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Tire normal forces are difficult to measure, but information on the vehicle normal force can be used in many automotive engineering applications, e.g., rollover detection and vehicle and wheel stability. Previous papers use algebraic equations to estimate the tire normal force. In this article, the estimation of tire normal force is formulated as an input estimation problem. Two observers are proposed to solve this problem by using a quarter-car suspension model. First, the Youla Controller Output Observer framework is presented. It converts the estimation problem into a control problem and produces a Youla parameterized controller as observer. Second, a Kalman filter approach is taken and the input estimation problem is addressed with an Unbiased Minimum Variance Filter. Both methods use accelerometer and suspension deflection sensors to determine the vehicle normal force. The design of the observers is validated in simulation and a sensitivity analysis is performed to evaluate their robustness.

This thesis addresses the problem of unbiased minimum variance filtering by two techniques: the proportional integral filter and the robust minimum variance filtering. In the first, the development of a multi-integral observer ($PI^p$) has allowed an unbiased estimation of the state and the unknown input for linear discrete time systems. Two new filters have also developed such as the PITSKF and the PIThSKF to solve the problem of the robust joint state and fault estimation in the presence of unknown inputs and uncertainties in the covariance matrices of different noises of the state, the measurement and the faults. Another filtering technique is also proposed to overcome the knowledge of the prior models of the faults and the unknown inputs, so, we have designed the ARThSKF. In addition, we have developed two new filters the EUMVF and the ORFSF to solve the problem posed by the arbitrary rank of the direct feedthrough matrix distribution of the fault., Cette thèse traite le problème de filtrage non biaisé et à minimum de variance par deux techniques : le filtrage proportionnel intégral et le filtrage robuste à minimum de variance. Dans la première, le développement d'un observateur multi-intégral ($PI^p$) a permi une estimation non biaisée de l'état pour les systèmes linéaires à temps discret en présence d'entrées inconnues. Deux nouveaux filtres ont était également développés tels que les filtres PITSKF et PIThSKF pour résoudre le problème d'estimation robuste et jointe d'état et des défauts en présence d'entrées inconnues et des incertitudes sur les matrices de covariance des différents bruits d'état, des mesures, des défauts et des entrées inconnues. Une autre technique de filtrage est également envisagée pour s'affranchir de la connaissance des modèles à priori des défauts et des entrées inconnues, on a donc développé le filtre ARThSKF. De plus, nous avons conçu deux nouveaux filtres EUMVF et ORFSF pour résoudre le problème posé par le rang arbitraire de la matrice directe d'injection des défauts sur les mesures.

Polynomial finite population functions can be expressed as totals over derived populations of batches, or ordered sequences of units from the original population. This paper extends the results of Godambe and Godambe and Joshi on nonexistence of best unbiased estimators and admissibility of the Horvitz-Thompson estimator to the real batch total case. The admissibility results are only partly extendible; an example is given to show that Horvitz-Thompson type estimators of the form $\sum \sum b_{ij}(y_i - y_j)^2/\pi_{ij}$ need not be admissible.