User interaction widgets for interactive theorem proving

Matita (that means pencil in Italian) is a new interactive theorem prover under development at the University of Bologna. When compared with state-of-the-art proof assistants, Matita presents both traditional and innovative aspects. The underlying calculus of the system, namely the Calculus of (Co)Inductive Constructions (CIC for short), is well-known and is used as the basis of another mainstream proof assistant—Coq—with which Matita is to some extent compatible. In the same spirit of several other systems, proof authoring is conducted by the user as a goal directed proof search, using a script for storing textual commands for the system. In the tradition of LCF, the proof language of Matita is procedural and relies on tactic and tacticals to proceed toward proof completion. The interaction paradigm offered to the user is based on the script management technique at the basis of the popularity of the Proof General generic interface for interactive theorem provers: while editing a script the user can move forth the execution point to deliver commands to the system, or back to retract (or “undo”) past commands. Matita has been developed from scratch in the past 8 years by several members of the Helm research group, this thesis author is one of such members. Matita is now a full-fledged proof assistant with a library of about 1.000 concepts. Several innovative solutions spun-off from this development effort. This thesis is about the design and implementation of some of those solutions, in particular those relevant for the topic of user interaction with theorem provers, and of which this thesis author was a major contributor. Joint work with other members of the research group is pointed out where needed. The main topics discussed in this thesis are briefly summarized below. Disambiguation. Most activities connected with interactive proving require the user to input mathematical formulae. Being mathematical notation ambiguous, parsing formulae typeset as mathematicians like to write down on paper is a challenging task; a challenge neglected by several theorem provers which usually prefer to fix an unambiguous input syntax. Exploiting features of the underlying calculus, Matita offers an efficient disambiguation engine which permit to type formulae in the familiar mathematical notation. Step-by-step tacticals. Tacticals are higher-order constructs used in proof scripts to combine tactics together. With tacticals scripts can be made shorter, readable, and more resilient to changes. Unfortunately they are de facto incompatible with state-of-the-art user interfaces based on script management. Such interfaces indeed do not permit to position the execution point inside complex tacticals, thus introducing a trade-off between the usefulness of structuring scripts and a tedious big step execution behavior during script replaying. In Matita we break this trade-off with tinycals: an alternative to a subset of LCF tacticals which can be evaluated in a more fine-grained manner. Extensible yet meaningful notation. Proof assistant users often face the need of creating new mathematical notation in order to ease the use of new concepts. The framework used in Matita for dealing with extensible notation both accounts for high quality bidimensional rendering of formulae (with the expressivity of MathMLPresentation) and provides meaningful notation, where presentational fragments are kept synchronized with semantic representation of terms. Using our approach interoperability with other systems can be achieved at the content level, and direct manipulation of formulae acting on their rendered forms is possible too. Publish/subscribe hints. Automation plays an important role in interactive proving as users like to delegate tedious proving sub-tasks to decision procedures or external reasoners. Exploiting the Web-friendliness of Matita we experimented with a broker and a network of web services (called tutors) which can try independently to complete open sub-goals of a proof, currently being authored in Matita. The user receives hints from the tutors on how to complete sub-goals and can interactively or automatically apply them to the current proof. Another innovative aspect of Matita, only marginally touched by this thesis, is the embedded content-based search engine Whelp which is exploited to various ends, from automatic theorem proving to avoiding duplicate work for the user. We also discuss the (potential) reusability in other systems of the widgets presented in this thesis and how we envisage the evolution of user interfaces for interactive theorem provers in the Web 2.0 era.

Interactive theorem provers: issues faced as a user and tackled as a developer

Interactive theorem provers (ITP for short) are tools whose final aim is to certify proofs written by human beings. To reach that objective they have to fill the gap between the high level language used by humans for communicating and reasoning about mathematics and the lower level language that a machine is able to “understand” and process. The user perceives this gap in terms of missing features or inefficiencies. The developer tries to accommodate the user requests without increasing the already high complexity of these applications. We believe that satisfactory solutions can only come from a strong synergy between users and developers. We devoted most part of our PHD designing and developing the Matita interactive theorem prover. The software was born in the computer science department of the University of Bologna as the result of composing together all the technologies developed by the HELM team (to which we belong) for the MoWGLI project. The MoWGLI project aimed at giving accessibility through the web to the libraries of formalised mathematics of various interactive theorem provers, taking Coq as the main test case. The motivations for giving life to a new ITP are: • study the architecture of these tools, with the aim of understanding the source of their complexity • exploit such a knowledge to experiment new solutions that, for backward compatibility reasons, would be hard (if not impossible) to test on a widely used system like Coq. Matita is based on the Curry-Howard isomorphism, adopting the Calculus of Inductive Constructions (CIC) as its logical foundation. Proof objects are thus, at some extent, compatible with the ones produced with the Coq ITP, that is itself able to import and process the ones generated using Matita. Although the systems have a lot in common, they share no code at all, and even most of the algorithmic solutions are different. The thesis is composed of two parts where we respectively describe our experience as a user and a developer of interactive provers. In particular, the first part is based on two different formalisation experiences: • our internship in the Mathematical Components team (INRIA), that is formalising the finite group theory required to attack the Feit Thompson Theorem. To tackle this result, giving an effective classification of finite groups of odd order, the team adopts the SSReflect Coq extension, developed by Georges Gonthier for the proof of the four colours theorem. • our collaboration at the D.A.M.A. Project, whose goal is the formalisation of abstract measure theory in Matita leading to a constructive proof of Lebesgue’s Dominated Convergence Theorem. The most notable issues we faced, analysed in this part of the thesis, are the following: the difficulties arising when using “black box” automation in large formalisations; the impossibility for a user (especially a newcomer) to master the context of a library of already formalised results; the uncomfortable big step execution of proof commands historically adopted in ITPs; the difficult encoding of mathematical structures with a notion of inheritance in a type theory without subtyping like CIC. In the second part of the manuscript many of these issues will be analysed with the looking glasses of an ITP developer, describing the solutions we adopted in the implementation of Matita to solve these problems: integrated searching facilities to assist the user in handling large libraries of formalised results; a small step execution semantic for proof commands; a flexible implementation of coercive subtyping allowing multiple inheritance with shared substructures; automatic tactics, integrated with the searching facilities, that generates proof commands (and not only proof objects, usually kept hidden to the user) one of which specifically designed to be user driven.

Context detection and abstraction in smart environments

Context-aware computing is currently considered the most promising approach to overcome information overload and to speed up access to relevant information and services. Context-awareness may be derived from many sources, including user profile and preferences, network information, sensor analysis; usually context-awareness relies on the ability of computing devices to interact with the physical world, i.e. with the natural and artificial objects hosted within the "environment”. Ideally, context-aware applications should not be intrusive and should be able to react according to user’s context, with minimum user effort. Context is an application dependent multidimensional space and the location is an important part of it since the very beginning. Location can be used to guide applications, in providing information or functions that are most appropriate for a specific position. Hence location systems play a crucial role. There are several technologies and systems for computing location to a vary degree of accuracy and tailored for specific space model, i.e. indoors or outdoors, structured spaces or unstructured spaces. The research challenge faced by this thesis is related to pedestrian positioning in heterogeneous environments. Particularly, the focus will be on pedestrian identification, localization, orientation and activity recognition. This research was mainly carried out within the “mobile and ambient systems” workgroup of EPOCH, a 6FP NoE on the application of ICT to Cultural Heritage. Therefore applications in Cultural Heritage sites were the main target of the context-aware services discussed. Cultural Heritage sites are considered significant test-beds in Context-aware computing for many reasons. For example building a smart environment in museums or in protected sites is a challenging task, because localization and tracking are usually based on technologies that are difficult to hide or harmonize within the environment. Therefore it is expected that the experience made with this research may be useful also in domains other than Cultural Heritage. This work presents three different approaches to the pedestrian identification, positioning and tracking: Pedestrian navigation by means of a wearable inertial sensing platform assisted by the vision based tracking system for initial settings an real-time calibration; Pedestrian navigation by means of a wearable inertial sensing platform augmented with GPS measurements; Pedestrian identification and tracking, combining the vision based tracking system with WiFi localization. The proposed localization systems have been mainly used to enhance Cultural Heritage applications in providing information and services depending on the user’s actual context, in particular depending on the user’s location.

Progetto di reti Sensori Wireless e tecniche di Fusione Sensoriale

Ambient Intelligence (AmI) envisions a world where smart, electronic environments are aware and responsive to their context. People moving into these settings engage many computational devices and systems simultaneously even if they are not aware of their presence. AmI stems from the convergence of three key technologies: ubiquitous computing, ubiquitous communication and natural interfaces. The dependence on a large amount of fixed and mobile sensors embedded into the environment makes of Wireless Sensor Networks one of the most relevant enabling technologies for AmI. WSN are complex systems made up of a number of sensor nodes, simple devices that typically embed a low power computational unit (microcontrollers, FPGAs etc.), a wireless communication unit, one or more sensors and a some form of energy supply (either batteries or energy scavenger modules). Low-cost, low-computational power, low energy consumption and small size are characteristics that must be taken into consideration when designing and dealing with WSNs. In order to handle the large amount of data generated by a WSN several multi sensor data fusion techniques have been developed. The aim of multisensor data fusion is to combine data to achieve better accuracy and inferences than could be achieved by the use of a single sensor alone. In this dissertation we present our results in building several AmI applications suitable for a WSN implementation. The work can be divided into two main areas: Multimodal Surveillance and Activity Recognition. Novel techniques to handle data from a network of low-cost, low-power Pyroelectric InfraRed (PIR) sensors are presented. Such techniques allow the detection of the number of people moving in the environment, their direction of movement and their position. We discuss how a mesh of PIR sensors can be integrated with a video surveillance system to increase its performance in people tracking. Furthermore we embed a PIR sensor within the design of a Wireless Video Sensor Node (WVSN) to extend its lifetime. Activity recognition is a fundamental block in natural interfaces. A challenging objective is to design an activity recognition system that is able to exploit a redundant but unreliable WSN. We present our activity in building a novel activity recognition architecture for such a dynamic system. The architecture has a hierarchical structure where simple nodes performs gesture classification and a high level meta classifiers fuses a changing number of classifier outputs. We demonstrate the benefit of such architecture in terms of increased recognition performance, and fault and noise robustness. Furthermore we show how we can extend network lifetime by performing a performance-power trade-off. Smart objects can enhance user experience within smart environments. We present our work in extending the capabilities of the Smart Micrel Cube (SMCube), a smart object used as tangible interface within a tangible computing framework, through the development of a gesture recognition algorithm suitable for this limited computational power device. Finally the development of activity recognition techniques can greatly benefit from the availability of shared dataset. We report our experience in building a dataset for activity recognition. Such dataset is freely available to the scientific community for research purposes and can be used as a testbench for developing, testing and comparing different activity recognition techniques.

Development and optimization of graphic user interfaces (GUIs) for infrared spectrometers at the Telescopio Nazionale Galileo

This Phd thesis was entirely developed at the Telescopio Nazionale Galileo (TNG, Roque de los Muchachos, La Palma Canary Islands) with the aim of designing, developing and implementing a new Graphical User Interface (GUI) for the Near Infrared Camera Spectrometer (NICS) installed on the Nasmyth A of the telescope. The idea of a new GUI for NICS has risen for optimizing the astronomers work through a set of powerful tools not present in the existing GUI, such as the possibility to move automatically, an object on the slit or do a very preliminary images analysis and spectra extraction. The new GUI also provides a wide and versatile image display, an automatic procedure to find out the astronomical objects and a facility for the automatic image crosstalk correction. In order to test the overall correct functioning of the new GUI for NICS, and providing some information on the atmospheric extinction at the TNG site, two telluric standard stars have been spectroscopically observed within some engineering time, namely Hip031303 and Hip031567. The used NICS set-up is as follows: Large Field (0.25'' /pixel) mode, 0.5'' slit and spectral dispersion through the AMICI prism (R~100), and the higher resolution (R~1000) JH and HK grisms.

Smart Sensors For Interoperable Smart Environment

Smart Environments are currently considered a key factor to connect the physical world with the information world. A Smart Environment can be defined as the combination of a physical environment, an infrastructure for data management (called Smart Space), a collection of embedded systems gathering heterogeneous data from the environment and a connectivity solution to convey these data to the Smart Space. With this vision, any application which takes advantages from the environment could be devised, without the need to directly access to it, since all information are stored in the Smart Space in a interoperable format. Moreover, according to this vision, for each entity populating the physical environment, i.e. users, objects, devices, environments, the following questions can be arise: “Who?”, i.e. which are the entities that should be identified? “Where?” i.e. where are such entities located in physical space? and “What?” i.e. which attributes and properties of the entities should be stored in the Smart Space in machine understandable format, in the sense that its meaning has to be explicitly defined and all the data should be linked together in order to be automatically retrieved by interoperable applications. Starting from this the location detection is a necessary step in the creation of Smart Environments. If the addressed entity is a user and the environment a generic environment, a meaningful way to assign the position, is through a Pedestrian Tracking System. In this work two solution for these type of system are proposed and compared. One of the two solution has been studied and developed in all its aspects during the doctoral period. The work also investigates the problem to create and manage the Smart Environment. The proposed solution is to create, by means of natural interactions, links between objects and between objects and their environment, through the use of specific devices, i.e. Smart Objects

Security control brought back to the user

The activity of the Ph.D. student Juri Luca De Coi involved the research field of policy languages and can be divided in three parts. The first part of the Ph.D. work investigated the state of the art in policy languages, ending up with: (i) identifying the requirements up-to-date policy languages have to fulfill; (ii) defining a policy language able to fulfill such requirements (namely, the Protune policy language); and (iii) implementing an infrastructure able to enforce policies expressed in the Protune policy language. The second part of the Ph.D. work focused on simplifying the activity of defining policies and ended up with: (i) identifying a subset of the controlled natural language ACE to express Protune policies; (ii) implementing a mapping between ACE policies and Protune policies; and (iii) adapting the ACE Editor to guide users step by step when defining ACE policies. The third part of the Ph.D. work tested the feasibility of the chosen approach by applying it to meaningful real-world problems, among which: (i) development of a security layer on top of RDF stores; and (ii) efficient policy-aware access to metadata stores. The research activity has been performed in tight collaboration with the Leibniz Universität Hannover and further European partners within the projects REWERSE, TENCompetence and OKKAM.

Troposphere Calibration Techniques for Deep Space Probe Tracking

Ground-based Earth troposphere calibration systems play an important role in planetary exploration, especially to carry out radio science experiments aimed at the estimation of planetary gravity fields. In these experiments, the main observable is the spacecraft (S/C) range rate, measured from the Doppler shift of an electromagnetic wave transmitted from ground, received by the spacecraft and coherently retransmitted back to ground. If the solar corona and interplanetary plasma noise is already removed from Doppler data, the Earth troposphere remains one of the main error sources in tracking observables. Current Earth media calibration systems at NASA’s Deep Space Network (DSN) stations are based upon a combination of weather data and multidirectional, dual frequency GPS measurements acquired at each station complex. In order to support Cassini’s cruise radio science experiments, a new generation of media calibration systems were developed, driven by the need to achieve the goal of an end-to-end Allan deviation of the radio link in the order of 3×〖10〗^(-15) at 1000 s integration time. The future ESA’s Bepi Colombo mission to Mercury carries scientific instrumentation for radio science experiments (a Ka-band transponder and a three-axis accelerometer) which, in combination with the S/C telecommunication system (a X/X/Ka transponder) will provide the most advanced tracking system ever flown on an interplanetary probe. Current error budget for MORE (Mercury Orbiter Radioscience Experiment) allows the residual uncalibrated troposphere to contribute with a value of 8×〖10〗^(-15) to the two-way Allan deviation at 1000 s integration time. The current standard ESA/ESTRACK calibration system is based on a combination of surface meteorological measurements and mathematical algorithms, capable to reconstruct the Earth troposphere path delay, leaving an uncalibrated component of about 1-2% of the total delay. In order to satisfy the stringent MORE requirements, the short time-scale variations of the Earth troposphere water vapor content must be calibrated at ESA deep space antennas (DSA) with more precise and stable instruments (microwave radiometers). In parallel to this high performance instruments, ESA ground stations should be upgraded to media calibration systems at least capable to calibrate both troposphere path delay components (dry and wet) at sub-centimetre level, in order to reduce S/C navigation uncertainties. The natural choice is to provide a continuous troposphere calibration by processing GNSS data acquired at each complex by dual frequency receivers already installed for station location purposes. The work presented here outlines the troposphere calibration technique to support both Deep Space probe navigation and radio science experiments. After an introduction to deep space tracking techniques, observables and error sources, in Chapter 2 the troposphere path delay is widely investigated, reporting the estimation techniques and the state of the art of the ESA and NASA troposphere calibrations. Chapter 3 deals with an analysis of the status and the performances of the NASA Advanced Media Calibration (AMC) system referred to the Cassini data analysis. Chapter 4 describes the current release of a developed GNSS software (S/W) to estimate the troposphere calibration to be used for ESA S/C navigation purposes. During the development phase of the S/W a test campaign has been undertaken in order to evaluate the S/W performances. A description of the campaign and the main results are reported in Chapter 5. Chapter 6 presents a preliminary analysis of microwave radiometers to be used to support radio science experiments. The analysis has been carried out considering radiometric measurements of the ESA/ESTEC instruments installed in Cabauw (NL) and compared with the requirements of MORE. Finally, Chapter 7 summarizes the results obtained and defines some key technical aspects to be evaluated and taken into account for the development phase of future instrumentation.

Cooperative Wireless Networks for Localization

This thesis adresses the problem of localization, and analyzes its crucial aspects, within the context of cooperative WSNs. The three main issues discussed in the following are: network synchronization, position estimate and tracking. Time synchronization is a fundamental requirement for every network. In this context, a new approach based on the estimation theory is proposed to evaluate the ultimate performance limit in network time synchronization. In particular the lower bound on the variance of the average synchronization error in a fully connected network is derived by taking into account the statistical characterization of the Message Delivering Time (MDT) . Sensor network localization algorithms estimate the locations of sensors with initially unknown location information by using knowledge of the absolute positions of a few sensors and inter-sensor measurements such as distance and bearing measurements. Concerning this issue, i.e. the position estimate problem, two main contributions are given. The first is a new Semidefinite Programming (SDP) framework to analyze and solve the problem of flip-ambiguity that afflicts range-based network localization algorithms with incomplete ranging information. The occurrence of flip-ambiguous nodes and errors due to flip ambiguity is studied, then with this information a new SDP formulation of the localization problem is built. Finally a flip-ambiguity-robust network localization algorithm is derived and its performance is studied by Monte-Carlo simulations. The second contribution in the field of position estimate is about multihop networks. A multihop network is a network with a low degree of connectivity, in which couples of given any nodes, in order to communicate, they have to rely on one or more intermediate nodes (hops). Two new distance-based source localization algorithms, highly robust to distance overestimates, typically present in multihop networks, are presented and studied. The last point of this thesis discuss a new low-complexity tracking algorithm, inspired by the Fano’s sequential decoding algorithm for the position tracking of a user in a WLAN-based indoor localization system.

New target tracking and monitoring guidance laws for UAV

A pursuer UAV tracking and loitering around a target is the problem analyzed in this thesis. The UAV is assumed to be a fixed-wing vehicle and constant airspeed together with bounded lateral accelerations are the main constraints of the problem. Three different guidance laws are designed for ensuring a continuos overfly on the target. Different proofs are presented to demonstrate the stability properties of the laws. All the algorithms are tested on a 6DoF Pioneer software simulator. Classic control design methods have been adopted to develop autopilots for implementig the simulation platform used for testing the guidance laws.

On-line adaptive visual tracking

Visual tracking is the problem of estimating some variables related to a target given a video sequence depicting the target. Visual tracking is key to the automation of many tasks, such as visual surveillance, robot or vehicle autonomous navigation, automatic video indexing in multimedia databases. Despite many years of research, long term tracking in real world scenarios for generic targets is still unaccomplished. The main contribution of this thesis is the definition of effective algorithms that can foster a general solution to visual tracking by letting the tracker adapt to mutating working conditions. In particular, we propose to adapt two crucial components of visual trackers: the transition model and the appearance model. The less general but widespread case of tracking from a static camera is also considered and a novel change detection algorithm robust to sudden illumination changes is proposed. Based on this, a principled adaptive framework to model the interaction between Bayesian change detection and recursive Bayesian trackers is introduced. Finally, the problem of automatic tracker initialization is considered. In particular, a novel solution for categorization of 3D data is presented. The novel category recognition algorithm is based on a novel 3D descriptors that is shown to achieve state of the art performances in several applications of surface matching.

Enabling Techniques and Algorithms for Integrated Communication and Navigation Satellite Systems

This thesis presents the outcomes of my Ph.D. course in telecommunications engineering. The focus of my research has been on Global Navigation Satellite Systems (GNSS) and in particular on the design of aiding schemes operating both at position and physical level and the evaluation of their feasibility and advantages. Assistance techniques at the position level are considered to enhance receiver availability in challenging scenarios where satellite visibility is limited. Novel positioning techniques relying on peer-to-peer interaction and exchange of information are thus introduced. More specifically two different techniques are proposed: the Pseudorange Sharing Algorithm (PSA), based on the exchange of GNSS data, that allows to obtain coarse positioning where the user has scarce satellite visibility, and the Hybrid approach, which also permits to improve the accuracy of the positioning solution. At the physical level, aiding schemes are investigated to improve the receiver’s ability to synchronize with satellite signals. An innovative code acquisition strategy for dual-band receivers, the Cross-Band Aiding (CBA) technique, is introduced to speed-up initial synchronization by exploiting the exchange of time references between the two bands. In addition vector configurations for code tracking are analyzed and their feedback generation process thoroughly investigated.

Enabling a direct path from end-user specifications to executable protocols in a biology laboratory environment

Biomedical analyses are becoming increasingly complex, with respect to both the type of the data to be produced and the procedures to be executed. This trend is expected to continue in the future. The development of information and protocol management systems that can sustain this challenge is therefore becoming an essential enabling factor for all actors in the field. The use of custom-built solutions that require the biology domain expert to acquire or procure software engineering expertise in the development of the laboratory infrastructure is not fully satisfactory because it incurs undesirable mutual knowledge dependencies between the two camps. We propose instead an infrastructure concept that enables the domain experts to express laboratory protocols using proper domain knowledge, free from the incidence and mediation of the software implementation artefacts. In the system that we propose this is made possible by basing the modelling language on an authoritative domain specific ontology and then using modern model-driven architecture technology to transform the user models in software artefacts ready for execution in a multi-agent based execution platform specialized for biomedical laboratories.

Web advertising. Le comunicazioni commerciali on-line.

La tesi ha ad oggetto lo studio e l’approfondimento delle forme di promozione commerciale presenti in Rete caratterizzate, più che da una normale evoluzione, da continue metamorfosi che ridefiniscono ogni giorno il concetto di pubblicità. L’intento è quello di analizzare il quadro giuridico applicabile alla pubblicità via Web, a fronte della varità di forme e di modalità che essa può assumere. Nel lavoro vengono passate in rassegna le caratteristiche che differenziano la pubblicità commerciale on-line rispetto a quella tradizionale; tra le quali, particolare rilievo assume la capacità d’istaurare una relazione – diretta e non mediata – tra impresa e consumatore. Nel prosieguo viene affrontato il problema dell’individuazione, stante il carattere a-territoriale della Rete, della legge applicabile al web advertising, per poi passare ad una ricognizione delle norme europee ed italiane in materia, senza trascurare quelle emanate in sede di autodisciplina. Ampio spazio è dedicato, infine, all’esame delle diverse e più recenti tecniche di promozione pubblicitaria, di cui sono messi in evidenza gli aspetti tecnico-informatici, imprescindibili ai fini di una corretta valutazione del tema giuridico. In particolare, vengono approfonditi il servizio di posizionamento a pagamento offerto dai principali motori di ricerca (keywords advertising) e gli strumenti di tracciamento dei “comportamenti” on-line degli utenti, che consentono la realizzazione di campagne pubblicitarie mirate (on-line behavioural advertising). Il Web, infatti, non offre più soltanto la possibilità di superare barriere spaziali, linguistiche o temporali e di ampliare la propria sfera di notorietà, ma anche di raggiungere l’utente “interessato” e, pertanto, potenziale acquirente. Di queste nuove realtà pubblicitarie vengono vagliati gli aspetti più critici ed esaminata la disciplina giuridica eventualmente applicabile anche alla luce delle principali decisioni giurisprudenziali nazionali ed europee in materia, nonché delle esperienze giuridiche nord-americane e di tipo autoregolamentare.

Development Of New Toolkits For Orbit Determination Codes For Precise Radio Tracking Experiments

This thesis describes the developments of new models and toolkits for the orbit determination codes to support and improve the precise radio tracking experiments of the Cassini-Huygens mission, an interplanetary mission to study the Saturn system. The core of the orbit determination process is the comparison between observed observables and computed observables. Disturbances in either the observed or computed observables degrades the orbit determination process. Chapter 2 describes a detailed study of the numerical errors in the Doppler observables computed by NASA's ODP and MONTE, and ESA's AMFIN. A mathematical model of the numerical noise was developed and successfully validated analyzing against the Doppler observables computed by the ODP and MONTE, with typical relative errors smaller than 10%. The numerical noise proved to be, in general, an important source of noise in the orbit determination process and, in some conditions, it may becomes the dominant noise source. Three different approaches to reduce the numerical noise were proposed. Chapter 3 describes the development of the multiarc library, which allows to perform a multi-arc orbit determination with MONTE. The library was developed during the analysis of the Cassini radio science gravity experiments of the Saturn's satellite Rhea. Chapter 4 presents the estimation of the Rhea's gravity field obtained from a joint multi-arc analysis of Cassini R1 and R4 fly-bys, describing in details the spacecraft dynamical model used, the data selection and calibration procedure, and the analysis method followed. In particular, the approach of estimating the full unconstrained quadrupole gravity field was followed, obtaining a solution statistically not compatible with the condition of hydrostatic equilibrium. The solution proved to be stable and reliable. The normalized moment of inertia is in the range 0.37-0.4 indicating that Rhea's may be almost homogeneous, or at least characterized by a small degree of differentiation.