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Introduction

**Skills and Expertise**

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November 1976 - June 2014

## Publications

Publications (63)

Build and operate multi-GNSS and multi-frequency receivers with state-of-the-art techniques using this up-to-date, thorough and easy-to-follow text. Covering both theory and practice and complemented by MATLAB© code and digital samples with which to test it, this package is a powerful learning tool for students, engineers and researchers everywhere...

Build and operate multi-GNSS and multi-frequency receivers with state-of-the-art techniques using this up-to-date, thorough and easy-to-follow text. Covering both theory and practice and complemented by MATLAB© code and digital samples with which to test it, this package is a powerful learning tool for students, engineers and researchers everywhere...

Build and operate multi-GNSS and multi-frequency receivers with state-of-the-art techniques using this up-to-date, thorough and easy-to-follow text. Covering both theory and practice and complemented by MATLAB© code and digital samples with which to test it, this package is a powerful learning tool for students, engineers and researchers everywhere...

Processing of GNSS signals from more than one frequency band enhances the accuracy and integrity of a position solution in both standalone and differential positioning. The modern GPS program and newly launched GNSS systems such as GALILEO, BeiDou allow civilians to access signals from multiple frequencies in the L-band spectrum. While there are so...

In traditional federated receiver, all the tracking channels work independently, and there is no interaction among them. However, in vectorized receiver, stronger channels aid others in their tracking. Such architecture makes a receiver to be of interest for positioning in urban canyons and harsh environments. On the other hand, the combination of...

Snapshot techniques are based on computing a position using only a set of digital signal samples captured over some milliseconds. Existing techniques require, in addition to the satellite ephemerides, a rough knowledge of the position and/or time at which the snapshot was captured. We propose a new method to instantaneously compute a snapshot posit...

Satellite navigation is quickly becoming a multidimensional complex challenge, with four Global Navigation Satellite Systems (GNSS) fully or partially deployed, more than 90 GNSS satellites currently in the sky, and 12 open-service GNSS signal types available to the end-user. Research papers about GNSS performance typically focus on single or dual...

This paper describes the main ideas of a GNSS SDR receiver and its implementation. Aims of the development, advantages, and some specific details are discussed. Particular attention is paid to the issue of security in GNSS receivers used for special purposes and some strategies of tracking. The idea of a snapshot receiver is briefly mentioned.

The first triangulation activity on Danish ground was carried out by the astronomer Tycho Brahe who resided on the island Hven. He wanted to determine the longitude difference of his observatory Uraniborg to Copenhagen. A by-product was a map of his island made in 1579. In 1761 the Royal Danish Academy of Sciences and Letters initiated a mapping pr...

Geodetic networks can be described by discrete models. The observations may be height differences, distances, and directions. Geodesists always make more observations than necessary and estimate the solution by using the principle of least squares. Contemporary networks often contain several thousand points. This leads to so large matrix problems t...

There are many applications which require continuous positioning in combined outdoor urban and indoor environments. For a long time GNSS has been used in outdoor environments while indoor positioning is still a challenging task. One of the major degradations that GNSS receivers experience indoors is the presence of multipath. The current paper anal...

This paper analyzes strengths and shortcomings of the existing aids for GNSS receiver development. A new set of tools is presented that provides to the developer debugging and optimization capabilities not supplied so far by existing tools. The proposed tools are simple and therefore very affordable, but never the less they are very functional. The...

There are many applications that require continuous positioning in combined outdoor urban and indoor environments. GNSS has been used for a long time in outdoor environments, while indoor positioning is still a challenging task. One of the major degradations that GNSS receivers experience indoors is the presence of multipath. The current paper anal...

A receiver for the Global Positioning System (GPS) signals provides information on its position and time. The position is
given in an Earth-Centered and Earth-Fixed coordinate system. This means that a static receiver keeps its coordinates over
time, apart from the influence of measurement errors. The system time (GPST) counts in weeks and seconds...

Atmosphere turbulence for low elevation angle reception is a noise source that is not well defined in existing systems using
satellite navigation signals. For high precision aviation purposes atmosphere turbulence needs to be assessed to meet the
future stringent requirements.
High precision receivers using open-loop mode data sampling at high sam...

The present and the following chapters are based on signals recorded according to parameters described in Section 4.3. The theory can be applied similarly to records with a different selection of parameters.

The acquisition provides only rough estimates of the frequency and code phase parameters. The main purpose of tracking is to refine these values, keep track, and demodulate the navigation data from the specific satellite (and provide an estimate of the pseudorange). A basic demodulation scheme is shown in Figure 7.1.

The signal processing for satellite navigation systems is based on a channelized structure. This is true for both GPS and Galileo. This chapter provides an overview of the concept of a receiver channel and the processing that occurs. In later chapters the specifics of the signal and data processing are outlined.

The output from the tracking loop is the value of the in-phase arm of the tracking block truncated to the values 1 and −1. Theoretically we could obtain a bit value every ms. However, we deal with noisy and weak signals, so a mean value for 20 ms is computed and truncated to −1 or 1. One navigation bit durates 20 ms.

Although the focus of this text is on the algorithms for software signal processing of the Global Navigation Satellite System (GNSS) signals, it is important to consider the source of that data stream to be processed. Since “software” signal processing is stated, it implies an input digital data stream. Thus, the purpose of this chapter is to provi...

The Galileo system offers several services, a few are free of charge and the rest are commercial. In this book we deal only with the L1 OS signal (OS for open service).

Satellite navigation receivers are used to receive, process, and decode space-based navigation signals, such as those provided by the GPS constellation of satellites. There is an increasing need for a unified open platform that will enable enhanced receiver development and design, as well as cost-effective testing procedures for various application...

The European navigation satellite system Galileo is moving ahead. We describe the open service signal L1 OS transmitted from the satellites. Compared to GPS some new features are introduced: Binary offset carrier modulation, coherent adaptive sub-carrier modulation, pilot signals, and tiered codes. These features make the GPS and Galileo signals li...

Geodetic levelling networks and networks with distance measurements are analysed in order to elucidate their special features. This analysis naturally leads one to look for continuous analogons of these networks. By means of tools known from the method of finite elements we derive the corresponding Green's functions for various boundary value probl...

Torsion balance observations in spherical approximation may be expressed as second-order partial derivatives of the anomalous (gravity) potential T: $$ T_{13} = \frac{{\partial ^2 T}} {{\partial x_1 \partial x_3 }}, T_{23} = \frac{{\partial ^2 T}} {{\partial x_2 \partial x_3 }}, T_{12} = \frac{{\partial ^2 T}} {{\partial x_1 \partial x_2 }}, T_\Del...

We discuss GPS receiver architectures based on software defined radio techniques. The reason for doing this is to obtain a reconfigurable receiver with a wide range of ap- plications. There is a need for a unified platform that will allow receiver development and testing for various applica- tions; this speeds the design process and reduces the cos...

Geodetic activities in Lithuania related to Aalborg university are discussed. In the summer of 1992, the Danish government granted eight GPS receivers and a lot of electronic equipment to the state of Lithuania. A subsequent era (1994-1995) opened with a grant from the Council of Nordic Ministers. In 1996-1998 the Danish Ministry for Education supp...

In this paper we illustrate the state of the art of the European Co-operation in the Field of Scientific and Technical Research, COST Action 625 “3-D Monitoring of Active Tectonic Structures” in Italy. The project is mainly focused on detecting strain variations and/or any phenomena that may precede future seismic events, in order to evaluate the t...

The Matlab computing environment has become a popular way to perform complex matrix calculations, and to produce sophisticated
graphics output in a relatively easy manner. Large collections of Matlab scripts are now available for a wide variety of applications
and are often used for university courses. The GPS Easy Suite is a collection of ten Matl...

This project investigates the problems in computing the position of a GPS receiver by pseudoranges. Based on three different algorithms (Iterative Least Squares Solution, Bancroft’s Method, Kleusberg’s Solution) it is determined how to obtain the fastest execution time and most accurate result. It shows that the best solution is obtained by a combi...

We describe the technique of block elimination. It is used for explaining Schreiber’s device. We use the technique to derive
the equations for sequential least-squares problems. In so doing we derive the basic equations for the Kaiman filter. Finally
we study the influence of changing the weight of observations. We bring a list of matrix identities...

Surely most geodesists have been occupied by seeking optimal shapes of a net work. I'm no exception. This book contains the more fruitful results on the topic. No matter how you choose to understand the adjective "optimal," it is no doubt useful as a beginning to understand error propagation in various types of net works. Basically, geodesists ar...

Having introduced some useful tools for analyzing a leveling network with three nodes we generalize to n nodes. At the same time we focus on eigenvectors and eigenvalues to derive the n by n pseudoinverse covariance matrix and deal with the SVD. We proceed to regular two-dimensional leveling networks; then random and systematic error propagation in...

So far we have been dealing with absolute observations. By this we understand that for distance measurements the unit of length is exactly unity and for direction measurements all directions are measured relative to true north.

We conclude by demonstrating a few applications of the theory developed. It might have become obvious that the theory demonstrates what is to be considered good design. Most geodetic works aim at having small and circular confidence ellipses. This is achieved by homogeneous and isotropic observations taken in regular networks. Yet some engineering...

This chapter states our fundamental ideas about transformation of discrete two-dimensional networks into continuous analogues.

The spectral density function describes the distribution of eigenvalues of a given problem. Networks may be characterized by the condition number of the normal equation matrix. The spectral condition number is defined as the largest eigenvalue divided by the smallest eigenvalue. Most often this number is several powers of ten. When designing networ...

Knowledge of the probability density function of the observables is not needed to routinely apply a least-squares algorithm and compute estimates for the parameters of interest. For the interpretation of the outcomes, and in particular for statements on the quality of the estimator, the probability density has to be known
A variety of tools and mea...

This article deals with the type of probability distribution of GPS code and phase data. It is common practice in the processing of GPS range observables to assume that these data are normally distributed, and in particular a procedure for quality control will directly rely on this assumption. The question to be answered reads: are GPS data indeed...

In the spring of 1991 the first author conceived the plan of establishing a fundamental network in Lithuania by means of GPS. In July 1992 the financial support for the plan was provided. The Danish Government payed for GPS receivers, personal computers, and other materials needed while the Lithuanian Government agreed to subsidize the renovation o...

Studies of error propagation in geodetic networks of an absolute type have already been carried through by several authors using various mathematical techniques. The geodetic elasticity theory relies on a continuation of the actual, discrete network. The traditional observation and normal equation matrices are substituted by partial differential eq...

The geodetic elasticity theory is broadly outlined. It relies heavily on the structure matrix which mainly is defined as weight
per area unit.
An actual computation of the structure matrix has been performed for distance measurements in the Danish fundamental network.
The mean value of the matrix unveils a fairly good isotropy in the network while...

BIOGRAPHIES Kai Borre is a Professor of Geodesy at the Aalborg Univer-sity since 1976. His recent software developments include a large collection of MATLAB files for postprocessing of GPS observations. In 1997 he coauthored the book Linear Algebra, Geodesy, and GPS with Gilbert Strang, Professor of Mathematics at the Massachusetts Institute of Tec...

Contenido: 1) Señales y sistemas; 2) Señales GPS; 3) Señal Galileo; 4) Antenas GNSS e interfaces; 5) Receptores GNSS de operación de repaso; 6) Adquisición; 7) Transmisor y código de seguimiento; 8) Procesamiento de datos para posicionamiento. -- Problemas: Código MATLAB; Simulación de señales GNSS.