Since the 1950s, hidden Markov models (HMMS) have seen widespread use in electrical engineering. Foremost has been their use in speech processing, pattern recognition, artificial intelligence, queuing theory, and communications theory. However, recent years have witnessed a renaissance in the application of HMMs to the analysis and simulation of digital communication systems. Typical applications have included signal estimation, frequency tracking, equalization, burst error characterization, and transmit power control. Of special significance to this thesis, however, has been the use of HMMs to model fading channels typical of wireless communications. This variegated use of HMMs is fueled by their ability to model time-varying systems with memory, their ability to yield closed form solutions to otherwise intractable analytic problems, and their ability to help facilitate simple hardware and/or software based implementations of simulation test-beds. The aim of this thesis is to employ and exploit hidden Markov fading models within an iterative (turbo) decoding framework. Of particular importance is the problem of channel estimation, which is vital for realizing the large coding gains inherent in turbo coded schemes. This thesis shows that a Markov fading channel (MFC) can be conceptualized as a trellis, and that the transmission of a sequence over a MFC can be viewed as a trellis encoding process much like convolutional encoding. The thesis demonstrates that either maximum likelihood sequence estimation (MLSE) algorithms or maximum <I> a posteriori</I> (MAP) algorithms operating over the trellis defined by the MFC can be used for channel estimation. Furthermore, the thesis illustrates sequential and decision-directed techniques for using the aforementioned trellis based channel estimators <I>en masse</I> with an iterative decoder. / Master of Science

In Natural Language Processing (NLP), speech and text are parsed and generated with language models and parser models, and translated with translation models. Each model contains a set of numerical parameters which are found by applying a suitable training algorithm to a set of training data. Many such training algorithms are instances of the Expectation-Maximization (EM) algorithm. In [BSV15], a generic EM algorithm for NLP is described. This work presents a particular speech model, the Hidden Markov model, and its standard training algorithm, the Baum-Welch algorithm. It is then shown that the Baum-Welch algorithm is an instance of the generic EM algorithm introduced by [BSV15], from which follows that all statements about the generic EM algorithm also apply to the Baum-Welch algorithm, especially its correctness and convergence properties.

In Natural Language Processing (NLP), speech and text are parsed and generated with language models and parser models, and translated with translation models. Each model contains a set of numerical parameters which are found by applying a suitable training algorithm to a set of training data. Many such training algorithms are instances of the Expectation-Maximization (EM) algorithm. In [BSV15], a generic EM algorithm for NLP is described. This work presents a particular speech model, the Hidden Markov model, and its standard training algorithm, the Baum-Welch algorithm. It is then shown that the Baum-Welch algorithm is an instance of the generic EM algorithm introduced by [BSV15], from which follows that all statements about the generic EM algorithm also apply to the Baum-Welch algorithm, especially its correctness and convergence properties.:1 Introduction 1.1 N-gram models 1.2 Hidden Markov model 2 Expectation-maximization algorithms 2.1 Preliminaries 2.2 Algorithmic skeleton 2.3 Corpus-based step mapping 2.4 Simple counting step mapping 2.5 Regular tree grammars 2.6 Inside-outside step mapping 2.7 Review 3 The Hidden Markov model 3.1 Forward and backward algorithms 3.2 The Baum-Welch algorithm 3.3 Deriving the Baum-Welch algorithm 3.3.1 Model parameter and countable events 3.3.2 Tree-shaped hidden information 3.3.3 Complete-data corpus 3.3.4 Inside weights 3.3.5 Outside weights 3.3.6 Complete-data corpus (cont.) 3.3.7 Step mapping 3.4 Review Appendix A Elided proofs from Chapter 3 A.1 Proof of Lemma 3.8 A.2 Proof of Lemma 3.9 B Formulary for Chapter 3 Bibliography

This thesis explored the possibilities of using a Hidden Markov Model approach for multi-target localisation in an urban environment, with observations generated from Wi-Fi sensors. The area is modelled as a network of nodes and arcs, where the arcs represent sidewalks in the area and constitutes the hidden states in the model. The output of the model is the expected amount of people at each road segment throughout the day. In addition to this, two methods for analyzing the impact of events in the area are proposed. The first method is based on a time series analysis, and the second one is based on the updated transition matrix using the Baum-Welch algorithm. Both methods reveal which road segments are most heavily affected by a surge of traffic in the area, as well as potential bottleneck areas where congestion is likely to have occurred. / I det här examensarbetet har lokalisering av gångtrafikanter med hjälp av Hidden Markov Models utförts. Lokaliseringen är byggd på data från Wi-Fi sensorer i ett område i Stockholm. Området är modellerat som ett graf-baserat nätverk där linjerna mellan noderna representerar möjliga vägar för en person att befinna sig på. Resultatet för varje individ är aggregerat för att visa förväntat antal personer på varje segment över en hel dag. Två metoder för att analysera hur event påverkar området introduceras och beskrivs. Den första är baserad på tidsserieanalys och den andra är en maskinlärningsmetod som bygger på Baum-Welch algoritmen. Båda metoderna visar vilka segment som drabbas mest av en snabb ökning av trafik i området och var trängsel är troligt att förekomma.