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Utilizzo del software goGPS per la navigazione di precisione con ricevitori a basso costo
Abstract
Riassunto goGPS è un software di navigazione sviluppato presso il Laboratorio di Geomatica del Politecnico di Milano (Polo di Como). Si basa su un filtro di Kalman in grado di elaborare differenze doppie di codice e di fase rispetto ad una rete di stazioni permanenti, sia in post-processamento che in tempo reale. Inoltre si avvale del supporto di un modello digitale del terreno per migliorare l'accuratezza in quota e può essere vincolato ad un reticolo di percorsi noti a priori (per esempio reticoli stradali o ferroviari). La principale innovazione introdotta da goGPS consiste nella possibilità di applicare un posizionamento cinematico relativo RTK a ricevitori di basso costo in singola frequenza, miglio-rando la loro accuratezza dagli usuali 2-4 metri a qualche decimetro. goGPS è stato sviluppato e collaudato utilizzando il ricevitore u-blox AEK-4T, in grado di restituire osservazioni grezze di co-dice e fase sulla portante L1, necessarie per calcolare le doppie differenze rispetto alla stazione di riferimento. Al fine di ottenere un posizionamento di precisione con tale ricevitore, si è reso neces-sario processare anche il rapporto segnale/rumore delle osservazioni GPS, definendo delle funzioni peso che non dipendano esclusivamente dall'elevazione del satellite. In questo lavoro sono presen-tati i risultati di una serie di prove volte alla calibrazione del software per ottenere un posizionamen-to ottimale con un ricevitore a basso costo. goGPS si dimostra generalmente in grado di posizionarsi con errori al di sotto del metro; tale errore si riduce significativamente introducendo vincoli di per-corso. goGPS è sviluppato in ambiente MATLAB ed il codice sorgente è distribuito sotto licenza open source per agevolarne la diffusione sia a scopi didattici che di ricerca. Abstract goGPS is a navigation software developed at the Geomatics Laboratory of Politecnico di Milano (Como Campus). It is based on a Kalman filter which can process double differences of code and phase with respect to a network of permanent stations, both in post-processing and in real time. It can exploit a digital terrain model (DTM) in order to enhance the height accuracy and it can be constrained to a road or railway network. The innovation introduced by goGPS is the chance to apply a real time kinematic (RTK) positioning to low cost receivers with single frequency, im-proving their accuracy up to some decimetres. Here some calibration test results are presented, us-ing the low cost receiver u-blox AEK-4T which can provide raw observations of code and phase; goGPS can generally make a positioning with errors lower than a metre; this error considerably decreases when path constraints are introduced. goGPS is developed in MATLAB environment and the source code is distributed under open source licence for facilitating its circulation with both educational and research purposes.
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goGPS is a software package designed to enhance the accuracy of standalone GPS receivers by exploiting networks of GNSS permanent stations to apply real-time relative positioning, extended Kalman filtering techniques to better model the kinematics of a roving GPS receiver, digital terrain model observations to mitigate the GPS weakness in the vertical direction and, if it is known in advance that the receiver is moving along a predefined path (e.g. a railway), linear paths to constrain the positioning. The principal innovation introduced by goGPS is the possibility to apply kinematic relative positioning in an effective way on low cost single frequency GPS receivers, enhancing their accuracy from the usual 2-4 m up to some decimeters. Though this kind of receivers is the main target for goGPS, also double frequency receivers are supported.
goGPS positioning capabilities have been assessed by testing it under different conditions of sky visibility, signal degradation and dynamics of the roving receiver. Since goGPS needs GPS raw observations (i.e. code pseudorange, phase measurement, signal-to-noise ratio, etc.) the u-blox AEK-4T evaluation kit was chosen as a roving receiver, since it provides them. goGPS performance using AEK-4T were compared both with other low cost instruments (eBonTek eGPS 597, TomTom MKII) and with high level professional receivers (Leica GS20 and Leica GPS System 1200). The results show that goGPS managed to get higher accuracy than low cost receivers during all the tests, in some cases obtaining accuracy levels of the same order of magnitude of those obtained by the single frequency professional receiver (Leica GS20).
goGPS is developed in a MATLAB environment and it can run either in real-time mode, receiving the low cost receiver data stream on a USB port and the master station data stream through the Internet, or in post-processing mode, reading master and rover RINEX files or goGPS data saved during a real-time session.
The global positioning system (GPS) equations are usually solved with an application of Newton's method or a variant thereof: Xn+1 = xn + H-1(t - f(xn)). (1) Here x is a vector comprising the user position coordinates together with clock offset, t is a vector of tour pseudorange measurements, and H is a measurement matrix of partial derivatives H = fx· In fact the first fix of a Kalman filter provides a solution of this type. If more than four pseudoranges are available for extended batch processing, H-1 may be replaced by a generalized inverse (HTWH)-1HTW, where W is a positive definite weighting matrix (usually taken to be the inverse of the measurement covariance matrix). This paper introduces a new method of solution that is algebraic and noniterative in nature, computationally efficient and numerically stable, admits extended batch processing, improves accuracy in bad geometric dilution of precision (GDOP) situations, and allows a "cold start" in deep space applications.
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