Visual SLAM for underwater vehicles using video velocity log and natural landmarks

A visual SLAM system has been implemented and optimised for real-time deployment on an AUV equipped with calibrated stereo cameras. The system incorporates a novel approach to landmark description in which landmarks are local sub maps that consist of a cloud of 3D points and their associated SIFT/SURF descriptors. Landmarks are also sparsely distributed which simplifies and accelerates data association and map updates. In addition to landmark-based localisation the system utilises visual odometry to estimate the pose of the vehicle in 6 degrees of freedom by identifying temporal matches between consecutive local sub maps and computing the motion. Both the extended Kalman filter and unscented Kalman filter have been considered for filtering the observations. The output of the filter is also smoothed using the Rauch-Tung-Striebel (RTS) method to obtain a better alignment of the sequence of local sub maps and to deliver a large-scale 3D acquisition of the surveyed area. Synthetic experiments have been performed using a simulation environment in which ray tracing is used to generate synthetic images for the stereo system

Multi-sensor Simultaneous Localization and Mapping

Simultaneous localization and mapping(SLAM) is a very important problem in mobile robotics. Many solutions have been proposed by different scientists during the last two decades, nevertheless few studies have considered the use of multiple sensors simultane��ously. The solution is on combining several data sources with the aid of an Extended Kalman Filter (EKF). Two approaches are proposed. The first one is to use the ordinary EKF SLAM algorithm for each data source separately in parallel and then at the end of each step, fuse the results into one solution. Another proposed approach is the use of multiple data sources simultaneously in a single filter. The comparison of the computational com��plexity of the two methods is also presented. The first method is almost four times faster than the second one.

Estudio de errores en la localizaci��n en espacios interiores, de dispositivos m��viles por medio de tecnolog��as WiFi

La localizaci��n en ambientes de interiores basada en dispositivos modernos de uso masivo, como los dispositivos m��viles, es un ��rea actual de investigaci��n y desarrollo que ha empezado a generar productos para diferentes aplicaciones. Sin embargo, la estimaci��n del error en estas mediciones, sus fuentes y la forma como se propaga, que evita tener mayor exactitud en la localizaci��n, a��n presenta un ��rea pendiente de estudio. Esta investigaci��n toma una de las t��cnicas comunes de estudio de localizaci��n de dispositivos por redes inal��mbricas WiFi para estudiar los diferentes errores que ella conlleva, sus fuentes y su propagaci��n. Este trabajo tambi��n propone un nuevo enfoque y nueva metodolog��a, que permite reducir el error en la localizaci��n de dispositivos WiFi, con base a la clasificaci��n de las redes inal��mbricas presentes en un escaneo, la identificaci��n de muestras y datos fortuitos, la estabilizaci��n de muestreos de potencias de redes WiFi, y la implementaci��n de un filtro de Kalman, para la predicci��n de medidas estables de estas potencias.

Sensor Fusion of Proprioception, Force and Vision in Estimation and Robot

Sensor-based robot control allows manipulation in dynamic environments with uncertainties. Vision is a versatile low-cost sensory modality, but low sample rate, high sensor delay and uncertain measurements limit its usability, especially in strongly dynamic environments. Force is a complementary sensory modality allowing accurate measurements of local object shape when a tooltip is in contact with the object. In multimodal sensor fusion, several sensors measuring different modalities are combined to give a more accurate estimate of the environment. As force and vision are fundamentally different sensory modalities not sharing a common representation, combining the information from these sensors is not straightforward. In this thesis, methods for fusing proprioception, force and vision together are proposed. Making assumptions of object shape and modeling the uncertainties of the sensors, the measurements can be fused together in an extended Kalman filter. The fusion of force and visual measurements makes it possible to estimate the pose of a moving target with an end-effector mounted moving camera at high rate and accuracy. The proposed approach takes the latency of the vision system into account explicitly, to provide high sample rate estimates. The estimates also allow a smooth transition from vision-based motion control to force control. The velocity of the end-effector can be controlled by estimating the distance to the target by vision and determining the velocity profile giving rapid approach and minimal force overshoot. Experiments with a 5-degree-of-freedom parallel hydraulic manipulator and a 6-degree-of-freedom serial manipulator show that integration of several sensor modalities can increase the accuracy of the measurements significantly.

Inversion and assimilation methods with applications in geophysical remote sensing

Stratospheric ozone can be measured accurately using a limb scatter remote sensing technique at the UV-visible spectral region of solar light. The advantages of this technique includes a good vertical resolution and a good daytime coverage of the measurements. In addition to ozone, UV-visible limb scatter measurements contain information about NO2, NO3, OClO, BrO and aerosols. There are currently several satellite instruments continuously scanning the atmosphere and measuring the UVvisible region of the spectrum, e.g., the Optical Spectrograph and Infrared Imager System (OSIRIS) launched on the Odin satellite in February 2001, and the Scanning Imaging Absorption SpectroMeter for Atmospheric CartograpHY (SCIAMACHY) launched on Envisat in March 2002. Envisat also carries the Global Ozone Monitoring by Occultation of Stars (GOMOS) instrument, which also measures limb-scattered sunlight under bright limb occultation conditions. These conditions occur during daytime occultation measurements. The global coverage of the satellite measurements is far better than any other ozone measurement technique, but still the measurements are sparse in the spatial domain. Measurements are also repeated relatively rarely over a certain area, and the composition of the Earth���s atmosphere changes dynamically. Assimilation methods are therefore needed in order to combine the information of the measurements with the atmospheric model. In recent years, the focus of assimilation algorithm research has turned towards filtering methods. The traditional Extended Kalman filter (EKF) method takes into account not only the uncertainty of the measurements, but also the uncertainty of the evolution model of the system. However, the computational cost of full blown EKF increases rapidly as the number of the model parameters increases. Therefore the EKF method cannot be applied directly to the stratospheric ozone assimilation problem. The work in this thesis is devoted to the development of inversion methods for satellite instruments and the development of assimilation methods used with atmospheric models.

Simulating the performance of paper machine control

The topic of this thesis is the simulation of a combination of several control and data assimilation methods, meant to be used for controlling the quality of paper in a paper machine. Paper making is a very complex process and the information obtained from the web is sparse. A paper web scanner can only measure a zig zag path on the web. An assimilation method is needed to process estimates for Machine Direction (MD) and Cross Direction (CD) profiles of the web. Quality control is based on these measurements. There is an increasing need for intelligent methods to assist in data assimilation. The target of this thesis is to study how such intelligent assimilation methods are affecting paper web quality. This work is based on a paper web simulator, which has been developed in the TEKES funded MASI NoTes project. The simulator is a valuable tool in comparing different assimilation methods. The thesis contains the comparison of four different assimilation methods. These data assimilation methods are a first order Bayesian model estimator, an ARMA model based on a higher order Bayesian estimator, a Fourier transform based Kalman filter estimator and a simple block estimator. The last one can be considered to be close to current operational methods. From these methods Bayesian, ARMA and Kalman all seem to have advantages over the commercial one. The Kalman and ARMA estimators seems to be best in overall performance.

Det osynligas arkitektur : om rumsligheten i Bo Carpelans f��rfattarskap

Bo Carpelan (f. 1926) har kallats ���rummets diktare��� och ���dr��markitekt���. I Carpelans f��rfattarskap hittar man formuleringar som ���Det ��r inte tiden som f��r��ndrar oss, det ��r rummet���, ���Rum bygger upp en startpunkt i hj��rtat och tanken, samtidigt.��� och ���Rum ��r levande n��r m��nniskor finns d��r, men n��r de d��r, upph��r rummen.��� Avhandlingen ��r en studie i den rumsliga betoningen i Carpelans f��rfattarskap. I en kontext av centrala litteratur- och id��historiska str��mningar och influenser fr��n bl.a. flaml��ndskt interi��rm��leri, uppst��r hos Carpelan med tiden en utpr��glat rumslig diktkonst och livs��sk��dning. I ljuset av rumsligheten i Carpelans f��rfattarskap framst��r verkligheten som ett slags hemlighetsfull skrift som m��nniskan kan l��ra sig l��sa men som aldrig helt l��ter sig tydas.

���Hollywood-syndromi���, jazzia ja dodekafoniaa : elokuvamusiikin funktioanalyysi nelj��ss�� 1950- ja 1960-luvun vaihteen suomalaisessa elokuvassa

Musiken som h��rdes i de finl��ndska filmerna vid skiftet av 1950- och 1960-talet var mycket varierande. Det fanns till exempel jazzschlager, modern konstmusik som innovativt kombinerats med Hollywood-klich��er, dodekafonisk musik och mainstream jazz. G��llande stilval, kompositionss��tt, instrumentering, harmonisering och anv��ndningss��tt av filmmusik r��dde det d�� m��jligen en st��rre frihet ��n n��gonsin i Finland. Anu Juvas avhandling behandlar musiken till fyra filmer genom filmmusikens funktionsanalys och i sitt kulturhistoriska sammanhang. N��ranalyserna har gjorts av Lasisyd��n ( Glashj��rtat 1959) och Komisario Palmun erehdys ( Mysteriet Rygseck [sic!] 1960), som Matti Kassila har regisserat, Maunu Kurkvaaras Yksityisalue ( Privatomr��de 1962) och Erkko Kivikoskis Kes��ll�� kello 5 ( Klockan 5 denna sommar 1963). Musiken till dessa filmer har komponerats av Jaakko Salo, Osmo Lindeman, Usko Meril��inen och Pentti Lasanen. Regiss��rerna och komposit��rerna till dessa filmer var alla p�� olika s��tt f��rnyare av sin tids konventioner. Funktionsanalysen avsl��jar, hur musiken i filmerna fungerar, dvs. vilka dess uppgifter ��r i dessa filmer som l��ter mycket olika. Vidare granskas det, hur musik valdes till olika filmer samt de olika genrernas st��llning inom det kulturella f��ltet. Unders��kningen ��ppnar en utsikt ��ver en av de mest intressanta tidpunkterna inom finl��ndsk filmmusik.

Myten om det rationella fl��det : en studie av hur organisatorisk ledning formas genom omv��rldsanalys och underr��ttelsearbete i kunskapsintensiva f��retagsmilj��er

Omv��rldsanalys, omv��rldsbevakning, competitive intelligence och business intelligence ��r begrepp i tiden. De anv��nds f��r att beskriva en v��xande yrkespraktik som spanar efter och analyserar omv��rldsinformation. I stort sett samtliga st��rre f��retag har idag inf��rt ett organiserat underr��ttelsearbete (OUA), men praktiken inskr��nker sig inte till kommersiell verksamhet utan ��terfinns ��ven till exempel i kommunal f��rvaltning och flertalet statliga myndigheter. I sin avhandling, Myten om det rationella fl��det, beskriver Magnus Hoppe hur organiserat underr��ttelsearbete anpassas till olika situationer men ocks�� hur det p��verkar organisationers strategi och utveckling. Samtidigt riktar Hoppe skarp kritik mot en ��vertro p�� rationalitet i organisationer och beskriver hur denna ��vertro vidmakth��ller f��r��ldrade id��er om hur ett v��l fungerande underr��ttelsearbete b��r organiseras och verka. F��rutom beskrivning och kritik av de i dagsl��get dominerande teorierna om organiserat underr��ttelsearbete, knyter Hoppe ihop sitt ��mne med ett urval organisationsteoretiska teman som kretsar kring ledarskap och beslutsfattande. D��rut��ver formar han flera egna modeller i en reflekterande text om hur informationsurval, analytiska processer samt sociala kontakter p��verkar organisationsmedlemmars uppfattningar om den egna organisationen, den v��rld de befinner sig i, men inte minst sin egen position. Ett ��terkommande konstaterande ��r att det inte g��r, som m��nga popul��rt h��llna b��cker g��r g��llande, att skapa ett rationellt informationsfl��de fr��n omv��rlden in i organisationens beslutsfattande processer. F��r detta ��r den inomorganisatoriska milj��n alltf��r komplex, h��vdar Hoppe, som st��der sina tankar p�� intervjuer med underr��ttelsearbetare vid fyra internationellt verksamma f��retag. Id��n om det rationella informationsfl��det ��r en myt som hindrar oss fr��n att se hur organiserat underr��ttelsearbete faktiskt g��r till, argumenterar han. Men det inneb��r inte samtidigt att myten l��tt l��ter sig avt��ckas eller avf��rdas. Ist��llet ��r myten en del av v��r kollektiva tro p�� organisationer som rationella och kontrollerbara samh��llsakt��rer. Med ett organiserat underr��ttelsearbete skapas f��rvisso goda f��ruts��ttningar f��r ett mer insiktsfullt beslutsfattande, men underr��ttelsearbetet g��r ocks�� att de organisationer som tar det till sig framst��r som rationellt styrda och omv��rldsanpassade. N��got som dagens organisationer och beslutfattare har ett stort behov av att kunna h��vda. Organiserat underr��ttelsearbete inneb��r inte automatiskt att vare sig beslut eller ledning blir b��ttre, men det ger sken av det. Hoppe avslutar avhandlingen med att g�� bortom myten d�� han beskriver organiserat underr��ttelsearbete som format av en kompletterande logik - att bidra till ett framv��xande koordinerat handlande, d��r beslut vare sig beh��ver vara uttalade eller ens n��dv��ndiga. Genom att p��verka informationsurval och delta i analytiska processer p�� skiftande underr��ttelsearenor intar underr��ttelsearbetare en central roll i den interna kampen om hur omv��rlden b��r tolkas och d��rmed vad som t��nks och g��rs i organisationens namn. Granskningsmannen, tillika opponenten, docent Bengt Gustavsson skriver i sitt utl��tande att "Kritiken mot rationalitet i organisationer har funnits sedan l��nge i organisationsteorin, inte minst sedan Herbert Simons dagar, men disputanden stannar inte vid denna kritik utan anv��nder den f��r att lyfta fram alternativa fenomen och funktioner som han funnit genom sina unders��kningar, t.ex. betydelser av sociala kontakter och sm��prat i underr��ttelsearbetet [...]; OUA som ideologisk agent i formandet av organisatoriskt t��nkande; OUA som redskap f��r organisationens medlemmar att transcendera tid, rum och ego; och t.o.m. OUA som organiseringsprincip." Den andre granskningsmannen, professor Sven Hamrefors som i flera studier unders��kt organisationers omv��rldsbevakning, g��r en kompletterande bed��mning och lyfter fram att "Forskningsfr��gan ��r relevant och angel��gen" och "ett v��lkommet bidrag till att skapa en relation mellan idealet och verkligheten, vilket definitivt kommer att f�� ett genomslag p�� utvecklingen av kunskapsomr��det." Hamrefors po��ngterar ocks�� att "det var l��nge sedan jag l��ste en s�� v��lformulerad svensk text", vilket borgar f��r att Hoppe n��r sitt m��l att f�� fler ��n bara forskarkollektivet att ta till sig avhandlingens po��nger och d��rmed lyckas synligg��ra fenomenet, vilket ��r hans prim��ra syfte. Organiserat underr��ttelsearbete ��r en verksamhet som vi fram till idag endast haft bristf��llig kunskap om. Med Hoppes avhandling ��ndras l��get, och vi kan nu utveckla en mer insiktsfull diskussion om vad detta v��xande fenomen inneb��r f��r b��de organisationer och samh��lle.

Causation and dominance : a study of Finnish causative verbs expressing social dominance

En v��sentlig fr��ga inom s��v��l lingvistiska som kognitiva teorier ��r, hur spr��ket beskriver kausala relationer. I finskan finns det en speciell typ av kausativa verb avledda med suffixet (U)ttA som anv��nds f��r att uttrycka att handlingen i fr��ga utf��rs av n��gon annan ��n subjektreferenten, t.ex. Maija haetuttaa Matilla kirjastosta kirjan ���Maija l��ter Matti h��mta boken fr��n biblioteket��� och Matti juoksuttaa Maijan kaupunkiin ���Matti l��ter Maija springa till staden���. Syftet med denna avhandling var att med exempel av sociala dominansens kausativer unders��ka ordbildningens natur samt begreppet ���socialt f��rorsakande���. F��r att beskriva avledningars regelbundna argumentstruktur i form av kopplingen mellan syntaxen och semantiken uppr��ttades deras prototypiska strukturer. Dessa verb har emellertid ocks�� specifika anv��ndningsomr��den som framh��ver variationer i sociala relationer. S��regna egenskaper hos den sociala dominansens kausativer inkluderades i unders��kningen och definierades som konstruktioner. Konstruktionerna omfattar speciella syntaktiska och/eller semantiska element och ut��ver det ocks�� pragmatiska v��rderande implikationer. Uppbyggnaden av den sociala dimensionen hos de unders��kta verben best��r av egenskaper f��rbundna med typen av f��rorsakande, argumentens agentiva egenskaper (aktivitet eller passivitet, dominans, kontroll, viljestyrdhet och ansvarighet) samt konventionaliserade attityder och tolkningar. Ett exempel p�� en s.k. 'tolkningskonstruktion��� ��r den negativa dominansens uttryck som i avhandlingen kallas Maktmissbrukskonstruktionen. Denna konstruktion inkluderar talarens starkt kritiska h��llning till den uttryckta situationen, t.ex. Asiakas juoksuttaa lentoem��nt���� ���Kunden l��ter flygv��rdinnan springa���. Dessa konstruktioner fyller en viktig funktion i spr��klig kommunikation: att beskriva avvikande av sociala normer och att foga expressivitet till budskapet. Metodologiskt kombinerar denna avhandling teorier som baseras p�� det aktuella spr��kbruket och teoretisk lingvistisk analys. Verbens samt konstruktionernas konceptuella lexikala struktur och prototypstrukturerna analyserades med hj��lp av den konceptuella semantikens verktyg, som har utvecklats av Jackendoff, Nikanne och P��rn.

Software for design of experiments and response modelling of cake ltration applications

Filtration is a widely used unit operation in chemical engineering. The huge variation in the properties of materials to be ltered makes the study of ltration a challenging task. One of the objectives of this thesis was to show that conventional ltration theories are di cult to use when the system to be modelled contains all of the stages and features that are present in a complete solid/liquid separation process. Furthermore, most of the ltration theories require experimental work to be performed in order to obtain critical parameters required by the theoretical models. Creating a good overall understanding of how the variables a ect the nal product in ltration is somewhat impossible on a purely theoretical basis. The complexity of solid/liquid separation processes require experimental work and when tests are needed, it is advisable to use experimental design techniques so that the goals can be achieved. The statistical design of experiments provides the necessary tools for recognising the e ects of variables. It also helps to perform experimental work more economically. Design of experiments is a prerequisite for creating empirical models that can describe how the measured response is related to the changes in the values of the variable. A software package was developed that provides a ltration practitioner with experimental designs and calculates the parameters for linear regression models, along with the graphical representation of the responses. The developed software consists of two software modules. These modules are LTDoE and LTRead. The LTDoE module is used to create experimental designs for di erent lter types. The lter types considered in the software are automatic vertical pressure lter, double-sided vertical pressure lter, horizontal membrane lter press, vacuum belt lter and ceramic capillary action disc lter. It is also possible to create experimental designs for those cases where the variables are totally user de ned, say for a customized ltration cycle or di erent piece of equipment. The LTRead-module is used to read the experimental data gathered from the experiments, to analyse the data and to create models for each of the measured responses. Introducing the structure of the software more in detail and showing some of the practical applications is the main part of this thesis. This approach to the study of cake ltration processes, as presented in this thesis, has been shown to have good practical value when making ltration tests.

Software for design of experiments and response modelling of cake filtration applications

Filtration is a widely used unit operation in chemical engineering. The huge variation in the properties of materials to be ltered makes the study of ltration a challenging task. One of the objectives of this thesis was to show that conventional ltration theories are di cult to use when the system to be modelled contains all of the stages and features that are present in a complete solid/liquid separation process. Furthermore, most of the ltration theories require experimental work to be performed in order to obtain critical parameters required by the theoretical models. Creating a good overall understanding of how the variables a ect the nal product in ltration is somewhat impossible on a purely theoretical basis. The complexity of solid/liquid separation processes require experimental work and when tests are needed, it is advisable to use experimental design techniques so that the goals can be achieved. The statistical design of experiments provides the necessary tools for recognising the e ects of variables. It also helps to perform experimental work more economically. Design of experiments is a prerequisite for creating empirical models that can describe how the measured response is related to the changes in the values of the variable. A software package was developed that provides a ltration practitioner with experimental designs and calculates the parameters for linear regression models, along with the graphical representation of the responses. The developed software consists of two software modules. These modules are LTDoE and LTRead. The LTDoE module is used to create experimental designs for di erent lter types. The lter types considered in the software are automatic vertical pressure lter, double-sided vertical pressure lter, horizontal membrane lter press, vacuum belt lter and ceramic capillary action disc lter. It is also possible to create experimental designs for those cases where the variables are totally user de ned, say for a customized ltration cycle or di erent piece of equipment. The LTRead-module is used to read the experimental data gathered from the experiments, to analyse the data and to create models for each of the measured responses. Introducing the structure of the software more in detail and showing some of the practical applications is the main part of this thesis. This approach to the study of cake ltration processes, as presented in this thesis, has been shown to have good practical value when making ltration tests.

K��velyn ja py��r��ilyn toimenpidesuunnitelma : Uudenmaan ELY-keskus: Uusimaa, Kanta-H��me ja P��ij��t-H��me

K��velyn ja py��r��ilyn edist��minen tukee liikennepolitiikan keskeisi�� tavoitteita toimivasta, terveellisest��, taloudellisesta ja ymp��rist��n kannalta kest��v��st�� liikennej��rjestelm��st��. K��velyn ja py��r��ilyn suosion kasvu edellytt���� sit��, ett�� arkimatkojen tekeminen jalan ja py��r��ll�� on sujuvaa ja turvallista ja ett�� p��ivitt��isten toimintojen edellytt��mien matkojen pituudet pysyv��t riitt��v��n lyhyin��. ELY-keskuksilla on merkitt��v�� rooli n��iden reunaehtojen kehitykselle niin maantievarsien jalankulku- ja py��r��ilyolosuhteista vastaavana tienpit��j��n��, kaupunkiseutujen ja taajamien liikennej��rjestelm��n suunnitteluun yhdess�� muiden tahojen kanssa osallistuvana asiantuntijatahoja kuin kuntien kaavoitusta ohjaavana viranomaisena. T��rkeimm��t keinot k��velyn ja py��r��ilyn olosuhteiden parantamiseksi ja suosion lis����miseksi on koottu eri tahojen yhteisty��n�� laadittuun, vuoden 2012 alussa valmistuneeseen K��velyn ja py��r��ilyn valtakunnalliseen toimenpidesuunnitelmaan 2020. Nyt laadittu Uudenmaan ELY-keskuksen k��velyn ja py��r��ilyn toimenpidesuunnitelma kertoo, miten Uudenmaan ELY-keskus toimii k��velyn ja py��r��ilyn edist��miseksi ja valtakunnallisen suunnitelman toteuttamiseksi. Uudenmaan ELY-keskuksen suunnitelmassa on valtakunnallisen suunnitelman tapaan nelj����n teemaan ryhmiteltyn�� 33 toimenpideotsikkoa, joiden alla konkreettiset toimenpiteet on kuvattu. Teemoja ovat asenteisiin ja liikkumistottumuksiin vaikuttaminen (T��rke��t valinnat), k��vely�� ja py��r��ily�� tukevan liikenneinfrastruktuurin ja liikkumisymp��rist��n kehitt��minen (Reitti selv��), jalan ja py��r��ll�� liikkumista suosivan yhdyskuntarakenteen ja palveluverkon edist��minen (Kaikki l��hell��) sek�� k��velyn ja py��r��ilyn asemaa hallinnossa, p����t��ksenteossa, rahoituksessa ja suunnittelussa koskevat kehitt��misehdotukset (J��rjestelm�� toimii). Uudenmaan ELY-keskuksen k��velyn ja py��r��ilyn toimenpidesuunnitelmaa aletaan toteuttaa heti. Monet suunnitelmassa kuvatut toimet ovat jo k��ynniss�� tai k��ynnistetty suunnitelman laatimisen aikana. Toimenpiteiden etenemist�� seurataan ja niiden tilannetta k��sitell����n jatkossa mm. seudullisissa k��velyn ja py��r��ilyn yhteisty��ryhmiss��.

On state and parameter estimation in chaotic systems

State-of-the-art predictions of atmospheric states rely on large-scale numerical models of chaotic systems. This dissertation studies numerical methods for state and parameter estimation in such systems. The motivation comes from weather and climate models and a methodological perspective is adopted. The dissertation comprises three sections: state estimation, parameter estimation and chemical data assimilation with real atmospheric satellite data. In the state estimation part of this dissertation, a new filtering technique based on a combination of ensemble and variational Kalman filtering approaches, is presented, experimented and discussed. This new filter is developed for large-scale Kalman filtering applications. In the parameter estimation part, three different techniques for parameter estimation in chaotic systems are considered. The methods are studied using the parameterized Lorenz 95 system, which is a benchmark model for data assimilation. In addition, a dilemma related to the uniqueness of weather and climate model closure parameters is discussed. In the data-oriented part of this dissertation, data from the Global Ozone Monitoring by Occultation of Stars (GOMOS) satellite instrument are considered and an alternative algorithm to retrieve atmospheric parameters from the measurements is presented. The validation study presents first global comparisons between two unique satellite-borne datasets of vertical profiles of nitrogen trioxide (NO3), retrieved using GOMOS and Stratospheric Aerosol and Gas Experiment III (SAGE III) satellite instruments. The GOMOS NO3 observations are also considered in a chemical state estimation study in order to retrieve stratospheric temperature profiles. The main result of this dissertation is the consideration of likelihood calculations via Kalman filtering outputs. The concept has previously been used together with stochastic differential equations and in time series analysis. In this work, the concept is applied to ���chaotic dynamical systems and used together with Markov chain Monte Carlo (MCMC) methods for statistical analysis. In particular, this methodology is advocated for use in numerical weather prediction (NWP) and climate model applications. In addition, the concept is shown to be useful in estimating the filter-specific parameters related, e.g., to model error covariance matrix parameters.

Numerical Simulation of Stochastic Di erential Equations

Stochastic differential equation (SDE) is a differential equation in which some of the terms and its solution are stochastic processes. SDEs play a central role in modeling physical systems like finance, Biology, Engineering, to mention some. In modeling process, the computation of the trajectories (sample paths) of solutions to SDEs is very important. However, the exact solution to a SDE is generally difficult to obtain due to non-differentiability character of realizations of the Brownian motion. There exist approximation methods of solutions of SDE. The solutions will be continuous stochastic processes that represent diffusive dynamics, a common modeling assumption for financial, Biology, physical, environmental systems. This Masters' thesis is an introduction and survey of numerical solution methods for stochastic differential equations. Standard numerical methods, local linearization methods and filtering methods are well described. We compute the root mean square errors for each method from which we propose a better numerical scheme. Stochastic differential equations can be formulated from a given ordinary differential equations. In this thesis, we describe two kind of formulations: parametric and non-parametric techniques. The formulation is based on epidemiological SEIR model. This methods have a tendency of increasing parameters in the constructed SDEs, hence, it requires more data. We compare the two techniques numerically.