Sur l'ambiguité de la localisation par réseaux d'antennes à large ouverture

In this report, we study the ambiguity of source localization using signal processing of large aperture antenna arrays under spherical wave propagation. This novel localization approach has been recently proposed, providing an estimate of the source position by means of two methods: geometrical and analytical. The former finds the source position as the estimate of circular loci, the latter as a solution of a linear system of equations. Although this method is proved to work for a general array geometry, we show that it suffers from ambiguities for a particular class of array geometries. Namely, in 2D, we prove that when the array geometry is linear or circular, there exist two possible solutions where only one corresponds to the actual position of the source. We also prove a relation of symmetry between the solutions with respect to the array geometry. This relation is very useful to assist the disambiguation process for discounting one of the estimates. By extension to 3D, planar (resp. spherical) arrays exhibit the same behavior i.e they provide two symmetrical estimates of the source position when the latter is not on the array plane (resp. sphere).Dans ce rapport, nous étudions l'ambiguïté d'une approche de localisation à base de traitement du signal de réseaux d'antennes à large ouverture sous propagation ondulatoire sphérique.Cette approche de localisation a été récemment proposée. Elle fournit une estimation de la position de la source au moyen de deux méthodes: géométrique et analytique. La première méthode localise la source à l'intersection de cercles. La seconde, permet de calculer la position de la source en résolvant un système d'équations linéaires. Bien que cette méthode ait été prouvée dans le cas général, nous démontrons qu'elle souffre d'ambiguïtés pour une classe particulière de géométrie de réseaux d'antennes. À savoir, on montre qu'en 2D, lorsque la géométrie du réseau est linéaire ou circulaire, il existe deux solutions possibles où seulement une correspond à la position réelle de la source. Nous prouvons aussi une relation de symétrie entre les solutions par rapport à la géométrie du réseau. Cette relation est très utile pour aider le processus de localisation à éliminer l'une des estimations. Par extension au 3D, les réseaux planaires (resp. sphériques) présentent le même comportement c.a.d ils fournissent deux estimations symétriques de la position de la source lorsque celle-ci n'est pas sur le plan (resp. la sphère) du réseau

Array Auto-calibration

In this thesis, efficient methods are presented to calibrate large or small aperture array systems containing different types of uncertainties. specifically the challenge of reducing the number of external sources required to calibrate an array is addressed and array calibration methods suitable for use when sources may be operating in the "near-far" field of the array are developed. Together, this can ease the overheads involved in calibrating and recalibrating an array system. In addition to presenting novel array calibration algorithms, this thesis also presents a novel transformation allowing a planar array to be expressed as a virtual uniform linear array of a much larger number of elements. This allows the array manifold of a planar array, which in general consists of non-hyperhelical curves, to be expressed using a number of hyperhelices which each correspond to the array manifold of a linear array. This hyperhelical structure has the potential to ease calibration overheads as well as having many other potential applications in array processing. This thesis presents novel pilot and auto array calibration schemes for estimating different types of array uncertainties. A novel pilot calibration algorithm is proposed whereby a single source transmitting from a known location (i.e. a pilot) at two carrier frequencies is used to estimate geometrical uncertainties in a planar array. This is achieved by exploiting the frequency dependence on the boundary between the "near-far" and "far" field of the array. In addition, an auto-calibration method is presented which doesn't require any external sources to estimate array uncertainties. Here, geometrical, complex gain and local oscillator (i.e. frequency and phase) uncertainties associated with the array elements are considered. In this approach, array elements transmit in turn to the others which operate as an array receiver. Large and small array apertures are investigated. Throughout the thesis, extensive computer simulations are presented to analyse the performance of the algorithms developed.Open Acces