GNSS algebraic structures

GNSS algebraic structures

The first objective of this paper is to show that some basic concepts used in global navigation satellite systems (GNSS) are similar to those introduced in Fourier synthesis for handling some phase calibration problems. In experimental astronomy, the latter are at the heart of what is called ‘phase closure imaging.’ In both cases, the analysis of the related structures appeals to the algebraic ...

Algebraic Structures

Algebraic Structures

In this text, we focus on operations of arity 2, 1, and 0. – For n = 2, f : A → A is a binary operation and is usually written in infix notation, using a binary operation symbol like ·, ∗, or +. Hence, instead of f(a1, a2) we write a1fa2. – For n = 1, f : A→ A is a unary operation. – For n = 0, f : A → A is a nullary operation or a constant. An algebra (or an algebraic structure) is a set A, th...

MAGMA-JOINED-MAGMAS: A CLASS OF NEW ALGEBRAIC STRUCTURES

By left magma-$e$-magma, I mean a set containingthe fixed element $e$, and equipped by two binary operations "$cdot$", $odot$ with the property $eodot (xcdot y)=eodot(xodot y)$, namelyleft $e$-join law. So, $(X,cdot,e,odot)$ is a left magma-$e$-magmaif and only if $(X,cdot)$, $(X,odot)$ are magmas (groupoids), $ein X$ and the left $e$-join law holds.Right (and two-sided) magma-$e$-magmas are de...

On signal structures for GNSS-2

This paper summarizes the main results of an early investigation on desirable signal structures for the European &Galileo' civil satellite navigation system. Stemming from the requirements for increased accuracy, reduced time-to-"rst-"x and integrity information provision, the report describes the logical steps and the related numerical results leading to a novel &Galileo' signal de"nition. Alt...