, Les preuves des propositions 7 et 8 restent valables lorsque la loi des indices de retirage n'est plus uniforme sans replacement sur 1:N. Cette loi peut en fait être choisie de manière quelconque du moment qu'elle reste indépendante des particules intermédiaires?xintermédiaires? intermédiaires?x elles-mêmes (en particulier

P. Agrawal and N. Patwari, Correlated link shadow fading in multi-hop wireless networks, IEEE Transactions on Wireless Communications, vol.8, issue.8, p.118, 2009.
DOI : 10.1109/twc.2009.071293
URL : http://arxiv.org/pdf/0804.2708

B. D. Anderson and J. B. Moore, Optimal Filtering, p.47, 1979.

C. Andrieu, A. Doucet, and R. Holenstein, Particle Markov chain Monte Carlo methods, Journal of the Royal Statistical Society Series B, vol.72, issue.3, p.97, 2010.
DOI : 10.1111/j.1467-9868.2009.00736.x
URL : https://rss.onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-9868.2009.00736.x

M. Arulampalam, S. Maskell, N. Gordon, and T. Clapp, A tutorial on particle filters for online nonlinear / non-Gaussian Bayesian tracking, IEEE Transactions on Signal Processing, vol.50, issue.2, p.47, 2002.

R. Bassett and J. Deride, Maximum a posteriori estimators as a limit of Bayes estimators, Mathematical Programming, p.22, 2018.

D. S. Baum, J. Hansen, and J. Salo, An interim channel model for beyond-3G systems : extending the 3GPP spatial channel model (SCM), Proc. of the 61st IEEE Vehicular Technology Conference, vol.5, p.121, 2005.

E. Bellone, J. P. Hughes, and P. Guttorp, A hidden Markov model for downscaling synoptic atmospheric patterns to precipitation amounts, Climate Research, vol.15, issue.1, pp.1-12, 2000.

T. Bengtsson, P. Bickel, and B. Li, Curse-of-dimensionality revisited : Collapse of the particle filter in very large scale systems, Collections, vol.2, p.52, 2008.

P. Billingsley, Probability and Measure, Wiley Series in Probability and Statistics, vol.150, 1995.

W. Blair, Design of nearly constant velocity track filters for tracking maneuvering targets, Proceedings of the 11th International Conference on Information Fusion, vol.130, pp.1-7, 2008.

A. Brockwell, P. Del-moral, and A. Doucet, Sequentially interacting Markov chain Monte Carlo methods, Ann. Statist, vol.38, issue.6, pp.3387-3411, 2010.
DOI : 10.1214/09-aos747
URL : https://doi.org/10.1214/09-aos747

M. F. Bugallo, V. Elvira, L. Martino, D. Luengo, J. Miguez et al., Adaptive importance sampling : The past, the present, and the future, IEEE Signal Processing Magazine, vol.34, issue.4, p.59, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01684850

R. E. Caflisch, Monte Carlo and quasi-Monte Carlo methods. ACTA NUMERICA, 1998.

. Bibliographie,

O. Cappé, R. Douc, A. Guillin, J. Marin, and C. P. Robert, Adaptive importance sampling in general mixture classes, Statistics and Computing, vol.18, issue.4, pp.447-459, 2008.

O. Cappé, A. Guillin, J. M. Marin, and C. P. Robert, Population Monte Carlo, Journal of Computational and Graphical Statistics, vol.13, issue.4, pp.907-929, 2004.

O. Cappé, É. Moulines, and T. Rydén, Inference in Hidden Markov Models, 2005.

G. Casella and R. Berger, Statistical Inference. Duxbury advanced series in statistics and decision sciences, vol.28, 2002.

S. Chib and E. Greenberg, Understanding the Metropolis-Hastings algorithm, The American Statistician, vol.49, pp.327-335, 1995.

P. , Feynman-Kac formulae. Genealogical and interacting particle systems with applications. Probability and its applications, vol.32, 2004.

R. Douc, O. Cappé, and É. Moulines, Comparison of resampling schemes for particle filtering, Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis (ISPA), 2005.
URL : https://hal.archives-ouvertes.fr/hal-00005883

R. Douc, A. Guillin, J. Marin, and C. P. Robert, Convergence of adaptive mixtures of importance sampling schemes, Ann. Statist, vol.35, issue.1, pp.420-448, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00432955

R. Douc, É. Moulines, and J. Olsson, Optimality of the auxiliary particle filter, Probability and Mathematical Statistics, vol.29, issue.1, p.56, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00471534

R. Douc, A. Guillin, J. Marin, R. , and C. P. , Minimum variance importance sampling via population Monte Carlo, ESAIM : PS, vol.11, pp.427-447, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00070316

A. Doucet, N. De-freitas, and N. Gordon, An introduction to sequential monte carlo methods, Sequential Monte Carlo Methods in Practice, p.53, 2001.

A. Doucet, N. De-freitas, and N. Gordon, Sequential Monte Carlo Methods in Practice. Statistics for Engineering and Information Science, p.133, 2001.

A. Doucet, S. J. Godsill, and C. Andrieu, On sequential Monte Carlo sampling methods for Bayesian filtering, Statistics and Computing, vol.10, issue.3, pp.197-208, 2000.

A. Doucet and A. M. Johansen, A Tutorial on Particle Filtering and Smoothing : Fifteen years later. In Oxford handbook of nonlinear filtering, vol.113, 2011.

R. F. Engle, Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, vol.50, issue.4, p.96, 1982.

B. Ferris, D. Hähnel, and D. Fox, Gaussian Processes for Signal Strength-Based Location Estimation, Proceedings of Robotics : Science and Systems, p.118, 2006.

A. Finke, A. Doucet, and A. M. Johansen, Limit theorems for sequential mcmc methods, p.126, 2018.

A. E. Gelfand and A. F. Smith, Sampling based approaches to calculating marginal densities, Journal of the American Statistical Association, vol.85, issue.410, pp.398-409, 1990.

J. Gentle, W. Härdle, and Y. Mori, Handbook of Computational Statistics : Concepts and Methods. Springer Handbooks of Computational Statistics, p.22, 2017.

M. Gerber, N. Chopin, and N. Whiteley, Negative association, ordering and convergence of resampling methods, vol.34, 2017.

J. Geweke, Bayesian inference in econometric models using Monte Carlo integration, Econometrica, vol.57, issue.6, pp.1317-1356, 1989.

W. R. Gilks and C. Berzuini, Following a Moving Target-Monte Carlo Inference for Dynamic Bayesian Models, Journal of the Royal Statistical Society : Series B (Statistical Methodology), vol.63, pp.127-146, 2001.

M. Girolami and B. Calderhead, Riemann manifold Langevin and Hamiltonian Monte Carlo methods, Journal of the Royal Statistical Society : Series B (Statistical Methodology), vol.73, issue.2, p.127, 2011.

G. Goertzel, Quota sampling and importance functions in stochastic solution of particle problems, vol.26, 1949.

N. J. Gordon, D. J. Salmond, and A. F. Smith, Novel approach to nonlinear/ nonGaussian Bayesian state estimation, IEE Proceedings-F, vol.140, issue.2, pp.107-113, 1993.

M. Gudmundson, Correlation model for shadow fading in mobile radio systems, Electronics Letters, vol.27, issue.23, pp.2145-2146, 1991.

I. Guvenc and C. Chong, A Survey on TOA Based Wireless Localization and NLOS Mitigation Techniques, IEEE Communications Surveys Tutorials, vol.11, issue.3, p.118, 2009.

J. M. Hammersley and D. C. Handscomb, Monte Carlo Methods. Methuen and Co, 1964.

J. M. Hammersley and K. W. Morton, Poor Man's Monte Carlo, Journal of the Royal Statistical Society. Series B, vol.16, issue.1, p.13, 1954.

H. Y. He and A. B. Owen, Optimal mixture weights in multiple importance sampling, p.59, 2014.

T. Hesterberg, Advances in Importance Sampling, vol.29, 1988.

T. Hesterberg, Weighted average importance sampling and defensive mixture distributions, Technometrics, vol.37, issue.2, p.59, 1995.

Y. Ho and R. Lee, A Bayesian approach to problems in stochastic estimation and control, IEEE Transactions on Automatic Control, vol.9, pp.333-339, 1964.

L. Hu and D. Evans, Localization for mobile sensor networks, Proceedings of the 10th Annual International Conference on Mobile Computing and Networking, MobiCom '04, p.132, 2004.

A. H. Jazwinski, Stochastic Processes and Filtering Theory, vol.64, 1970.

A. M. Johansen and A. Doucet, A note on the auxiliary particle filter, Statistics and Probability Letters, vol.78, issue.12, p.56, 2008.

S. Julier and J. Uhlmann, Unscented filtering and nonlinear estimation, Proceedings of the IEEE, vol.92, p.47, 2004.

H. Kahn and A. W. Marshall, Methods of reducing sample size in Monte Carlo computations, Journal of the Operations Research Society of America, vol.1, issue.5, pp.263-278, 1953.

T. Kailath, A. H. Sayed, and B. Hassibi, Linear estimation. Prentice Hall Information and System Sciences Series, vol.46, 2000.

R. E. Kalman, A new approach to linear filtering and prediction problems, J. Basic Eng., Trans. ASME, Series D, vol.82, issue.1, pp.35-45, 1960.

R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, J. Basic Eng., Trans. ASME, Series D, vol.83, issue.3, pp.95-108, 1961.

M. Klaas, N. D. Freitas, and A. Doucet, Toward practical N 2 Monte Carlo : the Marginal Particle Filter, Proceedings of Uncertainty in Artificial Intelligence, p.56, 2005.

A. Kong, J. S. Liu, and W. H. Wong, Sequential imputations and Bayesian missing data problems, Journal of the American Statistical Association, vol.89, issue.425, pp.278-88, 1994.

D. P. Kroese, R. Y. Rubinstein, and P. W. Glynn, Chapter 2-the cross-entropy method for estimation, Handbook of Statistics, vol.31, pp.19-34, 2013.

K. Lange, Numerical Analysis for Statisticians, p.22, 2014.

T. Li, M. Boli?, and P. M. Djuric, Resampling Methods for Particle Filtering : Classification, implementation, and strategies, IEEE Signal Processing Magazine, vol.32, issue.3, p.34, 2015.

X. Li and V. Jilkov, Survey of maneuvering target tracking. Part I. Dynamic models, IEEE Transactions on Aerospace and Electronic Systems, vol.39, issue.4, pp.1333-1364, 2003.

J. S. Liu, Monte Carlo Strategies in Scientific Computing, vol.29, p.28, 2008.

J. S. Liu and R. Chen, Blind deconvolution via sequential imputation, Journal of the American Statistical Association, vol.90, issue.430, pp.567-76, 1995.

A. W. Marshall, The use of multi-stage sampling schemes in Monte Carlo computations, Symposium on Monte Carlo Methods, pp.123-140, 1956.

L. Martino, V. Elvira, and G. Camps-valls, The Recycling Gibbs Sampler for Efficient Learning, p.126, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01684845

H. M. Menegaz, J. Y. Ishihara, G. A. Borges, and A. N. Vargas, A systematization of the unscented Kalman filter theory, IEEE Transactions on Automatic Control, vol.60, issue.10, p.47, 2015.

L. Mihaylova, D. Angelova, D. Bull, and N. Canagarajah, Localization of mobile nodes in wireless networks with correlated in time measurement noise, IEEE Transactions on Mobile Computing, vol.10, issue.1, p.118, 2011.

L. Mihaylova, D. Angelova, S. Honary, D. Bull, C. Canagarajah et al., Mobility tracking in cellular networks using particle filtering, IEEE Transactions on Wireless Communications, vol.6, issue.10, p.118, 2007.

C. Musso, N. Oudjane, and F. Le-gland, Improving regularized particle filters, Sequential Monte Carlo methods in practice, p.53, 2001.
URL : https://hal.archives-ouvertes.fr/hal-00912466

I. Nevat, G. W. Peters, K. Avnit, F. Septier, and L. Clavier, Location of Things : Geospatial Tagging for IoT Using Time-of-Arrival, IEEE Transactions on Signal and Information Processing over Networks, vol.2, issue.2, pp.174-185, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01359099

H. Noureddine, N. Gresset, D. Castelain, and R. Pyndiah, Auto-regressive modeling of the shadowing for RSS mobile tracking, Proceedings of the 2011 IEEE International Conference on Communications (ICC), pp.1-5, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00609313

A. B. Owen, Monte Carlo theory, methods and examples, p.28, 2013.

K. Pahlavan and A. H. Levesque, Wireless information networks, vol.95, 1995.

N. Patwari, J. N. Ash, S. Kyperountas, A. O. Hero, R. L. Moses et al., Locating the nodes : cooperative localization in wireless sensor networks, IEEE Signal Processing Magazine, vol.22, issue.4, pp.54-69, 2005.

N. Patwari, A. Hero, M. Perkins, N. Correal, and R. O'dea, Relative location estimation in wireless sensor networks, IEEE Transactions on Signal Processing, vol.51, issue.8, p.118, 2003.

M. Pereyra and S. Mclaughlin, Fast unsupervised Bayesian image segmentation with adaptive spatial regularisation, IEEE Transactions on Image Processing, vol.26, issue.6, pp.2577-2587, 2017.

Y. Petetin and F. Desbouvries, Optimal SIR algorithm vs. fully adapted auxiliary particle filter : a non asymptotical analysis, Statistics and computing, vol.23, issue.6, pp.759-775, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01354690

Y. Petetin and F. Desbouvries, Bayesian conditional Monte Carlo algorithms for non linear time-series state estimation, IEEE Transactions on Signal Processing, vol.63, issue.14, p.59, 2015.

M. K. Pitt and N. Shephard, Filtering via simulation : Auxiliary particle filter, Journal of the American Statistical Association, vol.94, issue.446, p.20, 1999.

C. Rao, Linear statistical inference and its applications. Wiley series in probability and mathematical statistics, vol.46, 1973.

T. Rappaport, Wireless Communications : Principles and Practice. Electrical engineering, vol.120, 1996.

B. Ristic, S. Arulampalam, and N. Gordon, Beyond the Kalman Filter : Particle Filters for Tracking Applications. Artec House, p.47, 2004.

C. Robert and G. Casella, Monte Carlo Statistical Methods (Springer Texts in Statistics)

C. P. Robert and G. Casella, Monte Carlo Statistical Methods (Springer Texts in Statistics), p.29, 2005.

G. O. Roberts and S. K. Sahu, Updating Schemes, Correlation Structure, Blocking and Parameterization for the Gibbs Sampler, Journal of the Royal Statistical Society : Series B (Statistical Methodology), vol.59, issue.2, p.126, 1997.

M. N. Rosenbluth and A. W. Rosenbluth, Monte Carlo calculation of the average extension of molecular chains, The Journal of Chemical Physics, vol.23, issue.2, p.13, 1955.

D. B. Rubin, Using the SIR algorithm to simulate posterior distributions, Bayesian Statistics III, vol.50, 1988.

R. Y. Rubinstein and D. P. Kroese, The Cross Entropy Method : A Unified Approach To Combinatorial Optimization, Monte-Carlo Simulation (Information Science and Statistics), vol.62, 2004.

S. Saha, P. K. Manda, Y. Boers, H. Driessen, and A. Bagchi, Gaussian proposal density using moment matching in SMC methods, Statistics and Computing, vol.19, issue.2, p.53, 2009.

N. Salman, L. Mihaylova, and A. Kemp, Localization of multiple nodes based on correlated measurements and shrinkage estimation, Sensor Data Fusion : Trends, Solutions, Applications (SDF), vol.118, pp.1-6, 2014.

F. Septier, S. K. Pang, A. Carmi, and S. Godsill, On MCMC-based particle methods for Bayesian filtering : Application to multitarget tracking, Proc. of the 3rd IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), vol.126, pp.360-363, 2009.
URL : https://hal.archives-ouvertes.fr/hal-00566647

F. Septier and G. W. Peters, An Overview of Recent Advances in Monte-Carlo Methods for Bayesian Filtering in High-Dimensional Spaces, Theoretical Aspects of Spatial-Temporal Modeling, vol.124, 2015.
URL : https://hal.archives-ouvertes.fr/hal-01198429

F. Septier and G. W. Peters, Langevin and Hamiltonian Based Sequential MCMC for Efficient Bayesian Filtering in High-Dimensional Spaces, IEEE Journal of Selected Topics in Signal Processing, vol.10, issue.2, p.127, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01238978

A. F. Smith and A. E. Gelfand, Bayesian statistics without tears : a samplingresampling perspective, The American Statistician, vol.46, issue.2, p.31, 1992.

C. Snyder, Particle filters, the optimal proposal and high-dimensional systems, Proceedings from the Seminar on Data assimilation for atmosphere and ocean, p.52, 2011.

C. Snyder, T. Bengtsson, P. Bickel, and J. Anderson, Obstacles to high-dimensional particle filtering, Monthly Weather Review, Special Collection : Mathematical Advances in Data Assimilation, vol.136, issue.12, pp.4629-4640, 2008.

W. Sun and Y. Yuan, Optimization Theory and Methods : Nonlinear Programming. Springer Optimization and Its Applications, vol.64, 2006.

H. Tanizaki, Nonlinear Filters, Estimation and Applications, p.47, 1996.

H. Tanizaki, On nonlinear and nonnormal filter using rejection sampling, IEEE Transactions on Automatic Control, vol.44, pp.314-319, 1999.

R. Van-der-merwe, A. Doucet, N. De-freitas, and E. Wan, The Unscented Particle Filter, Advances in Neural Information Processing Systems, p.53, 2000.

B. Van-veen and K. Buckley, Beamforming : a versatile approach to spatial filtering, IEEE ASSP Magazine, vol.5, issue.2, p.118, 1988.

N. Vaswani, Particle filtering for large-dimensional state spaces with multimodal observation likelihoods, IEEE Transactions on Signal Processing, vol.56, issue.10, pp.4583-4597, 2008.

E. Veach and L. J. Guibas, Optimally combining sampling techniques for Monte Carlo rendering, Proceedings of the 22Nd Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH '95, p.59, 1995.

C. Vergé, C. Dubarry, P. Del-moral, and É. Moulines, On parallel implementation of sequential Monte Carlo methods : the island particle model, Statistics and Computing, vol.25, issue.2, pp.243-260, 2015.

N. Whiteley and A. M. Johansen, Recent developments in auxiliary particle filtering, Inference and Learning in Dynamic Models, p.56, 2010.