Recent breakthrough studies by Gali and Gertler (1999), Sbordone (2002) and Roberts (2001) argue that the New Keynesian Phillips curve (based on Calvo pricing model) is empirically valid concept and they conclude that the real marginal costs are preferred driving force to output gap in inflation dynamics for open economies. Neiss and Nelson (2002) and Gali, Gertler and Salido (2001), in turn, contradict that to date, there has been only little empirical evidence to support this statement. Neiss and Nelson (2002) add that "once output gap is defined consistently with economic theory, the gap-based New Keynesian Phillips curve has a fit with data which is at least as good as the real marginal costs-based one". For this purpose, my study investigates relationship between output gap and inflation described in the hybrid New Keynesian Phillips curve. Study estimates key coefficients of the hybrid gap-based New Keynesian Phillips curve, with both forward- and backward-looking inflation components, in the Czech Republic for periods 2000Q1 - 2012Q4 using Kalman filtration. My findings suggest that (i) output gap has a significant impact on Czech inflation dynamics (ii) share of forward-looking agents predominates to backward-looking agents in the Czech Republic and (iii) Czech inflation seems to be significantly driven by change in import prices.

This thesis presents an investigation of the possibility of using the fixed-point arithmetic in the inertial navigation systems, which use the local level navigation frame mechanization equations. Two square root filtering methods, the Potter's square root Kalman filter and UD factorized Kalman filter, are compared with respect to the conventional Kalman filter and its Joseph's stabilized form. The effect of rounding errors to the Kalman filter optimality and the covariance matrix or its factors conditioning is evaluated for a various lengths of the fractional part of the fixed-point computational word. Main contribution of this research lies in an evaluation of the minimal fixed-point arithmetic word length for the Phi-angle error model with noise statistics which correspond to the tactical grade inertial measurements units.

This paper deals with the topic of design of a navigation system for an autonomous mobile robot in a park-like environment. Precisely, designing methods for road detection using available sensoric system, designing a mathematical model for fusion of these data, and suggesting a representation of an environment suitable for planning and local navigation.