M.H.A. Davis a introduit les processus markoviens déterministes par morceaux (PDMP) comme une classe générale de modèles stochastiques non diffusifs, donnant lieu à des trajectoires déterministes ponctuées, à des instants aléatoires, par des sauts aléatoires. Dans cette thèse, nous présentons et analysons des estimateurs non paramétriques des lois conditionnelles des deux aléas intervenant dans la dynamique de tels processus. Plus précisément, dans le cadre d'une observation en temps long de la trajectoire d'un PDMP, nous présentons des estimateurs de la densité conditionnelle des temps inter-sauts et du noyau de Markov qui gouverne la loi des sauts. Nous établissons des résultats de convergence pour nos estimateurs. Des simulations numériques pour différentes applications illustrent nos résultats. Nous proposons également un estimateur du taux de saut pour des processus de renouvellement, ainsi qu'une méthode d'approximation numérique pour un modèle de régression semi-paramétrique. / Piecewise-deterministic Markov processes (PDMP’s) have been introduced by M.H.A. Davis as a general family of non-diffusion stochastic models, involving deterministic motion punctuated by random jumps at random times. In this thesis, we propose and analyze nonparametric estimation methods for both the features governing the randomness of such a process. More precisely, we present estimators of the conditional density of the inter-jumping times and of the transition kernel for a PDMP observed within a long time interval. We establish some convergence results for both the proposed estimators. In addition, numerical simulations illustrate our theoretical results. Furthermore, we propose an estimator for the jump rate of a nonhomogeneous renewal process and a numerical approximation method based on optimal quantization for a semiparametric regression model.

Le contexte est la géométrie discrète dans Zn. Il s'agit de décrire les courbes et surfaces discrètes composées de voxels: les définitions usuelles de droites et plans discrets épais se comportent mal quand on passe à des ensembles courbes. Comment garantir un bon comportement topologique, les connexités requises, dans une situation qui généralise les droites et plans discrets?Le calcul de données sur ces courbes, normales, tangentes, courbure, ou des fonctions plus générales, fait appel à des moyennes utilisant des masques. Une question est la pertinence théorique et pratique de ces masques. Une voie explorée, est le calcul de masques fondés sur la marche aléatoire. Une marche aléatoire partant d'un centre donné sur une courbe ou une surface discrète, permet d'affecter à chaque autre voxel un poids, le temps moyen de visite. Ce noyau permet de calculer des moyennes et par là, des dérivées. L'étude du comportement de ce processus de diffusion, a permis de retrouver des outils classiques de géométrie sur des surfaces maillées, et de fournir des estimateurs de tangente et de courbure performants. La diversité du champs d'applications de ce processus de diffusion a été mise en avant, retrouvant ainsi des méthodes classiques mais avec une base théorique identique.} motsclefs{Processus Markovien, Géométrie discrète, Estimateur tangentes, normales, courbure, Noyau de diffusion, Analyse d'images / The context of discrete geometry is in Zn. We propose to discribe discrete curves and surfaces composed of voxels: how to compute classical notions of analysis as tangent and normals ? Computation of data on discrete curves use average mask. A large amount of works proposed to study the pertinence of those masks. We propose to compute an average mask based on random walk. A random walk starting from a point of a curve or a surface, allow to give a weight, the time passed on each point. This kernel allow us to compute average and derivative. The studied of this digital process allow us to recover classical notions of geometry on meshes surfaces, and give accuracy estimator of tangent and curvature. We propose a large field of applications of this approach recovering classical tools using in transversal communauty of discrete geometry, with a same theorical base.

Hybrid systems have been identified as one of the main directions in control theory and attracted increasing attention in recent years due to their huge diversity of engineering applications. Multiplemodel (MM) estimation is the state-of-the-art approach to many hybrid estimation problems. Existing MM methods with fixed structure usually perform well for problems that can be handled by a small set of models. However, their performance is limited when the required number of models to achieve a satisfactory accuracy is large due to time evolution of the true mode over a large continuous space. In this research, variable-structure multiple model (VSMM) estimation was investigated, further developed and evaluated. A fundamental solution for on-line adaptation of model sets was developed as well as several VSMM algorithms. These algorithms have been successfully applied to the fields of fault detection and identification as well as target tracking in this thesis. In particular, an integrated framework to detect, identify and estimate failures is developed based on the VSMM. It can handle sequential failures and multiple failures by sensors or actuators. Fault detection and target maneuver detection can be formulated as change-point detection problems in statistics. It is of great importance to have the quickest detection of such mode changes in a hybrid system. Traditional maneuver detectors based on simplistic models are not optimal and are computationally demanding due to the requirement of batch processing. In this presentation, a general sequential testing procedure is proposed for maneuver detection based on advanced sequential tests. It uses a likelihood marginalization technique to cope with the difficulty that the target accelerations are unknown. The approach essentially utilizes a priori information about the accelerations in typical tracking engagements and thus allows improved detection performance. The proposed approach is applicable to change-point detection problems under similar formulation, such as fault detection.

Dans cette thèse, on s'intéresse à l'estimation des fonctions de régression par polynômes et par splines dans le cadre des statistiques non-paramétriques. L'objectif est d'estimer la fonction cible f, à partir des observations Y=f+ϵ, où ϵ est un bruit gaussien. En appuyant sur la méthode d'estimation du risque sans biais, l'idée consiste à obtenir des inégalités d'oracle pour des familles d'estimateurs par polynômes et par splines. Etant donnée une famille d'estimateurs M, une telle inégalité permet de comparer, sans aucune hypothèse sur la fonction cible f, les performances de l'estimateur f ̂^* à l'estimateur d'oracle f ̂_or. Le point essentiel de notre approche consiste à sélectionner, à l'aide des données, un paramètre d'estimation adapté : lorsque on considère le problème de l'estimation par projection, ce paramètre est le degré du polynôme ; dans le cas de l'estimation par splines, ce paramètre correspond à un paramètre de lissage. Ainsi, on en déduit des bornes supérieures non-asymptotiques pour les risques quadratiques de notre adaptation.<br /> Afin d'obtenir des inégalités d'oracle, on applique l'inégalité de Doob pour le processus de Wiener pour l'estimation par polynômes ; dans le cas de l'estimation par splines, on introduit le processus ordonné en généralisant le processus de Wiener.

In this thesis, estimation in simple linear regression model with one-fold nested error is studied. To estimate the fixed effect parameters, generalized least squares and maximum likelihood estimation procedures are reviewed. Moreover, Minimum Norm Quadratic Estimator (MINQE), Almost Unbiased Estimator (AUE) and Restricted Maximum Likelihood Estimator (REML) of variance of primary units are derived. Also, confidence intervals for the fixed effect parameters and the variance components are studied. Finally, the aforesaid estimation techniques and confidence intervals are applied to a real-life data and the results are presented

Orthogonal frequency-division multiplexing (OFDM) has been adopted by many broadband wireless communication systems for the simplicity of the receiver technique to support high data rates and user mobility. However, studies also show that the advantage of OFDM over the single-carrier modulation schemes could be substantially compromised by timing or frequency estimation errors at the receiver. In this thesis we investigate the synchronization problem for practical OFDM systems using a system model generalized from the IEEE 802.11 and IEEE 802.16 standards. For preamble based synchronization schemes, which are most common in the downlink of wireless communication systems, we propose a novel timing acquisition algorithm which minimizes false alarm probability and indirectly improves correct detection probability. We then introduce a universal fractional carrier frequency offset (CFO) estimator that outperforms conventional methods at low signal to noise ratio with lower complexity. More accurate timing and frequency estimates can be obtained by our proposed frequency-domain algorithms incorporating channel knowledge. We derive four joint frequency, timing, and channel estimators with different approximations, and then propose a hybrid integer CFO estimation scheme to provide flexible performance and complexity tradeoffs. When the exact channel delay profile is unknown at the receiver, we present a successive timing estimation algorithm to solve the timing ambiguity. Both analytical and simulation results are presented to confirm the performance of the proposed methods in various realistic channel conditions. The ranging based synchronization scheme is most commonly used in the uplink of wireless communication systems. Here we propose a successive multiuser detection algorithm to mitigate multiple access interference and achieve better performance than that of conventional single-user based methods. A reduced-complexity version of the successive algorithm feasible for hardware real-time implementation is also presented in the thesis. To better understand the performance of a ranging detector from a system point of view, we develop a technique that can directly translate a detector�s missed detection probability into the maximum number of users that the method can support in one cell with a given number of ranging opportunities. The analytical results match the simulations reasonably well and show that the proposed successive algorithms allow a base station to serve more than double the number of users supported by the conventional methods. Finally, we investigate inter-carrier interference which is caused by the timevarying communication channels. We derive the bounds on the power of residual inter-carrier interference that cannot be mitigated by a frequency-domain equalizer with a given number of taps. We also propose a Turbo equalization scheme using the novel grouped Particle filter, which approaches the performance of the Maximum A Posterior algorithm with much lower complexity.

International Telemetering Conference Proceedings / October 20-23, 2003 / Riviera Hotel and Convention Center, Las Vegas, Nevada / A radiolocation problem using DS-CDMA waveforms with array-based receivers is considered. It is assumed that M snapshots of N(s) Nyquist sample long data are available, with a P element antenna array. In the handshaking radiolocation protocol assumed here, data training sequences are available for all K users. As a result, the received spatial-temporal matrix R ∈ C^(MN(s)x P) is approximated by a sum of deterministic signal matrices S(k)^b ∈ C^(MN(s) N(s)) multiplied by unconstrained array response matrices A(k) ∈ C^(N(s)x P). The unknown delays are not estimated directly. Rather, the delays are implicitly approximated as part of the symbol-length long channel, and solutions sparse in the rows of A are thus sought. The resulting ML cost function is J = ||R - ∑(k=1)^K S(k)^bA(k)||(F). The Generalized Successive Interference Cancellation (GSIC) algorithm is employed to iteratively estimate and cancel multiuser interference. Thus, at the k-th GSIC iteration, the index p(k) = arg min(l ≠ p(1),...,p(k-1)) {min(A(l)) ||R^k-S(l)^bA(l)||(F)} is computed, where R^k = ∑(l=1)^(k-1) S(pl)^bÂ(pl). Matching pursuits is embedded in the GSIC iterations to compute sparse channel/steering vector solutions Â(l). Simulations are presented for DS-CDMA signals received over channels computed using a ray-tracing propagation model.

ITC/USA 2006 Conference Proceedings / The Forty-Second Annual International Telemetering Conference and Technical Exhibition / October 23-26, 2006 / Town and Country Resort & Convention Center, San Diego, California / OFDM is a preferred physical layer for an increasing number of telemetry and LAN applications. However, joint estimation of the multipath channel and frequency offset in OFDM remains a challenging problem. The Unscented Kalman Filter (UKF) is presented to solve the offset/channel tracking problem. The advantages of the UKF are that it is less susceptible to divergence than the EKF, and does not require computation of a Jacobian matrix. A hybrid analysis/simulation approach is developed to rapidly evaluate UKF performance in terms of symbol-error rate and channel/offset error for the 802.11a OFDM format.

The presence of abnormally high signal levels beyond the horizon may be exploited for communication purposes. On the other hand, these high signal levels pose the threat of spatial co-channel interference. A long-term detailed investigation into the wideband characteristics of a typical transhorizon link was instigated by the Radiocommunications Agency (UK) to permit the compilation of the hitherto unknown channel parameter statistics. This thesis describes that investigation conducted at a frequency of 11.64 GHz on a 160 km transhorizon sea path between Cap d' Antifer (France) and Fort Widley (England). A channel sounder with a bandwidth of 31.25 MHz which allows the implementation of an automated time-critical continuous data acquisition strategy, is described in detail. The parametric estimation of time-domain model parameters, from measured channel transfer functions, in the context of multi path propagation is discussed. The Singular Value Decomposition Prony and Bayesian techniques are described in detail, having been chosen in preference to Fourier analysis because of their higher resolution potential. The deri vation and implementation of a novel Bayesian algorithm which incorporates prior knowledge concerning the channel parameters is presented. Multipath channel simulation data using differing channel models and varying signal-to-noise ratios has been generated and this data, together with field data, has been used to carry out a systematic and critical comparison between the Bayesian and the SVD_P approaches. It is shown that the Bayesian algorithm gives more accurate estimates of channel parameters, namely amplitudes and delays, especially when the signal-to-noise ratio is less than 30 dB. An 8 month long measurement campaign has generated a 110 Gbyte database of channel transfer functions. The estimated channel impulse response and the associated signal levels are used to discuss the underlying propagation phenomena on the link. It is shown that ducting propagation conditions occurred for a larger than expected period totalling 16% of the measurement time. This has been attributed to the dominance of surface ducting conditions in the summer. Troposcattering was found to be more prevalent in the winter. The risk of the channel being a source of interference was found to be greatest at about 20:00 GMT due to the presence of advection ducts and a minimum at about 10:00 GMT. Delay spread, Doppler spread, coherence bandwidth and fade depths have also been estimated from the database. The results show that there is a very strong correlation between these parameters and the wideband signal level. The median values of 35 ns and 6 Hz for the delay and Doppler spreads respectively, reveal that the transmission medium can be considered to be slowly varying. Coherence bandwidths greater than 250 MHz have been observed for 1 % of the time with a signal level of -2.7 dBf. Such a high value implies that to achieve acceptable interference levels on spatially aligned links, large frequency separations may well be required. Comparison with earlier CW investigation results (COST210 and follow-up research) show that the statistics of signal levels acquired from CW measurements also apply to wideband signals. However, there is a significant discrepancy between CW and wideband fading statistics due to frequency selective fading.

A gradient-independent model of gas fluxes was formulated and tested. The model is built on the relationship between gas flux and the time history of surface gas concentration, known as half-order derivative (HOD), when the transport of the gas in the boundary layer is described by a diffusion equation. The eddy-diffusivity of gas is parameterized based on the similarity theory of boundary layer turbulence combined with the MEP model of surface heat fluxes. Test of the new model using in-situ data of CO2 concentration and fluxes at several locations with diverse vegetation cover, geographic and climatic conditions confirms its usefulness and potential for monitoring and modeling greenhouse gases. The proposed model may also be used for estimating other GHGS fluxes such as methane (CH4) and Water vapor flux. This proof-of-concept study justifies the proposed model as a practical solution for monitoring and modeling global GHGS budget over remote areas and oceans where ground observations of GHGS fluxes are limited or non-existent. One focus of the on-going research is to investigate its application to producing regional and global distributions of carbon fluxes for identifying sinks and sources of carbon and re-evaluating the regional and global carbon budget at monthly and annual time scales.