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A Matlab Educational GUI for Analysis of GNSS Coverage and Precision
3rd IFAC Workshop on Internet Based Control Education 3rd IFAC Workshop on Internet Based Control Education November 4-6, 2015.on Brescia, Italy 3rd IFAC Workshop Internet Based Control Education November 4-6, 2015.on Brescia, Italy 3rd IFAC Workshop Internet Based Control Education November 4-6, 2015. Brescia, Italy Available online at www.sciencedirect.com November 4-6, 2015. Brescia, Italy
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Matlab Educational GUI for Analysis Matlab Educational GUI for Analysis Matlab Educational GUI for Analysis Matlab Educational GUI for Analysis GNSS Coverage and Precision GNSS Coverage and Precision GNSS Coverage and Precision GNSS Coverage and Precision∗ ∗
of of of of
Fernando Fernando Fernando Fernando
Lanagran-Soler Vazquez Lanagran-Soler ∗∗ Rafael Rafael Vazquez ∗∗ ∗∗ Lanagran-Soler Vazquez ∗ Rafael Manuel R. Arahal ∗∗ Lanagran-Soler Rafael Manuel R. Arahal ∗∗ Vazquez ∗ Manuel R. Arahal ∗∗ Manuel R. Arahal ∗ ∗ Departamento de Ingenier´ Departamento de Ingenier´ıa ıa Aeroespacial Aeroespacial ∗ ∗∗ de Ingenier´ ıa Aeroespacial ∗ Departamento de Ingenier´ ıa de Sistemas yy Autom´ a ∗∗ Departamento Departamento de Ingenier´ ıa Aeroespacial Departamento de Ingenier´ ıa de Sistemas Autom´ atica tica ∗∗ de Ingenier´ ıa de Sistemas y Autom´ a ∗∗ Departamento Universidad de Seville, Camino de los Descubrimientos s/n, 41092, Departamento Ingenier´ de Descubrimientos Sistemas y Autom´ atica tica Universidad de Seville,deCamino deıalos s/n, 41092, Universidad de Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain ([email protected],[email protected], Universidad de Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain ([email protected],[email protected], Seville, Spain ([email protected],[email protected], [email protected]) Seville, Spain ([email protected],[email protected], [email protected]) [email protected]) [email protected]) Abstract: This work reports on a Abstract: This work reports on a visual visual tool tool that that has has been been developed developed to to supplement supplement Abstract: This work reports on a visual tool that has been developed to theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies Abstract: This work reports on a visual tool Systems that has(GNSS) been developed to supplement supplement theoretical lessons on Global Navigation Satellite with real-world studies of of theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies of current constellations. The tool was created using Matlab’s Graphical User Interface theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies of current constellations. The tool was created using Matlab’s Graphical User Interface Design Design current constellations. The tool was using Graphical User Design Environment (GUIDE), and it for in engineering with current constellations. was created created intended using Matlab’s Matlab’s Graphical User Interface Interface Design Environment (GUIDE),The and tool it is is particularly particularly intended for courses courses in aerospace aerospace engineering with Environment (GUIDE), and it is particularly intended for courses in aerospace engineering with GNSS content. As such, it highlights the space segment of these navigation systems and concepts Environment and it is particularly courses in aerospace engineering with GNSS content.(GUIDE), As such, it highlights the spaceintended segment for of these navigation systems and concepts GNSS content. As such, the segment of these systems and concepts such visibility, and this tool, can visualize the GNSS Asgroundtracks such, it it highlights highlights the space spaceUsing segment these navigation navigation systems concepts such as ascontent. visibility, groundtracks and coverage. coverage. Using thisofgraphic graphic tool, students students can and visualize the such as visibility, groundtracks and coverage. Using this graphic tool, students can visualize the real position of all satellites in the GPS constellation at any time since its start of operation, such as visibility, groundtracks and coverage. Using this graphic tool, students can visualize the real position of all satellites in the GPS constellation at any time since its start of operation, real position of in GPS constellation at any time since its start operation, analyze the of that can be or study real position of all all satellites satellites in the the GPS any any timepoint sincein start of of analyze the number number of satellites satellites that canconstellation be visualized visualizedatfrom from any point initsEarth, Earth, or operation, study the the analyze the number of satellites that can be visualized from any point in Earth, or study the quality of the navigational solution which depends on the relative geometry of the user and analyze the of satellites that can depends be visualized any geometry point in Earth, study quality of thenumber navigational solution which on thefrom relative of the or user and the quality of the solution which on relative geometry of the user and satellites. tool to these aa flight between on quality of The the navigational navigational solution which depends depends on the thefor thetwo userpoints and the the satellites. The tool also also allows allows to perform perform these studies studies forrelative flightgeometry between ofany any two points on satellites. The tool also allows to perform these studies for aa flight between any two points on Earth, or for an user-defined region. A preliminary version of the tool was tried in a computer satellites. The tool also allows to perform these studies for flight between any two points on Earth, or for an user-defined region. A preliminary version of the tool was tried in a computer Earth, or for region. preliminary version of tool was tried in lab a in reported bugs satisfied Earth, for an an user-defined user-defined region. A A Students preliminary versionsome of the the toolbut waswere triedmostly in aa computer computer lab for for or a course course in Aerial Aerial Navigation. Navigation. Students reported some bugs but were mostly satisfied lab for a course in Aerial Navigation. Students reported some bugs but were mostly satisfied with the tool, as a survey shows. lab course Aerial shows. Navigation. Students reported some bugs but were mostly satisfied withfor thea tool, as in a survey with the tool, as shows. with theIFAC tool,(International as a a survey survey Federation shows. of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. © 2015, Keywords: Keywords: Educational Educational tool, tool, GNSS, GNSS, Aerial Aerial Navigation, Navigation, Matlab Matlab GUI, GUI, Navigation Navigation Accuracy Accuracy Keywords: Educational tool, GNSS, Aerial Navigation, Matlab GUI, Navigation Keywords: Educational tool, GNSS, Aerial Navigation, Matlab GUI, Navigation Accuracy Accuracy 1. satellites 1. INTRODUCTION INTRODUCTION satellites that that can can be be visualized visualized from from any any point point in in Earth, Earth, 1. INTRODUCTION satellites that can be visualized from any point in or study the quality of the navigational solution which 1. INTRODUCTION satellites can be visualized from any point in Earth, Earth, or study that the quality of the navigational solution which Global Navigation Satellite Systems (GNSS) have become or study the quality of the navigational solution which depends on the relative geometry of the user and the Global Navigation Satellite Systems (GNSS) have become or study on thethe quality of the navigational solution which depends relative geometry of the user and the Global Navigation Satellite Systems (GNSS) have become ubiquitous in everyday life. There is growing number of apdepends on the relative geometry of the user and the satellites. The tool also allows to perform these studies Global Navigation Satellite Systems (GNSS) have become ubiquitous in everyday life. There is growing number of ap- depends on thetool relative geometry of the user and the satellites. The also allows to perform these studies ubiquitous in life. There growing number of plications on precise positioning. The tool allows to these studies for between any two on or for ubiquitous in everyday everyday life. systems There is is for growing number of apap- satellites. plications relying relying on these these systems for precise positioning. satellites. tool also also to perform perform these for aa flight flightThe between any allows two points points on Earth, Earth, or studies for an an plications relying on these systems for precise positioning. As new constellations such as the Chinese Beidou or Eurofor a flight between any two points on Earth, or for an user-defined region. plications relying on these for precise positioning. As new constellations such systems as the Chinese Beidou or Euro- for a flight between user-defined region. any two points on Earth, or for an As new constellations such as the Chinese Beidou or European Galileo become joining the currently region. As new constellations such as the Chinese or active Euro- user-defined pean Galileo become available, available, joining the Beidou currently active user-defined region. There pean Galileo become available, joining the currently active American GPS or Russian Glonass, applications There are are commercial commercial tools, tools, such such as as AGI’s AGI’s Systems Systems pean Galileo become thenew currently active There American GPS or the theavailable, Russian joining Glonass, new applications are commercial tools, such as AGI’s Systems ToolKit (STK), which allows to perform these studies (see American GPS or the Russian Glonass, new applications There are commercial tools, such as AGI’s Systems are expected to appear. In particular, GNSS use is rising ToolKit (STK), which allows to perform these studies (see American GPS the Russian Glonass,GNSS new applications are expected to or appear. In particular, use is rising ToolKit (STK), which allows to perform these studies (see for instance one of AGI’s white papers by Gorski and are expected to appear. In particular, GNSS use is rising ToolKit (STK), which allows to perform these studies (see in aerial navigation, particularly in non-critical systems, for instance one of AGI’s white papers by Gorski and are expected to appear. In particular, GNSS use systems, is rising for in aerial navigation, particularly in non-critical instance one of AGI’s white papers by Gorski and Gerten (2007)). However, their price is usually prohibitive, in aerial navigation, particularly in non-critical systems, for instance one of AGI’s white papers by Gorski and such as Unmanned Aerial Vehicles (UAVs) or Remotely Gerten (2007)). However, their price is usually prohibitive, in aerial navigation, particularly in non-critical systems, such as Unmanned Aerial Vehicles (UAVs) or Remotely Gerten (2007)). However, their price usually prohibitive, whereas Matlab’s licenses usually available most such as Unmanned Aerial Vehicles (UAVs) or Remotely However, their price is is usually in prohibitive, Piloted Systems (RPAS). While its still whereas(2007)). Matlab’s licenses are are usually available in most uniunisuch as Aerial Unmanned Aerial Vehicles (UAVs) or is Piloted Aerial Systems (RPAS). While its use use isRemotely still not not Gerten whereas Matlab’s licenses are usually available in most universities and there is even a cheap student version that can Piloted Aerial Systems (RPAS). While its use is still not whereas Matlab’s licenses are usually available in most uniwidespread in manned aircraft (due to lack of integrity of versities and there is even a cheap student version that can Piloted Aerial Systems aircraft (RPAS).(due While its use is still not widespread in manned to lack of integrity of versities and there is even a cheap student version that can run the tool. While there are some previously developed widespread in manned aircraft (due to lack of integrity of versities and there is even a cheap student version that can basic systems) the introduction of augmentation systems run the tool. While there are some previously developed widespread in manned aircraft (due to lack of integrity of run basic systems) the introduction of augmentation systems the While are developed GPS-specific for the by basic systems) the introduction of augmentation systems the tool. tool. software While there there are some some previously previously is the regular in flights GPS-specific software for Matlab—see Matlab—see the papers papersdeveloped by Borre Borre basic systems) the to introduction augmentation is opening opening the way way to regular use use of GNSS GNSS in regular regularsystems flights run GPS-specific software for Matlab—see the papers by Borre (2003, 2009) or Jan et al. (2009)—they don’t provide is opening the way to regular use of GNSS in regular flights GPS-specific software for Matlab—see the papers by Borre within a few years. (2003, 2009) or Jan et al. (2009)—they don’t provide is opening theyears. way to regular use of GNSS in regular flights (2003, within a few 2009) or et al. (2009)—they don’t provide graphical interfaces easy This within a years. (2003, 2009) or Jan Janand et are al. not (2009)—they provide graphical interfaces and are not easy to to use. use.don’t This justifies justifies within a few fewthe years. Therefore, subject of GNSS if of great interest to graphical interfaces and are not easy to use. This justifies the use of Matlab GUIDE as a convenient development Therefore, the subject of GNSS if of great interest to graphical interfaces and are as notaeasy to use. This justifies the use of Matlab GUIDE convenient development Therefore, the of GNSS if of great interest to aerospace and such staple subject of use GUIDE as development environment that allow to benefit Therefore, the subject subject aerospace engineers engineers andofas as GNSS such it itifis isofa a great staple interest subject to of the the use of of Matlab Matlab GUIDE as aa convenient convenient environment that will will allow students students to easily easily development benefit from from aerospace engineers and as such it is a staple subject of most aerospace engineering curricula. Since GNSS perforenvironment that will allow students to easily the tool. aerospace engineers and as curricula. such it is Since a staple subject of environment most aerospace engineering GNSS perforthat will allow students to easily benefit benefit from from the tool. most aerospace engineering curricula. Since GNSS performance has dependence on relative geometry tool. most engineering curricula. Since GNSS perfor- the manceaerospace has a a strong strong dependence on the the relative geometry the tool. A preliminary version mance has a strong dependence on the relative geometry of the receiver with respect to the satellites, students can A preliminary version of of the the tool tool was was tried tried in in aa computer computer mance has a strong dependence on the relative geometry of the receiver with respect to the satellites, students can A preliminary version of the tool was tried in aa computer lab for aa course in Aerial Navigation. Students reported of the receiver with respect to the satellites, students can A preliminary version of the tool was tried in computer certainly benefit from virtual simulations, as argued in the lab for course in Aerial Navigation. Students reported of the receiver the satellites, students certainly benefitwith fromrespect virtualtosimulations, as argued in can the lab for a course in Aerial Navigation. Students reported some bugs but were mostly satisfied with the tool, as certainly benefit from virtual simulations, as argued in the lab for a course in Aerial Navigation. Students reported work by Li et al. (2010). In this paper, we report on a visual some bugs but were mostly satisfied with the tool, as a a certainly from virtual as argued in the some work by Libenefit et al. (2010). In thissimulations, paper, we report on a visual bugs but were mostly satisfied with the tool, as a survey shows. While the tool was developed for this particwork by Li et al. (2010). In this paper, we report on a visual some bugs but were mostly satisfied with the tool, as a tool that has been developed to supplement theoretical survey shows. While the tool was developed for this particwork by Lihas et al.been (2010). In this paper, we report theoretical on a visual survey tool that developed to supplement shows. While the tool developed for this ular it can applied to other not tool that has been developed to theoretical shows. tool was was developed forsubjects this particparticlessons on GNSS with real-world studies conular course, course, it While can be bethe applied to several several other subjects not tool that been developed to supplement supplement theoretical lessons on has GNSS with real-world studies of of current current con- survey ular course, it can be applied to several other subjects not necessarily taught in aerospace engineering. For instance, lessons on GNSS with real-world studies of current conular course, it can be applied to several other subjects not stellations. The tool was created using Matlab’s Graphical necessarily taught in aerospace engineering. For instance, lessons on GNSS with studies of current con- necessarily stellations. The tool wasreal-world created using Matlab’s Graphical taught in engineering. For instance, aa course autonomous vehicles (aerial land-based) stellations. The tool created Matlab’s Graphical in aerospace aerospace engineering. instance, User Environment (GUIDE). this course on ontaught autonomous vehicles (aerial or orFor land-based) stellations. TheDesign tool was was created using using Matlab’s Using Graphical User Interface Interface Design Environment (GUIDE). Using this necessarily a course on autonomous vehicles (aerial or land-based) would certainly benefit from the tool since these vehicles User Interface Design Environment (GUIDE). Using this a course on autonomous vehicles (aerial or land-based) graphic tool, aerospace engineering students can visualize would certainly benefit from the tool since these vehicles User Interface Design Environment (GUIDE). this would graphic tool, aerospace engineering students canUsing visualize certainly benefit from the tool since these vehicles typically have a critical depence on GNSS performance to graphic tool, aerospace engineering students can visualize would certainly benefit from the tool since these vehicles the real position of all satellites in the GPS constellation at typically have a critical depence on GNSS performance to graphic tool, aerospace engineering students can visualize the real position of all satellites in the GPS constellation at typically have a critical depence on GNSS performance to carry out their mission. A class on integrated navigation the real position of all in GPS at critical depence performance to any time since of the of carry outhave theira mission. A class on on GNSS integrated navigation the all satellites satellites in the theanalyze GPS constellation constellation any real timeposition since its itsofstart start of operation, operation, analyze the number number at of typically carry out their mission. A class on integrated navigation any any time time since since its its start start of of operation, operation, analyze analyze the the number number of of carry out their mission. A class on integrated navigation Copyright © 2015, 2015 IFAC 93 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2015 IFAC 93 Copyright ©under 2015 responsibility IFAC 93 Control. Peer review of International Federation of Automatic Copyright © 2015 IFAC 93 10.1016/j.ifacol.2015.11.219
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2.2 Orbital elements
systems and/or Kalman filtering could use the tool as part of a lab on GPS-aided inertial navigation systems design, to simulate the system under nominal or GPS-degraded conditions.
Orbital elements are a minimal set of parameters that describe an orbit. Typically, Kepler’s classical elements are used. These are:
The structure of this paper is as follows. In Section 2 we briefly review some orbital mechanics material that will be needed in the sequel. In Section 3 we define the GNSS concepts that are analyzed by our program. We follow with Section 4 where we describe the tool itself. Next, in Section 5, we describe a hands-on experience with students using a preliminary version of the tool. We finish with some concluding remarks in Section 6.
(1) Semi-major axis a: it describes the size of the orbit. It is directly related to the orbit’s energy. (2) Eccentricity e: it describes the shape of the orbit. Navigation satellites are usually almost circular, so their eccentricity is very close to zero. (3) Inclination i: it measures the angle between the orbit’s plane and the Equator. Inclinations between 0 and 90 degrees describe prograde orbits, whereas inclinations between 90 and 180 degrees describe retrograde orbits, however the latter are seldom used for navigation satellites. (4) Right ascension of the ascending node (RAAN, denoted as Ω): it measures the angle between the vernal point and the orbit’s ascending node (where the orbit intersects the Equator going towards North). (5) Argument of perigee ω: it measures the angle between the orbit’s ascending node and the orbit’s perigee (point of closest approach to Earth’s center of mass). (6) True anomaly θ: it describes the position of the satellite in its orbit, with respect to perigee.
2. BASIC CONCEPTS FROM ORBITAL MECHANICS Next we briefly review some basic concepts from Orbital Mechanics.
2.1 Reference systems This work requires three basic coordinate frames. We will define these loosely, since a precise definition requires more advanced concepts than required for a preliminary analysis.
If an orbit is exactly circular (e = 0), then the two last orbital elements are not well defined, as there is no perigee. Then a new orbital element, called the argument of latitude u, is used. The argument of latitude is defined as the angle between the ascending node and the satellite’s position in its orbit.
(1) Earth-centered inertial frame (ECI). Its origin is on Earth’s center of mass, the x-y plane is Earth’s equatorial plane, with the x axis points towards the vernal point (a fixed direction relative to the stars), and the z axis is aligned with Earth’s spin axis. (2) Earth-centered, Earth-fixed frame (ECEF). Its origin is on Earth’s center of mass, the x-y plane is Earth’s equatorial plane and the z axis is aligned with Earth’s spin axis, but now it rotates with the Earth so that the x axis points towards the Prime (Greenwich) meridian. Position is usually expressed in geodetical coordinates: latitud φ, longitude λ, and altitude h. These might be defined with respect to a reference ellipsoid (usually WGS’84), but for simplicity we will consider an spherical Earth. The angle formed between ECI and ECEF is called Greenwich Sidereal Time (GST) and it is a function of the actual date and hour. (3) Topocentric local frame. This is centered on an observer usually on the surface of the Earth. The xy plane is tangent to Earth’s surface, with the x axis pointing to North, y axis to East and z axis towards the center of the Earth (down direction). The position of an object in the observer’s field of view is usually described by using angular coordinates: Elevation (El), which is the angle above the x-y plane, Azimuth (Az), which is the angle formed between the projection of the object in the x-y plane and the North direction, measured counter-clockwise, and the distance to the object ρ.
2.3 Orbit propagation and ephemeris computation Orbit propagation is the process of determining the orbital elements of a satellite in a future time t, starting from their values at the present time t0 . If there are no orbital perturbations, then the two-body problem solution (see Curtis (2009)) can be applied and only the true anomaly (or the argument of latitude for circular orbits) changes with time. Otherwise some kind of perturbation model is required to determine the orbital element’s change with time. Once the orbital elements at some time are known, the ephemeris of the satellite, i.e., its position in the ECI frame, can be easily computed. Using the transformation between frames, one can calculate the position of a satellite in the ECEF frame (with respect to Earth) and in the topocentric frame (with respect to an observer). All these are useful for our tool, since 3D visualization of orbits is easier in the ECI frame, whereas 2D visualization on a map of the Earth is more convenient on the ECEF frame (where one can see the satellite’s groundtrack, which are the points of the Earth over which the satellite is passing). Finally, the topocentric frame is useful to determine if a satellite is visible or not; visibility depends on the elevation angle to be above some given value (called elevation mask ) depending on the surroundings.
The coordinate transformations between these reference systems (and more precise definitions) can be found in any basic orbital mechanics textbook such as Curtis (2009); Vallado and McClain (2007); Wie (1998). 94
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3. BASIC GNSS CONCEPTS
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available over the lifetime of the system, taking into account all the outages whatever their origins. (2) Integrity: Integrity relates to the trust which can be placed in the correctness of the information supplied by the Navigation System, it includes the ability of the system to provide timely warnings to the user when the system or data provided by the system should not be used for navigation. (3) Continuity: Continuity of GNSS is defined as the probability that the positioning service works “sufficiently well” (which as before is usually defined as the PDOP taking a sufficiently small value) throughout a flight operation.
Basic navigation using Global Navigation Satellite Systems (GNSS) is based on multilateration. A receiver acquires a navigation message from several satellites. From the message, the ephemeris of the satellites can be reconstructed using the transmitted orbital elements and a basic propagator, and the signal’s time of travel can be precisely calculated. Since this time and the distance to the satellites is related by the speed of travel of the signal (the speed of light), then in principle with at least three satellites it should be possible to compute the receiver’s position. However, since a receiver’s clock is unreliable (compared with the atomic clocks on board GNSS satellites), there is another unknown which is the offset of the receiver’s clock with respect to GNSS time. Thus, a minimum of four satellites is required to estimate the receiver’s position from satellite signals.
In our tool, we concentrate in studies of availability and continuity, by studying the PDOP evolution for a receiver in a fixed point of the Earth, on a flight, or for a region. 3.3 Nominal constellations and real constellations
However, the relative geometry of the visible satellites also influences the quality of the navigational solution. This effect is called “dilution of precision” and it is studied next.
Presently, there are a number of GNSS constellations giving service. These are summarized in Table 1 The nominal constellation is in most cases composed of medium-Earth orbit (MEO) satellites, but in some cases it includes geostationary (GEO) satellites and Inclined Geo-Synchronous Orbits (IGSO). More details can be found in GPS World (2015).
3.1 Dilution of precision If the satellites are close in the sky, it is intuitively clear that the estimated position will be less precise than if visible satellites are evenly distributed across the sky. This can be made more precise using the concept of dilution of precision, which is found when using a leastsquares estimation of the position (see for instance Kaplan (2006)). The covariance matrix found using that procedure is G = (H T H)−1 , where H is a matrix function only of the relative position of the satellites with respect to the receiver, as follows: cos El1 cos Az1 cos El1 sin Az1 sin El1 1 cos El2 cos Az2 cos El2 sin Az2 sin El2 1 H= , (1) .. .. .. .. . . . .
For the educational tool, the nominal or real constellations can be used. Real constellations data was obtained from the IGS service (see NASA (2015)), which is an online service that contains ephemeris for GNSS satellites since GPS started its operation in time intervals of 15 minutes. Using Lagrange interpolation, the data can be used to obtain the position of satellites with high precision at any given time (see Hofmann-Wellenhof et al. (2008)). 4. A GUI FOR ANALYSIS OF GNSS COVERAGE AND PRECISION
cos Eln cos Azn cos Eln sin Azn sin Eln 1 where the subindex makes reference to the i-th satellite visible in the sky, with given elevation El and azimut Az. Four or more satellites must be visible with linearly independent position or G becomes singular.
In this section, we will provide examples for the (real) GPS constellation, for a particular day (12/12/2012). However, the tool can analyze any other GNSS constellation or a combination of them. In Fig. 1 we provide a general view (in Spanish) of the visual tool to analyze a single point (station) on the Earth. Note the interface allows to set the coordinates of a point in Earth. The tool shows the groundtracks of the GPS satellites, as well as a 3D representation in ECI coordinates. This 3D visualization can be opened independently (see Fig. 2) and animated.
Once G is computed, a general measure of error due to the relative geometry of the visible satellites is the position dilution of precision, PDOP, which is defined as PDOP = √ G11 + G22 + G33 . This factor multiplies the error of the GNSS signals (coming from other sources such as orbit propagation errors, atomic clock errors, atmospheric effects, etc...). Thus, a small PDOP is desirable to obtain a higher level of accuracy.
The 3D representation can also show what satellites are seen by an Earth station; geometrically, this is represented by all satellites inside a cone whose angle with the station’s horizon is the elevation mask angle, as seen in Figure 3. Using the different buttons of the tool, we can perform several analysis. For instance, we can analyze the number of satellites viewed from Seville at all times during the day of analysis, as shown in Fig. 4.
3.2 Availability, Continuity and Integrity Besides accuracy, there are other important GNSS performance indicators. These are (1) Availability: Availability of GNSS is the probability that the positioning service works “sufficiently well”, which is usually defined as the PDOP taking a sufficiently small value. Availability is computed as the percentage of the time during which the service is
If one is interested in visualizing the windows of visibility for each satellite from Seville, this is also shown in a diagram, see Fig. 5. Finally, the PDOP from Seville at each time of the day is also shown in Fig. 6. 95
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satélite
da paso a los diferentes tipos de análisis que puede realizar la herramienta. En caso de querer Name Space segments Precision [m.] State En caso de querer Esta con ventana dala paso aCountry los diferentes tipos deseanálisis que puede realizar na fecha nueva, basta pulsar opción “Volver”. En este caso abre la ventana de inicio y ella herramienta. GPS USA 24+ MEO sats 5 Operational nueva, basta con pulsar la opción “Volver”. En este caso se abre la ventana de inicio y el seleccionar una seleccionar nueva fecha una parafecha el estudio. GLONASS Russia 24+ MEO sats usuario puede seleccionar una nueva fecha para el estudio. Galileo EU 24+ MEO sats Beidou
sis de estación en tierraIRNSS
China India
27 MEO, 5 GEO, 3 IGSO 3 GEO, 4 IGSO
5-10 1 10 10-20
Operational Under development Under development Operational in 2016, local only
1. GNSS in operation and under development. 8.3 Análisis de Table estación en constellation tierra
Figura 8.5. Ventana de análisis de una estación en tierra.
de una estación en tierra. 82 Fig. 1. General view of the tool.Figura 8.5. Ventana de análisis ar contamos con una visualización 3D de las órbitas:
Interfaz de la herramienta
En primer lugar contamos con una visualización 3D de las órbitas:
Figura 8.6. Visualización 3D de las órbitas. Fig. 2. 3D visualization of GPS orbits.
Figura 8.29. Animación 3D de la visibilidad de los satélites.
Fig. 3. 3D por visibility Seville. El cono de visibilidad supuesto ha defrom estar siempre situado con su vértice en la localización de la estación, por lo que se mueve solidario a la rotación de la Tierra. Además, como se aprecia en la Figura 8.29, los satélites aparecen numerados para permitir su identificación.
último, hay una etiqueta en lacan que se study muestra la all hora correspondiente durantefor la animación, del mismo 69 modifying the conditions, Por These analysis can be repeated In addition, one these values a moving modo que sucede con la animación de la traza. for instance changing the elevation mask or de- Estaobserver. In particular, we have included the possibility of Figuraangle, 8.6. Visualización 3D de las representación puedeórbitas. rotarse, ampliarse o reducirse como el usuario desee para facilitar una visualización activating some satellites, to see how the constellation lo más studying flights, which are simplified to either orthodromic cómoda posible. performs in degraded conditions. or loxodromic arcs over the surface of the Earth moving
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Fernando Lanagran-Soler / IFAC-PapersOnLine 48-29 (2015) 093–098 Interfaz deetla al. herramienta
El botón “Número de satélites visibles” proporciona una gráfica en la que se puede ver el número total de Herramenta para el satélites visibles desde la estación para cada época:
Figura 8.15. Número de satélites visibles desde Sevilla el día 12/12/2012 con 32 satélites.
HerramentaAsí para el 4. cálculo de precisión y coberturas un sistemaentendida de navegación satélite Fig. viewed Seville. mismo, se Satellites proporciona información acercafrom de ladedisponibilidad como el por número mínimo de satélites necesarios para proporcionar información sobre la posición del observador. Como se explicó en el capítulo 5, dicho número mínimo de forma que podamos las de ecuaciones (5.11). Finalmente, la opción “Visibilidad de es los4,satélites” muestra elresolver historial visibilidad de cada satélite.
Por lo tanto la herramienta calcula el tiempo que hay 4 o más satélites visibles. En el caso de la gráfica anterior, sería el 100% del tiempo.
97
cálculo de precisión y coberturas de un sistema de navegación por satélite
77 Herramenta para el cálculo de precisión y coberturas de un sistema de navegación por satélite
89
En esta ocasión no disponemos de un mapa con las trazas, ya que este puede consultarse fácilmente en los dos módulos anteriores, además, si se quiere saber con exactitud que satélites son más o menos tiempo visibles en la región, más adelante veremos que existe la opción de ver el historial de visibilidad de cada uno de ellos, como en los análisis en tierra y vuelo. En este modulo el mapa se muestra para permitir al usuario visualizar la región seleccionada.
Figura 8.33. Visualización del vuelo. En la figura, entre Sevilla y Hamburgo.
Fig. 7. Analyzing a flight from Seville to Hamburg.
Figura 8.16. Muestra de la disponibilidad en pantalla.
Esta imagen nos permite observar sobre qué puntos pasa cada satélite, así como la posición exacta de de ellos a la hora que desee el usuario. Lo mismo sucede con la trayectoria de la aeronave. Para esto e barra deslizante que permite al usuario modificar la hora, de modo que se puedan visualizar las posi todos los elementos de forma estática en la época que se desee. Esta barra se encuentra a la dere imagen de las trazas (Figura 8.31). Los puntos de origen y destino son modificables, así como la velocidad de vuelo.
Figura 8.41. Mapa con la región de Europa seleccionada.
Fig. 8. Regional analysis showing the discretization grid. 93 Herramenta para el cálculo de precisión y coberturas de un sistema de navegación por satélite Los límites de la región son seleccionables, así como el nivel de discretización del mismo. Como venimos
74
comentando en los anteriores la proyección para el mapa deforma la imagen. Esto significa To visualize, for capítulos, instance, theutilizada variations of PDOP over the que puntos con mayores latitudes aparecen ampliados en cuanto a longitud se refiere. Por lo tanto dichas zonas La opción muestra el en mapa la evolución del PDOP en laas región. verde muestran los se puntos regions a map ofenfina colors can be used, inEnyaFig. 9. This map tienen una “Animar” discretización más cuanto a puntos sobre la superficie real, que lasediscretización está con mejor PDOP y ende rojo aquellos con peores Dicha información se hace en relación los valores en valores y longitud, quevalores. sí guardan una escala lineal y uniforme en laa proyección isrealizando dynamic andlatitud changes evolves. mínimo yequidistante. máximo calculados. De modo que laas zonastime rojas tienen valores en torno al mayor PDOP que se haya cilíndrica
Figura 8.21. Visibilidad para cada satélite en el caso de las Figuras 8.17-19.
Fig. 5. Visibility of each satellite from Seville.
Herramenta para el cálculo de precisión y coberturas de un sistema de navegación por satélite
75
opción PDOP muestra la evolución estelaa lo largo del tiempo. gráficaLanos permite ver qué satélitesdede constelación son
y las zonas verdes Esta visibles y en qué momentos, lo cualproducido, nos muestra el paso del tiempo. permite por ejemplo conocer qué satélites son más importantes para una u otra posición en la superficie según sean más o menos tiempo visibles.
los menores valores. En la esquina superior derecha hay una etiqueta que
Un recurso importante para analizar estas gráficas es la herramienta “Data cursor” de MATLAB.
Figura 8.34. Modificaciones de los parámetros del vuelo. El tipo de ruta (Capítulo 6) es seleccionable con una lista desplegable: ortodrómica o loxodrómica.
Por último, del mismo modo que se explicó en el apartado anterior, se puede seleccionar la con nominal y la constelación real. Figura 8.22. Herramienta “Data Cursor”.
Un panel similar al de las Figuras 8.12-13 aparece en esta ventana, que nos permite desactivar o a satélites disponibles para personalizar el análisis. 89 Figura 8.47. Animación del PDOP para Europa.
Esta herramienta nos permite seleccionar un punto de la gráfica y ver su información de forma precisa. Figura 8.17. Ejemplo de evolución de PDOP en el tiempo.
Fig. 6. PDOP from Seville.
Fig. 9. Regional analysis showing PDOP variation with a Por último una observación color code. respecto a los datos de salida. La herramienta muestra gráficas y datos de los valores de PDOP, que dan una idea general de la precisión en la posición.
Así mismo realiza un cálculo de la disponibilidad en base al valor del PDOP máximo impuesto por el usuario Sin embargo es sencillo obtener otros datos como el HDOP o el VDOP. Tan solo debemos sustituir en el 8.12-13). Por ejemplo,(Figura en una gráfica de PDOP, nos permite observar el valor en una época. Esto nos puede servir tanto proceso seguido la ecuación (7.2) por: para simplemente observar la la información como para obtener 3máximos o mínimos y conocer qué momento Por ejemplo, tomando constelación nominal y desactivando satélites, con un ángulo de máscara deen7.5º, (8.1) HDOP (t j ) 85 G11 (t j ) G22 (t j ) se producen.obtenemos la siguiente evolución del PDOP:
Finally, it is possible to do global availability analysis. For instance, Fig. 10 shows gaps in availability for the nominal VDOP(t ) G (t ) constellation when the elevation mask angle is set to 5 (8.2) and Sin embargo no se ha implementado por simplicidad de la herramienta de cara al usuario, del mismo modo 3 que satellites are deactivated. The darker region correspond no se implementó la opción de ángulo de máscara variable, aunque se explica cómo en el apartado 7.1.1. to the largest gaps in availability, up to 45 minutes.
at constant speed. In Fig 7 we show a flight from Seville to Hamburg using an orthodromic route.
j
Our tool can also be used to analyze whole regions, whose discretization level can be defined in the tool. A finer discretization grid provides 77 more detailed analysis, but a the cost of increased computation times. An example grid is shown in Fig. 8.
33
j
It must be noted that the tool uses the free M Map package for representations on the surface of the Earth (available at Pawlowicz (2014)). 97
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Average Typical Deviation 92
User-friendliness of the application 4.62 0.61
Clarity of bulletin 4.28 0.82
Interest for learning 4.40 0.65
Table 2. Survey results (values between 0 and 5). Interfaz de la herramienta
year. In addition, more realistic models will be introduced, such as an Earth ellipsoidal shape or orbital perturbations. Space augmentation systems will also be included in the studies. In addition, real data from new constellations such as Beidou or Galileo will be included as soon as these systems become operative. An extension of this work could combine simulated inputs from an inertial measurement unit and a Kalman filter to test the performance of GPS-aided inertial navigation under nominal or degraded conditions. ACKNOWLEDGMENTS Figura 8.45. Análisis global de disponibilidad de la constelación GPS nominal realizado con la herramienta, con un ángulo de máscara de 5 grados y 3 satélites retirados del servicio. Las zonas más oscuras corresponden a un intervalo de 45 minutos sin disponibilidad.
Fig. 10. Gaps in availability, global analysis.
The authors gratefully acknowledge spanish government grant number DPI2012-37580-C02-02 for partially funding the work.
5. COMPUTER LAB EXPERIENCE
Si pulsamos la opción “Disponibilidad Región” la herramienta muestra una gráfica como la siguiente:
Finally, we report on a hands-on experience with the tool. A preliminary version was tried in a computer lab for a course in Aerial Navigation, with about 45 students, in three sessions of 2 hours of duration. Students were handed a bulletin with basic instructions and the teacher helped them with any problems they had. Since it was a preliminary version, students reported some bugs. They were mostly satisfied with the tool, as a survey that was given after the lab shows (see Table 2).
REFERENCES Borre, K. (2003). The Easy Suite—Matlab code for the GPS newcomer. GPS Solutions, 7(1), 47–51. Borre, K. (2009). GPS Easy Suite II: A Matlab companion. Inside GNSS, May/June, 48–51. Curtis, H.D. (2009). Orbital Mechanics for Engineering Students. Butterworth-Heinemann, 2nd edition. Gorski, A. and Gerten, G. (2007). GNSS performance possibilities. AnalyticalGraphics Inc. (AGI) White Paper. GPS World (2015). The Almanac. http://gpsworld. com/the-almanac/. [Online; accessed 1-May-2015]. Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2008). GNSS — Global Navigation Satellite Systems. Springer-Verlag Wien. Jan, S.S., Wyant, C., and Walter, T. (2009). Matlab algorithm availability simulation tool. GPS Solutions, 13(4), 327–332. Kaplan, E.D. (2006). Understanding GPS: principles and applications; 2nd ed. Artech House, Boston, MA. Li, J., Jarvis, C.H., and Brunsdon, C. (2010). The use of immersive real-time 3D computer graphics for visualisation of dilution of precision in virtual environments. International Journal of Geographical Information Science, 24(4), 591–605. NASA (2015). International GNSS Service (IGS), Product Availability. https://igscb.jpl.nasa.gov/ components/prods\_cb.html. [Online; accessed 2June-2015]. Pawlowicz, R. (2014). M Map: A mapping package for Matlab. http://www.eos.ubc.ca/~rich/map.html. [Online; accessed 1-May-2015]. Vallado, D. and McClain, W. (2007). Fundamentals of Astrodynamics and Applications. Microcosm Press/Springer, 3rd edition. Wie, B. (1998). Space vehicle dynamics and control. AIAA.
Beside bugs, some additional feedback reported by students were, for instance: • Lack of a clock that indicates the hour in the animation. • 8.46. Absence ofdean option to del pause the animation and desee Figura Disponibilidad la región como función PDOP impuesto, con un ángulo de máscara 5º. the constellation’s atservicio a given time, orde the Esta gráfica, a modo de ejemplo, nos muestrageometry la disponibilidad del para diferentes valores PDOP imponiendo ángulo de máscara 5º. Si necesitamos valorestime de PDOP muy pequeños la disponibilidad es possibility ofdemanipulating during animation. pequeña, pero a partir de valores del orden de 2, la disponibilidad ronda el 90%. • Need of a zoom to see better the limits of a region. It’s 92 not possible to know what satellites fly over a region at a given time. These comments were used to produce an improved version, which will be tried again in the same lab next year. 6. CONCLUDING REMARKS We have presented a visual tool to supplement theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies of current constellations. The tool was created using Matlab’s Graphical User Interface Design Environment (GUIDE), and it is particularly intended for courses in aerospace engineering with GNSS content. The tool allows to study visibility and availability for an station (fixed point on Earth), a flight between any two points on Earth, or for an user-defined region. A preliminary version of the tool was tried in a computer lab for a course in Aerial Navigation. Students reported some bugs but were mostly satisfied with the tool, as a survey shows Using the students’ feedback, a better version is being developed, which will be tried again in a computer lab next 98
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Matlab Educational GUI for Analysis Matlab Educational GUI for Analysis Matlab Educational GUI for Analysis Matlab Educational GUI for Analysis GNSS Coverage and Precision GNSS Coverage and Precision GNSS Coverage and Precision GNSS Coverage and Precision∗ ∗
of of of of
Fernando Fernando Fernando Fernando
Lanagran-Soler Vazquez Lanagran-Soler ∗∗ Rafael Rafael Vazquez ∗∗ ∗∗ Lanagran-Soler Vazquez ∗ Rafael Manuel R. Arahal ∗∗ Lanagran-Soler Rafael Manuel R. Arahal ∗∗ Vazquez ∗ Manuel R. Arahal ∗∗ Manuel R. Arahal ∗ ∗ Departamento de Ingenier´ Departamento de Ingenier´ıa ıa Aeroespacial Aeroespacial ∗ ∗∗ de Ingenier´ ıa Aeroespacial ∗ Departamento de Ingenier´ ıa de Sistemas yy Autom´ a ∗∗ Departamento Departamento de Ingenier´ ıa Aeroespacial Departamento de Ingenier´ ıa de Sistemas Autom´ atica tica ∗∗ de Ingenier´ ıa de Sistemas y Autom´ a ∗∗ Departamento Universidad de Seville, Camino de los Descubrimientos s/n, 41092, Departamento Ingenier´ de Descubrimientos Sistemas y Autom´ atica tica Universidad de Seville,deCamino deıalos s/n, 41092, Universidad de Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain ([email protected],[email protected], Universidad de Seville, Camino de los Descubrimientos s/n, 41092, Seville, Spain ([email protected],[email protected], Seville, Spain ([email protected],[email protected], [email protected]) Seville, Spain ([email protected],[email protected], [email protected]) [email protected]) [email protected]) Abstract: This work reports on a Abstract: This work reports on a visual visual tool tool that that has has been been developed developed to to supplement supplement Abstract: This work reports on a visual tool that has been developed to theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies Abstract: This work reports on a visual tool Systems that has(GNSS) been developed to supplement supplement theoretical lessons on Global Navigation Satellite with real-world studies of of theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies of current constellations. The tool was created using Matlab’s Graphical User Interface theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies of current constellations. The tool was created using Matlab’s Graphical User Interface Design Design current constellations. The tool was using Graphical User Design Environment (GUIDE), and it for in engineering with current constellations. was created created intended using Matlab’s Matlab’s Graphical User Interface Interface Design Environment (GUIDE),The and tool it is is particularly particularly intended for courses courses in aerospace aerospace engineering with Environment (GUIDE), and it is particularly intended for courses in aerospace engineering with GNSS content. As such, it highlights the space segment of these navigation systems and concepts Environment and it is particularly courses in aerospace engineering with GNSS content.(GUIDE), As such, it highlights the spaceintended segment for of these navigation systems and concepts GNSS content. As such, the segment of these systems and concepts such visibility, and this tool, can visualize the GNSS Asgroundtracks such, it it highlights highlights the space spaceUsing segment these navigation navigation systems concepts such as ascontent. visibility, groundtracks and coverage. coverage. Using thisofgraphic graphic tool, students students can and visualize the such as visibility, groundtracks and coverage. Using this graphic tool, students can visualize the real position of all satellites in the GPS constellation at any time since its start of operation, such as visibility, groundtracks and coverage. Using this graphic tool, students can visualize the real position of all satellites in the GPS constellation at any time since its start of operation, real position of in GPS constellation at any time since its start operation, analyze the of that can be or study real position of all all satellites satellites in the the GPS any any timepoint sincein start of of analyze the number number of satellites satellites that canconstellation be visualized visualizedatfrom from any point initsEarth, Earth, or operation, study the the analyze the number of satellites that can be visualized from any point in Earth, or study the quality of the navigational solution which depends on the relative geometry of the user and analyze the of satellites that can depends be visualized any geometry point in Earth, study quality of thenumber navigational solution which on thefrom relative of the or user and the quality of the solution which on relative geometry of the user and satellites. tool to these aa flight between on quality of The the navigational navigational solution which depends depends on the thefor thetwo userpoints and the the satellites. The tool also also allows allows to perform perform these studies studies forrelative flightgeometry between ofany any two points on satellites. The tool also allows to perform these studies for aa flight between any two points on Earth, or for an user-defined region. A preliminary version of the tool was tried in a computer satellites. The tool also allows to perform these studies for flight between any two points on Earth, or for an user-defined region. A preliminary version of the tool was tried in a computer Earth, or for region. preliminary version of tool was tried in lab a in reported bugs satisfied Earth, for an an user-defined user-defined region. A A Students preliminary versionsome of the the toolbut waswere triedmostly in aa computer computer lab for for or a course course in Aerial Aerial Navigation. Navigation. Students reported some bugs but were mostly satisfied lab for a course in Aerial Navigation. Students reported some bugs but were mostly satisfied with the tool, as a survey shows. lab course Aerial shows. Navigation. Students reported some bugs but were mostly satisfied withfor thea tool, as in a survey with the tool, as shows. with theIFAC tool,(International as a a survey survey Federation shows. of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. © 2015, Keywords: Keywords: Educational Educational tool, tool, GNSS, GNSS, Aerial Aerial Navigation, Navigation, Matlab Matlab GUI, GUI, Navigation Navigation Accuracy Accuracy Keywords: Educational tool, GNSS, Aerial Navigation, Matlab GUI, Navigation Keywords: Educational tool, GNSS, Aerial Navigation, Matlab GUI, Navigation Accuracy Accuracy 1. satellites 1. INTRODUCTION INTRODUCTION satellites that that can can be be visualized visualized from from any any point point in in Earth, Earth, 1. INTRODUCTION satellites that can be visualized from any point in or study the quality of the navigational solution which 1. INTRODUCTION satellites can be visualized from any point in Earth, Earth, or study that the quality of the navigational solution which Global Navigation Satellite Systems (GNSS) have become or study the quality of the navigational solution which depends on the relative geometry of the user and the Global Navigation Satellite Systems (GNSS) have become or study on thethe quality of the navigational solution which depends relative geometry of the user and the Global Navigation Satellite Systems (GNSS) have become ubiquitous in everyday life. There is growing number of apdepends on the relative geometry of the user and the satellites. The tool also allows to perform these studies Global Navigation Satellite Systems (GNSS) have become ubiquitous in everyday life. There is growing number of ap- depends on thetool relative geometry of the user and the satellites. The also allows to perform these studies ubiquitous in life. There growing number of plications on precise positioning. The tool allows to these studies for between any two on or for ubiquitous in everyday everyday life. systems There is is for growing number of apap- satellites. plications relying relying on these these systems for precise positioning. satellites. tool also also to perform perform these for aa flight flightThe between any allows two points points on Earth, Earth, or studies for an an plications relying on these systems for precise positioning. As new constellations such as the Chinese Beidou or Eurofor a flight between any two points on Earth, or for an user-defined region. plications relying on these for precise positioning. As new constellations such systems as the Chinese Beidou or Euro- for a flight between user-defined region. any two points on Earth, or for an As new constellations such as the Chinese Beidou or European Galileo become joining the currently region. As new constellations such as the Chinese or active Euro- user-defined pean Galileo become available, available, joining the Beidou currently active user-defined region. There pean Galileo become available, joining the currently active American GPS or Russian Glonass, applications There are are commercial commercial tools, tools, such such as as AGI’s AGI’s Systems Systems pean Galileo become thenew currently active There American GPS or the theavailable, Russian joining Glonass, new applications are commercial tools, such as AGI’s Systems ToolKit (STK), which allows to perform these studies (see American GPS or the Russian Glonass, new applications There are commercial tools, such as AGI’s Systems are expected to appear. In particular, GNSS use is rising ToolKit (STK), which allows to perform these studies (see American GPS the Russian Glonass,GNSS new applications are expected to or appear. In particular, use is rising ToolKit (STK), which allows to perform these studies (see for instance one of AGI’s white papers by Gorski and are expected to appear. In particular, GNSS use is rising ToolKit (STK), which allows to perform these studies (see in aerial navigation, particularly in non-critical systems, for instance one of AGI’s white papers by Gorski and are expected to appear. In particular, GNSS use systems, is rising for in aerial navigation, particularly in non-critical instance one of AGI’s white papers by Gorski and Gerten (2007)). However, their price is usually prohibitive, in aerial navigation, particularly in non-critical systems, for instance one of AGI’s white papers by Gorski and such as Unmanned Aerial Vehicles (UAVs) or Remotely Gerten (2007)). However, their price is usually prohibitive, in aerial navigation, particularly in non-critical systems, such as Unmanned Aerial Vehicles (UAVs) or Remotely Gerten (2007)). However, their price usually prohibitive, whereas Matlab’s licenses usually available most such as Unmanned Aerial Vehicles (UAVs) or Remotely However, their price is is usually in prohibitive, Piloted Systems (RPAS). While its still whereas(2007)). Matlab’s licenses are are usually available in most uniunisuch as Aerial Unmanned Aerial Vehicles (UAVs) or is Piloted Aerial Systems (RPAS). While its use use isRemotely still not not Gerten whereas Matlab’s licenses are usually available in most universities and there is even a cheap student version that can Piloted Aerial Systems (RPAS). While its use is still not whereas Matlab’s licenses are usually available in most uniwidespread in manned aircraft (due to lack of integrity of versities and there is even a cheap student version that can Piloted Aerial Systems aircraft (RPAS).(due While its use is still not widespread in manned to lack of integrity of versities and there is even a cheap student version that can run the tool. While there are some previously developed widespread in manned aircraft (due to lack of integrity of versities and there is even a cheap student version that can basic systems) the introduction of augmentation systems run the tool. While there are some previously developed widespread in manned aircraft (due to lack of integrity of run basic systems) the introduction of augmentation systems the While are developed GPS-specific for the by basic systems) the introduction of augmentation systems the tool. tool. software While there there are some some previously previously is the regular in flights GPS-specific software for Matlab—see Matlab—see the papers papersdeveloped by Borre Borre basic systems) the to introduction augmentation is opening opening the way way to regular use use of GNSS GNSS in regular regularsystems flights run GPS-specific software for Matlab—see the papers by Borre (2003, 2009) or Jan et al. (2009)—they don’t provide is opening the way to regular use of GNSS in regular flights GPS-specific software for Matlab—see the papers by Borre within a few years. (2003, 2009) or Jan et al. (2009)—they don’t provide is opening theyears. way to regular use of GNSS in regular flights (2003, within a few 2009) or et al. (2009)—they don’t provide graphical interfaces easy This within a years. (2003, 2009) or Jan Janand et are al. not (2009)—they provide graphical interfaces and are not easy to to use. use.don’t This justifies justifies within a few fewthe years. Therefore, subject of GNSS if of great interest to graphical interfaces and are not easy to use. This justifies the use of Matlab GUIDE as a convenient development Therefore, the subject of GNSS if of great interest to graphical interfaces and are as notaeasy to use. This justifies the use of Matlab GUIDE convenient development Therefore, the of GNSS if of great interest to aerospace and such staple subject of use GUIDE as development environment that allow to benefit Therefore, the subject subject aerospace engineers engineers andofas as GNSS such it itifis isofa a great staple interest subject to of the the use of of Matlab Matlab GUIDE as aa convenient convenient environment that will will allow students students to easily easily development benefit from from aerospace engineers and as such it is a staple subject of most aerospace engineering curricula. Since GNSS perforenvironment that will allow students to easily the tool. aerospace engineers and as curricula. such it is Since a staple subject of environment most aerospace engineering GNSS perforthat will allow students to easily benefit benefit from from the tool. most aerospace engineering curricula. Since GNSS performance has dependence on relative geometry tool. most engineering curricula. Since GNSS perfor- the manceaerospace has a a strong strong dependence on the the relative geometry the tool. A preliminary version mance has a strong dependence on the relative geometry of the receiver with respect to the satellites, students can A preliminary version of of the the tool tool was was tried tried in in aa computer computer mance has a strong dependence on the relative geometry of the receiver with respect to the satellites, students can A preliminary version of the tool was tried in aa computer lab for aa course in Aerial Navigation. Students reported of the receiver with respect to the satellites, students can A preliminary version of the tool was tried in computer certainly benefit from virtual simulations, as argued in the lab for course in Aerial Navigation. Students reported of the receiver the satellites, students certainly benefitwith fromrespect virtualtosimulations, as argued in can the lab for a course in Aerial Navigation. Students reported some bugs but were mostly satisfied with the tool, as certainly benefit from virtual simulations, as argued in the lab for a course in Aerial Navigation. Students reported work by Li et al. (2010). In this paper, we report on a visual some bugs but were mostly satisfied with the tool, as a a certainly from virtual as argued in the some work by Libenefit et al. (2010). In thissimulations, paper, we report on a visual bugs but were mostly satisfied with the tool, as a survey shows. While the tool was developed for this particwork by Li et al. (2010). In this paper, we report on a visual some bugs but were mostly satisfied with the tool, as a tool that has been developed to supplement theoretical survey shows. While the tool was developed for this particwork by Lihas et al.been (2010). In this paper, we report theoretical on a visual survey tool that developed to supplement shows. While the tool developed for this ular it can applied to other not tool that has been developed to theoretical shows. tool was was developed forsubjects this particparticlessons on GNSS with real-world studies conular course, course, it While can be bethe applied to several several other subjects not tool that been developed to supplement supplement theoretical lessons on has GNSS with real-world studies of of current current con- survey ular course, it can be applied to several other subjects not necessarily taught in aerospace engineering. For instance, lessons on GNSS with real-world studies of current conular course, it can be applied to several other subjects not stellations. The tool was created using Matlab’s Graphical necessarily taught in aerospace engineering. For instance, lessons on GNSS with studies of current con- necessarily stellations. The tool wasreal-world created using Matlab’s Graphical taught in engineering. For instance, aa course autonomous vehicles (aerial land-based) stellations. The tool created Matlab’s Graphical in aerospace aerospace engineering. instance, User Environment (GUIDE). this course on ontaught autonomous vehicles (aerial or orFor land-based) stellations. TheDesign tool was was created using using Matlab’s Using Graphical User Interface Interface Design Environment (GUIDE). Using this necessarily a course on autonomous vehicles (aerial or land-based) would certainly benefit from the tool since these vehicles User Interface Design Environment (GUIDE). Using this a course on autonomous vehicles (aerial or land-based) graphic tool, aerospace engineering students can visualize would certainly benefit from the tool since these vehicles User Interface Design Environment (GUIDE). this would graphic tool, aerospace engineering students canUsing visualize certainly benefit from the tool since these vehicles typically have a critical depence on GNSS performance to graphic tool, aerospace engineering students can visualize would certainly benefit from the tool since these vehicles the real position of all satellites in the GPS constellation at typically have a critical depence on GNSS performance to graphic tool, aerospace engineering students can visualize the real position of all satellites in the GPS constellation at typically have a critical depence on GNSS performance to carry out their mission. A class on integrated navigation the real position of all in GPS at critical depence performance to any time since of the of carry outhave theira mission. A class on on GNSS integrated navigation the all satellites satellites in the theanalyze GPS constellation constellation any real timeposition since its itsofstart start of operation, operation, analyze the number number at of typically carry out their mission. A class on integrated navigation any any time time since since its its start start of of operation, operation, analyze analyze the the number number of of carry out their mission. A class on integrated navigation Copyright © 2015, 2015 IFAC 93 Hosting by Elsevier Ltd. All rights reserved. 2405-8963 © IFAC (International Federation of Automatic Control) Copyright © 2015 IFAC 93 Copyright ©under 2015 responsibility IFAC 93 Control. Peer review of International Federation of Automatic Copyright © 2015 IFAC 93 10.1016/j.ifacol.2015.11.219
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2.2 Orbital elements
systems and/or Kalman filtering could use the tool as part of a lab on GPS-aided inertial navigation systems design, to simulate the system under nominal or GPS-degraded conditions.
Orbital elements are a minimal set of parameters that describe an orbit. Typically, Kepler’s classical elements are used. These are:
The structure of this paper is as follows. In Section 2 we briefly review some orbital mechanics material that will be needed in the sequel. In Section 3 we define the GNSS concepts that are analyzed by our program. We follow with Section 4 where we describe the tool itself. Next, in Section 5, we describe a hands-on experience with students using a preliminary version of the tool. We finish with some concluding remarks in Section 6.
(1) Semi-major axis a: it describes the size of the orbit. It is directly related to the orbit’s energy. (2) Eccentricity e: it describes the shape of the orbit. Navigation satellites are usually almost circular, so their eccentricity is very close to zero. (3) Inclination i: it measures the angle between the orbit’s plane and the Equator. Inclinations between 0 and 90 degrees describe prograde orbits, whereas inclinations between 90 and 180 degrees describe retrograde orbits, however the latter are seldom used for navigation satellites. (4) Right ascension of the ascending node (RAAN, denoted as Ω): it measures the angle between the vernal point and the orbit’s ascending node (where the orbit intersects the Equator going towards North). (5) Argument of perigee ω: it measures the angle between the orbit’s ascending node and the orbit’s perigee (point of closest approach to Earth’s center of mass). (6) True anomaly θ: it describes the position of the satellite in its orbit, with respect to perigee.
2. BASIC CONCEPTS FROM ORBITAL MECHANICS Next we briefly review some basic concepts from Orbital Mechanics.
2.1 Reference systems This work requires three basic coordinate frames. We will define these loosely, since a precise definition requires more advanced concepts than required for a preliminary analysis.
If an orbit is exactly circular (e = 0), then the two last orbital elements are not well defined, as there is no perigee. Then a new orbital element, called the argument of latitude u, is used. The argument of latitude is defined as the angle between the ascending node and the satellite’s position in its orbit.
(1) Earth-centered inertial frame (ECI). Its origin is on Earth’s center of mass, the x-y plane is Earth’s equatorial plane, with the x axis points towards the vernal point (a fixed direction relative to the stars), and the z axis is aligned with Earth’s spin axis. (2) Earth-centered, Earth-fixed frame (ECEF). Its origin is on Earth’s center of mass, the x-y plane is Earth’s equatorial plane and the z axis is aligned with Earth’s spin axis, but now it rotates with the Earth so that the x axis points towards the Prime (Greenwich) meridian. Position is usually expressed in geodetical coordinates: latitud φ, longitude λ, and altitude h. These might be defined with respect to a reference ellipsoid (usually WGS’84), but for simplicity we will consider an spherical Earth. The angle formed between ECI and ECEF is called Greenwich Sidereal Time (GST) and it is a function of the actual date and hour. (3) Topocentric local frame. This is centered on an observer usually on the surface of the Earth. The xy plane is tangent to Earth’s surface, with the x axis pointing to North, y axis to East and z axis towards the center of the Earth (down direction). The position of an object in the observer’s field of view is usually described by using angular coordinates: Elevation (El), which is the angle above the x-y plane, Azimuth (Az), which is the angle formed between the projection of the object in the x-y plane and the North direction, measured counter-clockwise, and the distance to the object ρ.
2.3 Orbit propagation and ephemeris computation Orbit propagation is the process of determining the orbital elements of a satellite in a future time t, starting from their values at the present time t0 . If there are no orbital perturbations, then the two-body problem solution (see Curtis (2009)) can be applied and only the true anomaly (or the argument of latitude for circular orbits) changes with time. Otherwise some kind of perturbation model is required to determine the orbital element’s change with time. Once the orbital elements at some time are known, the ephemeris of the satellite, i.e., its position in the ECI frame, can be easily computed. Using the transformation between frames, one can calculate the position of a satellite in the ECEF frame (with respect to Earth) and in the topocentric frame (with respect to an observer). All these are useful for our tool, since 3D visualization of orbits is easier in the ECI frame, whereas 2D visualization on a map of the Earth is more convenient on the ECEF frame (where one can see the satellite’s groundtrack, which are the points of the Earth over which the satellite is passing). Finally, the topocentric frame is useful to determine if a satellite is visible or not; visibility depends on the elevation angle to be above some given value (called elevation mask ) depending on the surroundings.
The coordinate transformations between these reference systems (and more precise definitions) can be found in any basic orbital mechanics textbook such as Curtis (2009); Vallado and McClain (2007); Wie (1998). 94
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available over the lifetime of the system, taking into account all the outages whatever their origins. (2) Integrity: Integrity relates to the trust which can be placed in the correctness of the information supplied by the Navigation System, it includes the ability of the system to provide timely warnings to the user when the system or data provided by the system should not be used for navigation. (3) Continuity: Continuity of GNSS is defined as the probability that the positioning service works “sufficiently well” (which as before is usually defined as the PDOP taking a sufficiently small value) throughout a flight operation.
Basic navigation using Global Navigation Satellite Systems (GNSS) is based on multilateration. A receiver acquires a navigation message from several satellites. From the message, the ephemeris of the satellites can be reconstructed using the transmitted orbital elements and a basic propagator, and the signal’s time of travel can be precisely calculated. Since this time and the distance to the satellites is related by the speed of travel of the signal (the speed of light), then in principle with at least three satellites it should be possible to compute the receiver’s position. However, since a receiver’s clock is unreliable (compared with the atomic clocks on board GNSS satellites), there is another unknown which is the offset of the receiver’s clock with respect to GNSS time. Thus, a minimum of four satellites is required to estimate the receiver’s position from satellite signals.
In our tool, we concentrate in studies of availability and continuity, by studying the PDOP evolution for a receiver in a fixed point of the Earth, on a flight, or for a region. 3.3 Nominal constellations and real constellations
However, the relative geometry of the visible satellites also influences the quality of the navigational solution. This effect is called “dilution of precision” and it is studied next.
Presently, there are a number of GNSS constellations giving service. These are summarized in Table 1 The nominal constellation is in most cases composed of medium-Earth orbit (MEO) satellites, but in some cases it includes geostationary (GEO) satellites and Inclined Geo-Synchronous Orbits (IGSO). More details can be found in GPS World (2015).
3.1 Dilution of precision If the satellites are close in the sky, it is intuitively clear that the estimated position will be less precise than if visible satellites are evenly distributed across the sky. This can be made more precise using the concept of dilution of precision, which is found when using a leastsquares estimation of the position (see for instance Kaplan (2006)). The covariance matrix found using that procedure is G = (H T H)−1 , where H is a matrix function only of the relative position of the satellites with respect to the receiver, as follows: cos El1 cos Az1 cos El1 sin Az1 sin El1 1 cos El2 cos Az2 cos El2 sin Az2 sin El2 1 H= , (1) .. .. .. .. . . . .
For the educational tool, the nominal or real constellations can be used. Real constellations data was obtained from the IGS service (see NASA (2015)), which is an online service that contains ephemeris for GNSS satellites since GPS started its operation in time intervals of 15 minutes. Using Lagrange interpolation, the data can be used to obtain the position of satellites with high precision at any given time (see Hofmann-Wellenhof et al. (2008)). 4. A GUI FOR ANALYSIS OF GNSS COVERAGE AND PRECISION
cos Eln cos Azn cos Eln sin Azn sin Eln 1 where the subindex makes reference to the i-th satellite visible in the sky, with given elevation El and azimut Az. Four or more satellites must be visible with linearly independent position or G becomes singular.
In this section, we will provide examples for the (real) GPS constellation, for a particular day (12/12/2012). However, the tool can analyze any other GNSS constellation or a combination of them. In Fig. 1 we provide a general view (in Spanish) of the visual tool to analyze a single point (station) on the Earth. Note the interface allows to set the coordinates of a point in Earth. The tool shows the groundtracks of the GPS satellites, as well as a 3D representation in ECI coordinates. This 3D visualization can be opened independently (see Fig. 2) and animated.
Once G is computed, a general measure of error due to the relative geometry of the visible satellites is the position dilution of precision, PDOP, which is defined as PDOP = √ G11 + G22 + G33 . This factor multiplies the error of the GNSS signals (coming from other sources such as orbit propagation errors, atomic clock errors, atmospheric effects, etc...). Thus, a small PDOP is desirable to obtain a higher level of accuracy.
The 3D representation can also show what satellites are seen by an Earth station; geometrically, this is represented by all satellites inside a cone whose angle with the station’s horizon is the elevation mask angle, as seen in Figure 3. Using the different buttons of the tool, we can perform several analysis. For instance, we can analyze the number of satellites viewed from Seville at all times during the day of analysis, as shown in Fig. 4.
3.2 Availability, Continuity and Integrity Besides accuracy, there are other important GNSS performance indicators. These are (1) Availability: Availability of GNSS is the probability that the positioning service works “sufficiently well”, which is usually defined as the PDOP taking a sufficiently small value. Availability is computed as the percentage of the time during which the service is
If one is interested in visualizing the windows of visibility for each satellite from Seville, this is also shown in a diagram, see Fig. 5. Finally, the PDOP from Seville at each time of the day is also shown in Fig. 6. 95
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satélite
da paso a los diferentes tipos de análisis que puede realizar la herramienta. En caso de querer Name Space segments Precision [m.] State En caso de querer Esta con ventana dala paso aCountry los diferentes tipos deseanálisis que puede realizar na fecha nueva, basta pulsar opción “Volver”. En este caso abre la ventana de inicio y ella herramienta. GPS USA 24+ MEO sats 5 Operational nueva, basta con pulsar la opción “Volver”. En este caso se abre la ventana de inicio y el seleccionar una seleccionar nueva fecha una parafecha el estudio. GLONASS Russia 24+ MEO sats usuario puede seleccionar una nueva fecha para el estudio. Galileo EU 24+ MEO sats Beidou
sis de estación en tierraIRNSS
China India
27 MEO, 5 GEO, 3 IGSO 3 GEO, 4 IGSO
5-10 1 10 10-20
Operational Under development Under development Operational in 2016, local only
1. GNSS in operation and under development. 8.3 Análisis de Table estación en constellation tierra
Figura 8.5. Ventana de análisis de una estación en tierra.
de una estación en tierra. 82 Fig. 1. General view of the tool.Figura 8.5. Ventana de análisis ar contamos con una visualización 3D de las órbitas:
Interfaz de la herramienta
En primer lugar contamos con una visualización 3D de las órbitas:
Figura 8.6. Visualización 3D de las órbitas. Fig. 2. 3D visualization of GPS orbits.
Figura 8.29. Animación 3D de la visibilidad de los satélites.
Fig. 3. 3D por visibility Seville. El cono de visibilidad supuesto ha defrom estar siempre situado con su vértice en la localización de la estación, por lo que se mueve solidario a la rotación de la Tierra. Además, como se aprecia en la Figura 8.29, los satélites aparecen numerados para permitir su identificación.
último, hay una etiqueta en lacan que se study muestra la all hora correspondiente durantefor la animación, del mismo 69 modifying the conditions, Por These analysis can be repeated In addition, one these values a moving modo que sucede con la animación de la traza. for instance changing the elevation mask or de- Estaobserver. In particular, we have included the possibility of Figuraangle, 8.6. Visualización 3D de las representación puedeórbitas. rotarse, ampliarse o reducirse como el usuario desee para facilitar una visualización activating some satellites, to see how the constellation lo más studying flights, which are simplified to either orthodromic cómoda posible. performs in degraded conditions. or loxodromic arcs over the surface of the Earth moving
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El botón “Número de satélites visibles” proporciona una gráfica en la que se puede ver el número total de Herramenta para el satélites visibles desde la estación para cada época:
Figura 8.15. Número de satélites visibles desde Sevilla el día 12/12/2012 con 32 satélites.
HerramentaAsí para el 4. cálculo de precisión y coberturas un sistemaentendida de navegación satélite Fig. viewed Seville. mismo, se Satellites proporciona información acercafrom de ladedisponibilidad como el por número mínimo de satélites necesarios para proporcionar información sobre la posición del observador. Como se explicó en el capítulo 5, dicho número mínimo de forma que podamos las de ecuaciones (5.11). Finalmente, la opción “Visibilidad de es los4,satélites” muestra elresolver historial visibilidad de cada satélite.
Por lo tanto la herramienta calcula el tiempo que hay 4 o más satélites visibles. En el caso de la gráfica anterior, sería el 100% del tiempo.
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En esta ocasión no disponemos de un mapa con las trazas, ya que este puede consultarse fácilmente en los dos módulos anteriores, además, si se quiere saber con exactitud que satélites son más o menos tiempo visibles en la región, más adelante veremos que existe la opción de ver el historial de visibilidad de cada uno de ellos, como en los análisis en tierra y vuelo. En este modulo el mapa se muestra para permitir al usuario visualizar la región seleccionada.
Figura 8.33. Visualización del vuelo. En la figura, entre Sevilla y Hamburgo.
Fig. 7. Analyzing a flight from Seville to Hamburg.
Figura 8.16. Muestra de la disponibilidad en pantalla.
Esta imagen nos permite observar sobre qué puntos pasa cada satélite, así como la posición exacta de de ellos a la hora que desee el usuario. Lo mismo sucede con la trayectoria de la aeronave. Para esto e barra deslizante que permite al usuario modificar la hora, de modo que se puedan visualizar las posi todos los elementos de forma estática en la época que se desee. Esta barra se encuentra a la dere imagen de las trazas (Figura 8.31). Los puntos de origen y destino son modificables, así como la velocidad de vuelo.
Figura 8.41. Mapa con la región de Europa seleccionada.
Fig. 8. Regional analysis showing the discretization grid. 93 Herramenta para el cálculo de precisión y coberturas de un sistema de navegación por satélite Los límites de la región son seleccionables, así como el nivel de discretización del mismo. Como venimos
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comentando en los anteriores la proyección para el mapa deforma la imagen. Esto significa To visualize, for capítulos, instance, theutilizada variations of PDOP over the que puntos con mayores latitudes aparecen ampliados en cuanto a longitud se refiere. Por lo tanto dichas zonas La opción muestra el en mapa la evolución del PDOP en laas región. verde muestran los se puntos regions a map ofenfina colors can be used, inEnyaFig. 9. This map tienen una “Animar” discretización más cuanto a puntos sobre la superficie real, que lasediscretización está con mejor PDOP y ende rojo aquellos con peores Dicha información se hace en relación los valores en valores y longitud, quevalores. sí guardan una escala lineal y uniforme en laa proyección isrealizando dynamic andlatitud changes evolves. mínimo yequidistante. máximo calculados. De modo que laas zonastime rojas tienen valores en torno al mayor PDOP que se haya cilíndrica
Figura 8.21. Visibilidad para cada satélite en el caso de las Figuras 8.17-19.
Fig. 5. Visibility of each satellite from Seville.
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opción PDOP muestra la evolución estelaa lo largo del tiempo. gráficaLanos permite ver qué satélitesdede constelación son
y las zonas verdes Esta visibles y en qué momentos, lo cualproducido, nos muestra el paso del tiempo. permite por ejemplo conocer qué satélites son más importantes para una u otra posición en la superficie según sean más o menos tiempo visibles.
los menores valores. En la esquina superior derecha hay una etiqueta que
Un recurso importante para analizar estas gráficas es la herramienta “Data cursor” de MATLAB.
Figura 8.34. Modificaciones de los parámetros del vuelo. El tipo de ruta (Capítulo 6) es seleccionable con una lista desplegable: ortodrómica o loxodrómica.
Por último, del mismo modo que se explicó en el apartado anterior, se puede seleccionar la con nominal y la constelación real. Figura 8.22. Herramienta “Data Cursor”.
Un panel similar al de las Figuras 8.12-13 aparece en esta ventana, que nos permite desactivar o a satélites disponibles para personalizar el análisis. 89 Figura 8.47. Animación del PDOP para Europa.
Esta herramienta nos permite seleccionar un punto de la gráfica y ver su información de forma precisa. Figura 8.17. Ejemplo de evolución de PDOP en el tiempo.
Fig. 6. PDOP from Seville.
Fig. 9. Regional analysis showing PDOP variation with a Por último una observación color code. respecto a los datos de salida. La herramienta muestra gráficas y datos de los valores de PDOP, que dan una idea general de la precisión en la posición.
Así mismo realiza un cálculo de la disponibilidad en base al valor del PDOP máximo impuesto por el usuario Sin embargo es sencillo obtener otros datos como el HDOP o el VDOP. Tan solo debemos sustituir en el 8.12-13). Por ejemplo,(Figura en una gráfica de PDOP, nos permite observar el valor en una época. Esto nos puede servir tanto proceso seguido la ecuación (7.2) por: para simplemente observar la la información como para obtener 3máximos o mínimos y conocer qué momento Por ejemplo, tomando constelación nominal y desactivando satélites, con un ángulo de máscara deen7.5º, (8.1) HDOP (t j ) 85 G11 (t j ) G22 (t j ) se producen.obtenemos la siguiente evolución del PDOP:
Finally, it is possible to do global availability analysis. For instance, Fig. 10 shows gaps in availability for the nominal VDOP(t ) G (t ) constellation when the elevation mask angle is set to 5 (8.2) and Sin embargo no se ha implementado por simplicidad de la herramienta de cara al usuario, del mismo modo 3 que satellites are deactivated. The darker region correspond no se implementó la opción de ángulo de máscara variable, aunque se explica cómo en el apartado 7.1.1. to the largest gaps in availability, up to 45 minutes.
at constant speed. In Fig 7 we show a flight from Seville to Hamburg using an orthodromic route.
j
Our tool can also be used to analyze whole regions, whose discretization level can be defined in the tool. A finer discretization grid provides 77 more detailed analysis, but a the cost of increased computation times. An example grid is shown in Fig. 8.
33
j
It must be noted that the tool uses the free M Map package for representations on the surface of the Earth (available at Pawlowicz (2014)). 97
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User-friendliness of the application 4.62 0.61
Clarity of bulletin 4.28 0.82
Interest for learning 4.40 0.65
Table 2. Survey results (values between 0 and 5). Interfaz de la herramienta
year. In addition, more realistic models will be introduced, such as an Earth ellipsoidal shape or orbital perturbations. Space augmentation systems will also be included in the studies. In addition, real data from new constellations such as Beidou or Galileo will be included as soon as these systems become operative. An extension of this work could combine simulated inputs from an inertial measurement unit and a Kalman filter to test the performance of GPS-aided inertial navigation under nominal or degraded conditions. ACKNOWLEDGMENTS Figura 8.45. Análisis global de disponibilidad de la constelación GPS nominal realizado con la herramienta, con un ángulo de máscara de 5 grados y 3 satélites retirados del servicio. Las zonas más oscuras corresponden a un intervalo de 45 minutos sin disponibilidad.
Fig. 10. Gaps in availability, global analysis.
The authors gratefully acknowledge spanish government grant number DPI2012-37580-C02-02 for partially funding the work.
5. COMPUTER LAB EXPERIENCE
Si pulsamos la opción “Disponibilidad Región” la herramienta muestra una gráfica como la siguiente:
Finally, we report on a hands-on experience with the tool. A preliminary version was tried in a computer lab for a course in Aerial Navigation, with about 45 students, in three sessions of 2 hours of duration. Students were handed a bulletin with basic instructions and the teacher helped them with any problems they had. Since it was a preliminary version, students reported some bugs. They were mostly satisfied with the tool, as a survey that was given after the lab shows (see Table 2).
REFERENCES Borre, K. (2003). The Easy Suite—Matlab code for the GPS newcomer. GPS Solutions, 7(1), 47–51. Borre, K. (2009). GPS Easy Suite II: A Matlab companion. Inside GNSS, May/June, 48–51. Curtis, H.D. (2009). Orbital Mechanics for Engineering Students. Butterworth-Heinemann, 2nd edition. Gorski, A. and Gerten, G. (2007). GNSS performance possibilities. AnalyticalGraphics Inc. (AGI) White Paper. GPS World (2015). The Almanac. http://gpsworld. com/the-almanac/. [Online; accessed 1-May-2015]. Hofmann-Wellenhof, B., Lichtenegger, H., and Wasle, E. (2008). GNSS — Global Navigation Satellite Systems. Springer-Verlag Wien. Jan, S.S., Wyant, C., and Walter, T. (2009). Matlab algorithm availability simulation tool. GPS Solutions, 13(4), 327–332. Kaplan, E.D. (2006). Understanding GPS: principles and applications; 2nd ed. Artech House, Boston, MA. Li, J., Jarvis, C.H., and Brunsdon, C. (2010). The use of immersive real-time 3D computer graphics for visualisation of dilution of precision in virtual environments. International Journal of Geographical Information Science, 24(4), 591–605. NASA (2015). International GNSS Service (IGS), Product Availability. https://igscb.jpl.nasa.gov/ components/prods\_cb.html. [Online; accessed 2June-2015]. Pawlowicz, R. (2014). M Map: A mapping package for Matlab. http://www.eos.ubc.ca/~rich/map.html. [Online; accessed 1-May-2015]. Vallado, D. and McClain, W. (2007). Fundamentals of Astrodynamics and Applications. Microcosm Press/Springer, 3rd edition. Wie, B. (1998). Space vehicle dynamics and control. AIAA.
Beside bugs, some additional feedback reported by students were, for instance: • Lack of a clock that indicates the hour in the animation. • 8.46. Absence ofdean option to del pause the animation and desee Figura Disponibilidad la región como función PDOP impuesto, con un ángulo de máscara 5º. the constellation’s atservicio a given time, orde the Esta gráfica, a modo de ejemplo, nos muestrageometry la disponibilidad del para diferentes valores PDOP imponiendo ángulo de máscara 5º. Si necesitamos valorestime de PDOP muy pequeños la disponibilidad es possibility ofdemanipulating during animation. pequeña, pero a partir de valores del orden de 2, la disponibilidad ronda el 90%. • Need of a zoom to see better the limits of a region. It’s 92 not possible to know what satellites fly over a region at a given time. These comments were used to produce an improved version, which will be tried again in the same lab next year. 6. CONCLUDING REMARKS We have presented a visual tool to supplement theoretical lessons on Global Navigation Satellite Systems (GNSS) with real-world studies of current constellations. The tool was created using Matlab’s Graphical User Interface Design Environment (GUIDE), and it is particularly intended for courses in aerospace engineering with GNSS content. The tool allows to study visibility and availability for an station (fixed point on Earth), a flight between any two points on Earth, or for an user-defined region. A preliminary version of the tool was tried in a computer lab for a course in Aerial Navigation. Students reported some bugs but were mostly satisfied with the tool, as a survey shows Using the students’ feedback, a better version is being developed, which will be tried again in a computer lab next 98