : 10.1109/TASSP.1986.1164935

C. [. Steinhardt and . Bretherton, Thresholds in frequency estimation, ICASSP '85. IEEE International Conference on Acoustics, Speech, and Signal Processing, pp.1273-1276, 1985.
DOI : 10.1109/ICASSP.1985.1168170

]. R. Sch81, . E. Schmidtsgb67-]-c, R. G. Shannon, E. R. Galleger, and . Berlekamp, A signal subspace approach to multiple emitter location and spectral estimation Lower bounds to error probability for coding on discrete memoryless channels i. Information and Control, pp.65-103, 1967.

T. [. Scharf, . T. Mcwhortersmi05a-]-s, and . Smith, Geometry of the Cramer Rao bound Covariance, subspace, and intrinsic Cramer Rao bounds, [Smi05b] S. T. Smith. Statistical resolution limits and the complexified Cramer Rao bound. [SN89] P. Stoica and A. Nehorai. MUSIC, maximum likelihood and the Cramer Rao bound, pp.301-3111610, 1993.

]. P. Sn90b, A. Stoica, and . Nehorai, Performances study of conditional and unconditional direction of arrival estimation, IEEE Trans. Acoust., Speech, Signal Processing, vol.38, pp.1783-1795, 1990.

J. [. Tabrikian and . Krolik, Barankin bound for source localization in shallow water, 1997 IEEE International Conference on Acoustics, Speech, and Signal Processing, 1997.
DOI : 10.1109/ICASSP.1997.599684

J. [. Tabrikian and . Krolik, Barankin bounds for source localization in an uncertain ocean environment, IEEE Transactions on Signal Processing, vol.47, issue.11, pp.2917-2927, 1999.
DOI : 10.1109/78.796428

L. [. Thomas, D. W. Scharf, and . Tufts, The probability of a subspace swap in the SVD, IEEE Transactions on Signal Processing, vol.43, issue.3, pp.730-736, 1994.
DOI : 10.1109/78.370627

]. H. Van68 and . Vantrees, Detection, Estimation and Modulation Theory, 1968.

]. H. Van01 and . Vantrees, Detection, Estimation and Modulation Theory : Radar-Sonar Signal Processing and Gaussian Signals in Noise Asymptotic Statistics, Van02] H. L. VanTrees. Detection, Estimation and Modulation theory : Optimum Array Processing, 1998.

B. [. Viberg, M. Ottersten, B. Viberg, T. Ottersten, and . Kailath, Sensor array processing based on subspace fitting, IEEE Transactions on Signal Processing, vol.39, issue.5, pp.1110-1121, 1991.
DOI : 10.1109/78.80966

B. [. Viberg, A. Ottersten, and . Nehorai, Performance analysis of direction finding with large arrays and finite data, IEEE Transactions on Signal Processing, vol.43, issue.2, pp.469-477, 1995.
DOI : 10.1109/78.348129

]. E. Wei88 and . Weinstein, Relations between Belini-Tartara, Chazan-Zakai-Ziv, and Wax-Ziv lower bounds, IEEE Trans. Inform. Theory, vol.34, pp.342-343, 1988.

E. [. Weiss and . Weinstein, Fundamental limitations in passive time delay estimation--Part I: Narrow-band systems, IEEE Transactions on Acoustics, Speech, and Signal Processing, vol.31, issue.2, pp.472-486, 1983.
DOI : 10.1109/TASSP.1983.1164061

E. [. Weiss and . Weinstein, A lower bound on the mean-square error in random parameter estimation (Corresp.), IEEE Transactions on Information Theory, vol.31, issue.5, pp.680-682, 1985.
DOI : 10.1109/TIT.1985.1057094

A. [. Weinstein and . Weiss, A general class of lower bounds in parameter estimation, IEEE Transactions on Information Theory, vol.34, issue.2, pp.338-342, 1988.
DOI : 10.1109/18.2647

]. J. Xb04a, V. Xavier, ]. J. Barrosoxb04b, V. Xavier, and . Barroso, Intrinsic variance lower bound (IVLB) : an extension of the Cramer Rao bound to Riemannian manifolds The Riemannian geometry of certain parameter estimation problems with singular Fisher information matrices, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing, pp.1033-1036, 2004.

A. [. Xu, K. Baggeroer, and . Bell, A Bound on Mean-Square Estimation Error With Background Parameter Mismatch, IEEE Transactions on Information Theory, vol.50, issue.4, pp.621-632, 2004.
DOI : 10.1109/TIT.2004.825023

A. [. Xu, C. D. Baggeroer, and . Richmond, Bayesian Bounds for Matched-Field Parameter Estimation, IEEE Transactions on Signal Processing, vol.52, issue.12, pp.3293-3305, 2004.
DOI : 10.1109/TSP.2004.837437

]. W. Xu01 and . Xu, Performances bounds on matched-field methods for source localization and estimation of ocean environmental parameters, 2001.

A. [. Yetik, . [. Nehorai, Z. Zou, R. J. Lin, and . Ober, Performance bounds on image registration, ZN90] A. Zeira and A. Nehorai. Frequency domain Cramer Rao bound for Gaussian processes, pp.1737-17361666, 1990.
DOI : 10.1109/TSP.2006.870552

M. [. Ziv and . Zakai, Some lower bounds on signal parameter estimation, IEEE Transactions on Information Theory, vol.15, issue.3, pp.386-391, 1969.
DOI : 10.1109/TIT.1969.1054301