ABSTRACT DETERMINATION OF STOCHASTIC MODEL PARAMETERS OF INERTIAL SENSORS &Uuml / nver, Alper PhD, Department of Electric Electronic Engineering Supervisor: Prof. Dr. M&uuml / beccel Demirekler January 2013, 82 pages Gyro and accelerometer systematic errors due to biases, scale factors, and misalignments can be compensated via an on-board Kalman filtering approach in a Navigation System. On the other hand, sensor random noise sources such as Quantization Noise (QN), Angular Random Walk (ARW), Flicker Noise (FN), and Rate Random Walk (RRW) are not easily estimated by an on-board filter, due to their random characteristics. In this thesis a new method based on the variance of difference sequences is proposed to compute the powers of the above mentioned noise sources. The method is capable of online or offline estimation of stochastic model parameters of the inertial sensors. Our aim in this study is the estimation of ARW, FN and RRW parameters besides the quantization and the Gauss-Markov noise parameters of the inertial sensors. The proposed method is tested both on the simulated and the real sensor data and the results are compared with the Allan variance method. Comparison shows very satisfactory results for the performance of the method. Computational load of the new method is less than the computational load of the Allan variance on the order of tens. One of the usages of this method is the individual noise characterization. A noise, whose power spectral density has a constant slope, can be identified accurately by the proposed method. In addition to this, the parameters of the GM noise can also be determined. Another idea developed here is to approximate the overall error source as a combination of ARW and some number of GM sources only. The reasons of selecting such a structure is the feasibility of using these models in a Kalman filter framework for error propagation as well as their generality of modeling other noise sources.

This master thesis deals with measurement and modeling of MEMS inertial sensors. This paper describes basic principles of inertial sensors along with their most often errors. The next part shows results from inertial sensor market analysis, which enabling a selection of sensors to be measured. The following two chapters present methods for inertial sensor modeling and testing. The biggest part of text is dedicated to presentation of measurement results showing us static measurement of Allan variance, Earth rotation, temperature dependent bias and dynamic measurement of gyroscope sensitivity testing over temperature. In the last part of the thesis is presented a design of sensor error model by autocorrelation function and Allan variance and also an evaluation of achieved results.

Nous présentons dans ce mémoire un modèle d'interaction outil-roche qui calcule les efforts de forage en fonction du déplacement dans la roche d'un outil de forage de type PDC, et permet d'évaluer ses propriétés directionnelles, à savoir, son indice d'anisotropie (steerability) et son angle de walk. Le mouvement de l'outil est défini par une translation suivant trois axes et une rotation suivant deux axes. L'angle de tilt, qui définit l'inclinaison de l'outil par rapport à l'axe du trou en cours de forage, est pris en compte dans le calcul des surfaces d'interactions effectives entre les différentes composantes de l'outil (structure de coupe, garde active et garde passive) et la roche. Ce modèle outil est établi à partir d'une modélisation de la coupe de roche par un taillant. Ce modèle de coupe élémentaire est construit de manière à être applicable aux différentes parties de l'outil. Les efforts élémentaires de coupe sont intégrés sur toute la structure de l'outil de forage afin de calculer ses propriétés directionnelles. Le modèle d'interaction outil-roche est validé à partir d'essais de forage directionnel réalisés sur un banc spécialement conçu pour reproduire le comportement des systèmes de forage dirigé existants. Il constitue un outil d'aide à la décision pour la sélection de l'outil de forage en fonction du système au bout duquel il sera fixé. Ce modèle pourra aussi être intégré dans une boucle de régulation automatique ou semi-automatique de contrôle et de correction de la trajectoire en temps réel. / This work deals with the formulation of global relationships between kinematic variables describing the penetration of a PDC bit into the rock and drilling forces acting on it. This allows us determine the bit directional properties in terms of steerability, which corresponds to the bit lateral aggressiveness, and walk, which describes the bit azimuth displacement with respect to the side force. The bit kinematic quantities are divided into a three-axis penetration vector and a two-axis angular penetration vector. The bit tilt, which describes the angle between the bit revolution axis and the borehole tangent, is used to compute the effective interaction surface between the bit's different components (cutting structure, active gauge and passive gauge) and the rock. A new cutter-rock interface law is set up and experimentally validated in order to compute elementary forces acting on all parts of a drill bit. Bit directional properties are computed after the integration of these elementary forces. The bit-rock interaction model is experimentally validated with directional drilling tests held on a full-scale drilling bench developed to reproduce Rotary Steerable Systems (RSS) directional behavior. Tests and theoretical results enabled us to fully understand the roles of tilt angle, bit design, operating parameters and rock properties in the deviation process of a PDC bit. The bit-rock interaction model is a decision support tool for optimal drill bit selection according to the RSS being used. It could also be embedded in a real-time Closed-Loop Guided Directional Drilling controller in order to correct the drilling direction or follow a planned borehole trajectory.

The thesis is aimed on measurement and modeling of MEMS gyroscopes based on input-output characteristics. The first part briefs the state of the art. The second part is dedicated to measurement methodology. Critical points and sources of uncertainty are discussed and evaluated using measurements or simulations. The last part shows key characteristics of MEMS gyroscopes based on the survey of a group of different sensor types. The results have revealed significant influence of supply voltage that causes bias drift of the gyroscope and bias drift of the internal temperature sensor. The error can be comparable to temperature drift; however, this effect is not addressed in the literature. The second observed effect is temperature dependency of angle random walk. In the last part, a general model of a MEMS gyroscope is rewritten to reflect observed effects. Moreover, the structure is selected to be easily extendable and the coefficients are expressed to allow a comparison of nominal parameters of different sensors.