Existing estimations of implicit inflation target are primarily based on the assumption of parameter stability over time horizon. This work relaxes this assumption and proposes alternative framework based on time-varying parameter model. We aim on behaviour of European Central Bank in order to compare its official proclamations of price stability levels with our implicit estimations. We will also examine how two pillar strategy of European Central Bank is practically used.

Title: Methods of dynamical analysis of portfolio composition Author: Ivana Meňhartová Department: Department of Probability and Mathematical Statistics Supervisor: Mgr. Tomáš Hanzák, KPMS, MFF UK Abstract: In the presented thesis we study methods used for dynamic analysis of portfolio based on it's revenues. The thesis focuses on Kalman filter and local- ly weighted regression as two basic methods for dynamic analysis. It describes in detail theory for these methods as well as their utilization and it discusses their proper settings. Practical applications of both methods on artificial data and real data from Prague stock-exchange are presented. Using artificial data we demonstrate practical importance of Kalman filter's assumptions. Afterwards we introduce term multicolinearity as a possible complication to real data applicati- ons. At the end of the thesis we compare results and usage of both methods and we introduce possibility of enhancing Kalman filter by projection of estimations or by CUSUM tests (change detection tests). Keywords: Kalman filter, locally weighted regression, multicollinearity, CUSUM test

This thesis is concerned with attitude estimation of small flying robots using low cost, small-sized inertial and magnetic sensors. A quaternion-based extended Kalman filter is used, which adaptively compensates external acceleration. External acceleration is the main source of estimation error. If external acceleration is detected, the accelerometer measurement covariance matrix of the Kalman filter is adjusted. The proposed algorithms are verified through experiments. Selected algorithm is implemented on STM32F4DISCOVERY development board.

The diploma work concerns on an issue of data collection of speed and electrical angle based on informations from Hall sensor with the necessary resolution for control of BLDC motor. Specifically, concenred on a section with low speed. Most of moors use Hall sensor for detecting speed and position of the rotor. At low speed section, becomes the situation when we can not determine the position of the rotor with (the) required (sufficient) resolution, this situation creates a „wince“ in the control (ripple torque). The task is to design and evaluate the possibilities of the algorithm for control and acquisition speed and rotor position with the required accuracy.

The aim of this term project was to analyze wireless indoor localization. It contains analysis of some wireless localization techniques such as Time of Arrival or Time Difference of Arrival. The paper also describes the system of SEWIO Company. Main part of the master’s thesis is description, design and implementation of the Kalman filter. The Kalman filter is used to improve two-dimensional positional data and synchronization of anchors (devices for finding a position of an object in SEWIO system). There are described a few system models for the Kalman filter.

Rýchlosť vozidla je jednou z kľúčových stavových premenných, ktorej znalosť je potrebná v reálnom čase a s vysokou presnosťou, aby mohla slúžiť ako vstupná veličina pre systémy kontroly dynamiky vozidla. Jej priame meranie vo vozidle je však finančne náročné. Riešením tohoto problému môže byť použitie meraní zo senzorov bežne dostupných na palube vozidla a ich následný prepočet na rýchlosť vozidla. Tieto merania sú však veľmi zaťažené procesným šumom, čo vyplýva z komplexnosti pohybu vozidla. Preto je nutné vyvinúť algoritmus so schopnosťou vysporiadať sa s týmito negatívnymi vplyvmi. Algoritmus prezentovaný v tejto práci odhaduje pozdĺžnu rýchlosť vozidla s použitím meraní uhlových rýchlostí štyroch kolies, pozdĺžnej akcelerácie, momentov motora, rýchlosti otáčania okolo zvislej osi a natočenia volantu. Algoritmus bol testovaný na veľkom počte situácií považovaných za kritické na odhad rýchlosti vozidla, ako napríklad prudká akcelerácia na vozovke s nízkym koeficientom trenia, núdzové brzdenie s aktiváciou ABS, či jazda v kopci s kolesami v preklze, prinášajúc uspokojujúce výsledky.

This paper deals with study of inertial navigation, global navigation satellite system, and their fusion into the one navigation solution. The first part of the work is to calculate the trajectory from accelerometers and gyroscopes measurements. Navigation equations calculate rotation with quaternions and remove gravity sensed by accelerometers. The equation’s output is in earth centred fixed navigation frame. Then, inertial navigation errors are discussed and focused to the bias correction. Theory about INS/GNSS inte- gration compares different integration architecture. The Kalman filter is used to obtain navigation solution for attitude, velocity and position with advantages of both systems.