Digital Surface Models for GNSS Mission Planning in ...

Journal of Surveying Engineering. Submitted February 11, 2013; accepted July 10, 2013; posted ahead of print July 12, 2013. doi:10.1061/(ASCE)SU.1943-5428.0000119

Digital Surface Models for GNSS Mission Planning in Critical Environments

Abstract: GNSS (Global Navigation Satellite System) surveys performed in critical environments (e.g. urban canyons, mountainous or dense vegetation areas) usually suffer from lack of satellite coverage due to obstacles such as buildings and vegetation. A GNSS mission planning software provides an estimate of satellite visibility and DOP (Dilution Of Precision) values along a planned trajectory in order to establish the best time laps to perform the survey. However, such an estimate is not reliable in a complex scenario, as the surrounding environment morphology is not considered. This introduces a new method to improve the prediction of GNSS satellite visibility. This method involves computing GNSS satellites position by means of the orbital parameters, as well as using 3D DSM (3 Dimensional Digital Surface Models) to get a more reliable mission plan. The time evolution of key parameters describing the GNSS constellation is computed through a visibility georeferenced map, for both dynamic and static surveys.

Ac N ce ot p C ted op M ye a di nu te s d cr ip t

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S. Ackermann1, A. Angrisano2 , S. Del Pizzo3, S. Gaglione4 , C. Gioia5, S. Troisi6

Keywords: Navigation, Surveying, Digital Cartography, Geodesy

Introduction Global Position System (GPS) is one of the most important technologies introduced in the last quarter of century and it is nowadays widely used for several applications, both military and civilian. Since the introduction of GPS, other autonomous satellites systems have been developed or are under development (GLONASS, Galileo, Compass and IRNSS) for geospatial positioning purposes. More Global Navigation Satellite Systems (GNSS) means more satellites in space, thus allowing the users to obtain a more accurate navigation solution and to avoid circumstances where satellite coverage would be inadequate if a single positioning system were used. The quality of a positioning survey depends on the number of satellites that are visible by the receiver and on their geometry (Han and Li 2010). When surveys have to be performed within morphologically complex environments (e.g. urban areas), lack of satellites coverage and degradation of position accuracy due to unwanted reflections of signal (multipath) are usually to be expected because of the presence of obstacles such as buildings and vegetation. MMS (Mobile Mapping System) (Li 1997) vehicles (e.g. Google StreetView) are an example of survey application strictly related to the GNSS satellite availability. Indeed, the data collected with the main instruments they employ (e.g. cameras, video-cameras, laser

1

Post-Doc, Department of Applied Sciences, Parthenope University of Naples, Italy Post-Doc, Department of Applied Sciences, Parthenope University of Naples, Italy 3 Post-Doc, Department of Applied Sciences, Parthenope University of Naples, Italy 4 Assistant Professor, Department of Applied Sciences, Parthenope University of Naples, Italy 5 PhD Student, Department of Applied Sciences, Parthenope University of Naples, Italy 6 Full Professor, Department of Applied Sciences, Parthenope University of Naples, Italy 2

1 Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.

scanning. etc.) need to be georeferenced in a coordinate system. For this reason the precision of the navigation instruments (mainly GNSS and IMU) plays a key role. These kinds of vehicles are mostly employed in city centres where the availability of GNSS satellites and quality of their signals are not optimal. In these cases, an a-priori knowledge of the satellite visibility along a planned route would provide an estimation of the GNSS DOP (HofmannWellenhof et al. 2001; Leick 2004) thus making it possible to establish the best time laps to perform the survey. In the case of complex environments, such as high-density urban areas, locally flat Earth approximation is not adequate for reliable GNSS mission planning, even assuming a constant cut-off angle. So, knowledge of the surrounding morphology can improve the planning quality, thus yielding a better estimation of the visible satellite configuration and so the computation of a more reliable DOP. Land Digital Surface Models (DSMs) are widely used today in several fields and mainly for geospatial analysis purposes (e.g. urban city modelling, analysis of mobile network signal wave propagation, flood hazard simulation); information about DSMs and their construction are available in Coppa et al. (2009), Mikhail et al. (2001), Taylor et al. (2005), Oude Elberink (2009), Ackermann and Troisi (2010). A GNSS mission-planning algorithm requires the orbital parameters of the specific constellation to be taken into account. The methodology proposed here is intended for the use of GPS and/or GLONASS constellations. For a given epoch, the visible satellites are obtained in the first instance by removing those one below the mask angle; in a second step, the introduction of the DSM allows to refine such inter-visibility. Only the satellites above the threshold of local visibility are used to compute the DOP values. Many GNSS mission planning algorithms reported in literature are developed to perform a visibility analysis just for a single position (Han et al. 2012). Unlike these methods, the algorithm presented here has been thought for dynamic surveys purposes, in which a receiver is usually installed in a vehicle or carried by an operator. Therefore, the visibility analysis has to be performed for several points (instead of a single one) belonging to an a-priori planned route, representing the path the receiver will follow during the real survey. The algorithm has been developed to operate in the Earth Centred Earth Fixed (ECEF) coordinates frame: this choice restricts the number of reference system transformation, thus minimizing the computational time and avoiding the introduction of further errors due to the coordinate system transformation. In the next paragraphs the steps followed to achieve the mission planning will be discussed and attention will be focussed on the main tasks of the proposed method. The software has been implemented in MATLAB environment by following the flowchart shown in figure 1. The graphical user interface is shown in figure 2, where input data and parameters that must be chosen are located on the left side, while on the right one an example result is plotted in terms of coloured points according to the legend and to the selected epoch (that can be changed by pressing the backward and forward buttons).




Figure 1 Figure 2


Orbital Propagator GNSS surveying is based on the reception of signals transmitted by satellites, its performances are related to the signal quality and the operational scenario; hence, an accurate mission planning is required to prevent GNSS outages and to obtain an accurate survey. The use of the satellite systems in difficult scenarios, such as urban canyons and mountainous areas, is critical because many GNSS signals are either blocked or strongly degraded by natural and artificial obstacles (Angrisano et al. 2012, Angrisano et al. 2013a,b). GPS by itself does not guarantee a continuous and accurate solution in a hostile environment; in performing this work, a multi-constellation approach was adopted in order to fill this gap. The main candidates, as components of the multi-constellation, are GPS and GLONASS. Although GPS and GLONASS are very similar, there are several meaningful differences, classified in terms of constellation, signal and reference differences (Cai 2009). The most significant differences for our purpose are relative to the parameterization of the ephemerides. The determination of the satellites position is necessary to compute the receiver position and for the mission planning. The algorithms for GPS and GLONASS are different due to the parameterization of their ephemerides and so the two cases are treated separately. The GLONASS ICD (ICD-GLONASS 2008) recommends to use the 4th order Runge-Kutta method for the numerical integration of differential equations describing the satellite motion in PZ90.02 frame and to keep the integration time within the 15 minutes interval around the reference epoch; in this work, the satellites positions are computed by using GPS broadcast ephemerides with perturbation parameters set to zero to obtain an almanac-like product, and GLONASS almanac.




Figure 3

The GPS broadcast ephemerides are Keplerian parameters used to compute satellite position in ECEF frame using the orbital propagation algorithm (IS-GPS-200 2004); the GLONASS almanac, instead, is directly expressed in ECEF frame (ICD-GLONASS 2008), but a propagation algorithm is in any case necessary to compute the satellite position in the computation epoch.

Mission Schedule A GNSS mission planning software requires that the mission starting time and the session period must be set. In addition, it must be specified the acquisition frequency, usually by setting the time lap between two following epochs. Once the epochs are so computed, the orbital propagator computes the satellite positions, allowing, in a subsequent step, to check the satellite-receiver inter-visibility. In dynamic missions, a roadmap has to be planned too. Indeed, the GNSS session duration depends on the length of the planned route and on the receiver speed as well. This approach allows computing the expected arrival time ( t0 , t1 , t2 , t3 ,..., tn1 in figure 4) for all the n route points. However, the computation of the satellite visibility in a single epoch for each point is not enough, as the updating of the roadmap cannot be insured. For this reason, the prediction for each receiver position is not made just for a single epoch, but for a 2't time 3 Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.


window centered on t j (see figure 4); this approach allows to keep the position covered by



the satellite prediction even in the case when the receiver is late or early with respect to the roadmap. The window amplitude must be adapted mainly according to the expected vehicle speed or to other possible obstacle (e.g. road traffic or traffic lights if the receiver is installed on a vehicle). This approach has been implemented in the method proposed, allowing the choice of: a starting time related to the first acquisition point of the route, a medium vehicle speed, a time window size and a frequency parameter depending upon the discretization interval G t (figure 4) between two subsequent epochs. Figure 4

Satellite Visibility Analysis One of the main task of the proposed method is the use of a Digital Surface Model to perform satellites visibility analysis. The software developed will upload the DSM as a point cloud in standard ASCII format, whose coordinates can be expressed either in UTM projection or in geographic format. The surfaced DSM is obtained by performing a Delaunay Triangulation on the point cloud dataset. Then, a transformation in the ECEF coordinates system of the DSM is carried out. The planned route points can be loaded in geographic coordinates only (standard ASCII or KML format): the same coordinates transformation adopted for the DSM is applied to the planned route too in order to keep the same ECEF coordinate system. By keeping a unique reference system for all the input data involved in the satellite visibility computation, the error propagation due to transformations is limited. Figure 5

Once the satellites positions have been estimated, according to the mission scheduled epochs, the satellite visibility for the planned route can be accomplished. The visibility can be determined by performing a line-of-sight (LOS) analysis between receiver and the generic satellite (Han and Li 2010). Basically, the method consists in determining the sight vector between the receiver and the generic satellite and to establish, by using the topographic data, whether this vector is blocked by any obstruction (Guth 2004). The implemented method considers the generic receiver position, which coordinates are φ o, λo and ho (Xo, Yo, Zo in ECEF coordinates), the generic satellite of coordinates X s, Ys, Zs and the plane containing the ellipsoidal normal and the receiver-satellite vector. Only the triangles of DSM which intersect with this plane, are considered for slicing, so limiting the algorithm time of execution. In this way the obstruction angle, corresponding to the zenith distance threshold, is computed; by comparing this threshold with the satellite zenith distance, it is possible to define whether the satellite is visible (Sat. A of figure 5) or not (Sat. B of figure 5) by the receiver at a given epoch. Figure 6



Figure 7



Once the visible satellites have been detected, the relative DOP computation is performed by applying one of the methods described in the literature (Hofmann-Wellenhof et al. 2001; Parkinson 1996). In the following the mathematical derivation of the obstacle angle is provided. φo, λo and ho are the geographic coordinates of the generic observer (receiver) position O and Xo, Yo, Zo its ECEF coordinates (figure 6). The prime meridian plane cosine directors are ª 0º « 1» « » ¬« 0 ¼»

assuming the normal direction of the planes to be opposite to the Y ECEF axis. The receiver meridian plane cosine directors are achieved by rotating the plane by an angle λo around the Z axis:

nˆ o

ªa o º « » « bo » «¬ co »¼

ªcos Oo « « sin Oo «¬ 0

sin Oo cos Oo 0

0º ª 0 º 0 »» «« 1»» 1 »¼ «¬ 0 »¼

(1)

In order to obtain the plane that will be used to slice the DSM, and so to compute the obstacle angle for a generic satellite direction, it is first necessary to define the plane containing the ellipsoidal receiver and the satellite LOS. By using the two unit vectors oˆ and sˆ (figure 7), where

oˆ

ªxo º « » « yo » «¬ z o »¼

ªcos Mo cos Oo º « » «cos Mo sin Oo » «¬sin Mo »¼

(2)

ªxs º «y » « s» «¬ z s »¼

ª Xs X0 º « » « OS » « Y Y » 0 « s » « OS » « » « Zs Z 0 » « OS » ¬ ¼

(3)

and

sˆ

with OS

OS OS

2 2 2 X s X o Ys Yo Z s Zo , it is possible to compute the satellite zenithal

distance z that can be compared with the mask angle threshold: 5 Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.


cos

oˆ sˆ T

§ ªxs º · ¨ « »¸ cos ¨ > x o ,yo ,z o @ « ys » ¸ ¨ «¬ zs »¼ ¸ © ¹ 1

(4)

If the satellite is above the mask angle, the plane passing through the satellite S and containing the two unit vectors oˆ and sˆ will be computed, otherwise the satellite will not be considered neither for the visibility map nor for the DOP calculation. As the plane will not pass through the ECEF system origin (unless it matches with the meridian plane), all the four parameters of the general plane equation must be computed. The first three parameters are the cosine directors of the normal of plane itself and they can be easily calculated by performing a cross product between oˆ and sˆ :



z

1

ª iˆ « «xo «x ¬ s

ªa s º « b » oˆ u sˆ « s» «¬ cs »¼

nˆ s

ˆj yo ys

kˆ º » zo » zs » ¼

(5)

By considering the general plane equation,

aX bY cZ d

0

(6)

the fourth coefficient can be obtained by:

ds =- a s Xo +bs Yo +cs Zo

(7)

In addition, the Azimuth of the satellite, necessary to calculate the DOP, is also computed with the two unit vectors normal to the plane involved:

Az

cos

1

nˆ

T

s

nˆ o

§ ªa o º · ¨ ¸ cos ¨ > a s ,bs ,cs @× «« bo »» ¸ ¨ «¬ co »¼ ¸¹ © 1

(8)

Once the plane parameters have been computed, the obstruction angle (or zenith distance limit) can be obtained by intersecting such plane with the triangulated DSM (figure 8). This operation has been implemented with three simple steps: 1) the X, Y, Z variables of the plane equation are filled with the ECEF coordinates of the DSM vertices. It is thus possible to recognize if the vertices belong to the positive half-space limited by the plane or to the negative one, and to flag them in accordance; Figure 8

2) as the TIN triangle sides are known, a two columns relation table is compiled, in which each row identifies a triangle side and each cell a TIN vertex: by filling the vertices cells with the relative flags computed at point 1), we can detect the sides that intersect the plane, simply by identifying the rows having the flags with opposite sign;



3) the intersection between these segments and the plane allows the extraction of the DSM profile in the satellite direction, according to the least squares solution:

A A T ij

xk

1

ij

AijT bij

(9)

where ª 0 «Z Z i « j « Y j Yi « ¬ as

Y j Yi º X i X j »» 0 » » cs ¼

i z j

Y j Z i Z i º » X j X i Zi » » Y j Z i X i »» » ¼

i z j



Aij dim( 4u3)

Zi Z j 0 Xi X j bs

ª Z i Z j Yi « « Z Z X j i « i « X X Y j i « i « -d s ¬

bij dim(4u1)

and

xk

dim(3u1)

ªXk º «Y » . « k» «¬ Z k »¼

Figure 9

Once each point of the profile is defined, the obstruction angle is computed by calculating the minimum zenith distances z k ( k 1, 2, ... , n ) of all the point having the same azimuth Az of the generic satellite S (figure 9). The coordinates (Xk, Yk, Zk) of a given point Pk , are:

pk

ªxk º «y » « k» ¬« z k ¼»

OPk OPk

ª Xk X0 º « » « OPk » « Y Y » « k 0 » « OPk » « » « Z k Z0 » « OP » k ¬ ¼

k

1, 2, ... , n

(10)

where

X k X o Yk Yo Zk Zo 2

OPk

2

2

and zk

cos

1

oˆ

T

∙ pˆ k

§ ª xˆk º · ¨ « »¸ cos ¨ > xˆo , yˆ o , zˆo @∙« yˆ k » ¸ ¨ «¬ zˆk »¼ ¸ © ¹ 1


(11)


Obstacle Map GNSS mission planning software usually reports sky plots showing the satellite positions and its orbital trace in the sky with respect to the receiver position. When 3D topographical data are employed, an obstacle map is also drawn, showing the surrounding visibility situation at the observer position. As established in the previous section, the visibility analysis has been computed without checking obstruction in all azimuth direction (Han and Li 2010) but only for directions of interest (matching the satellite LOSs). For this reason applying the proposed method, an all-around obstacle is no longer necessary.



The above procedure has to be performed for each satellite and for each time window epoch.

Figure 10

An obstacle map (figure 10) is also computed by slicing the TIN around the receiver position with normal planes, according to the procedure introduced in previous section to achieve the obstruction angles. However, in order to minimize the computational time, low angular (Azimuth) resolution is used for this step. The receiver meridian plane (Az = 0°) is defined in the beginning, while all the remaining planes are computed by rotating the first plane around the receiver ellipsoid normal axis, according to the angular resolution and to the rotation matrix:

R

ª r1 «r «4 «¬ r7

r2 r5 r8

r3 º r6 »» r9 »¼

(12)

where

r1 =x o2 +(1-x o2 )cos(-Az r ); ° °r2 =(1-cos(-Az r ))x o yo -(sin(-Az r ))z o °r =(1-cos(-Az ))x z +(sin(-Az ))y r o o r o °3 °r4 =(1-cos(-Az r ))yo x o +(sin(-Az r ))z o ° 2 2 ®r5 =yo +(1-yo )cos(-Az r ) °r =(1-cos(-Az ))y z -(sin(-Az ))x r o o r o °6 °r7 =(1-cos(-Az r ))z o x o -(sin(-Az r ))yo ° °r8 =(1-cos(-Az r ))z o yo +(sin(-Az r ))x o °r =z 2 +(1-z 2 )cos(-Az ) o r ¯9 o

with

r 1,2,..., m

and

m

(13)

180q . angular resolution

Dilution of Precision (DOP) Computation The availability of a reasonable number of satellites by using more than one GNSS, can sensibly improve the probability to obtain a reliable fix when the survey is performed in 8 Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.




difficult scenarios. However, the quality of the coordinates in terms of precision can be negatively influenced by both intrinsic and extrinsic phenomena. Dilution Of Precision is a fundamental quality indicator, which focuses on the geometry of visible satellites. The mathematics behind the DOP computing have been extensively explained in literature (Hofmann-Wellenhof 2001, Parkinson 1996). The determination of this parameter depends on the relative position between the receiver and satellites; the GDOP (Geometric Dilution of Precision) matrix is thus related to the observer position. Starting from the azimuth and zenith distances of each obstacle free satellite in view for a given receiver position, the GNSS measurement model design matrix G is computed according to the equation:

G dim( nx 4)

ª sin z1 «sin z 2 « « « «sin zk « « ¬«sin zn

sin i Az1 sin i Az2

sin i z1 cos Az1 sin i z2 cos Az2

i Azk sin

i zk cos Azk sin

i Azn sin

i zn cos Azn sin

cos z1 1º cos z2 1»» » » cos zk 1» » » cos zn 1¼»

with n≥4. Considering the same variance on the ranging error, the GDOP matrix is defined as:

ª¬G T G º¼

1

dim(4u4)

ª(East DOP)2 « « « « «¬ covariance

covariance

(North DOP)

2

(Vertical DOP) 2

terms

º » » » » (Time DOP) 2 »¼ terms

All the DOP parameters can be obtained according to the following equations: GDOP

(East DOP)2 (North DOP)2 (Vertical DOP)2 (Time DOP)2

PDOP

(East DOP)2 (North DOP) 2 (Vertical DOP) 2

HDOP

(East DOP)2 (North DOP)2

VDOP

TDOP

(Vertical DOP)2

(Time DOP)2

Table 1.

Method Validation The implemented method has been tested by performing a GNSS survey within the Pompei area (Naples, Italy) on July 29th 2011, employing a GPS / GLONASS receiver. For this area an Airborne Laser Scanning survey, performed on July 2008, was available. The test consisted in performing a GPS/GLONASS session and to use the registered waypoints as an input planning path in order to compare the observed satellites with the ones predicted by the 9 Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.


software and by considering the same registered waypoint epochs. The goal of the test was to compare the predicted against the observed number of visible satellites and also to check the PRN code correspondence.

The survey was conducted with two synchronized GNSS receivers: a 14 channel Novatel FlexPak-G2 series OEMStar receiver (figure 11a) set on 10 + 4 channels configuration (10 for GPS and 4 for GLONASS constellations) and a second GPS/IMU XSens MTi-G integrated receiver (figure 11b). The two antennas were located on the top of a small van travelling over the test route. Due to the presence of narrow streets and vegetation in the testing area, waypoint coordinates registered with the Novatel receiver showed high errors on 3D coordinates compared to the real vehicle path, thus making them unusable for the test purposes. Therefore the output coordinates of the XSens MTi-G receiver have been preferred, since the inertial system corrections allowed a much more reliable route.



Figure 11.

Figure 12.

A further correction of the points’ height has been also performed in order to verify if possible DSM errors may have influenced the results: by taking into account that the antenna’s height above the street level is constant, the relative height of all the waypoints from the DSM has been constrained to H s 2 meters (figure 12). The Novatel receiver has instead been used to collect the observed satellites for each registered waypoint. The two tracks (the original registered by the XSens MTi-G and the one with the corrected height) have been compared.

Results In table 1, the classification criterion adopted for the validation test is reported; Figure 13 shows the test trajectory, whose points have been colored in according to the classification policy (referred to table 2), overlying the DSM point cloud. The type 1 results show a perfect match between predicted and observed satellites; this class also includes the cases where the predicted number of satellites is higher than the number of channels. The type 2 results are relative to the case in which observed satellites are included in the predicted set, with difference of at most 2 satellites. The type 3 results are similar to type 2 case but with larger difference. Results for type 2 and 3 indicate that the prevision is too optimistic: the difference can be due either to plane position error for the XSens coordinates or to the unreliability of the DSM. The same causes can also lead to Type 0 and Type 4 classification, but with worse results. In fact the type 4 condition indicates that the predicted satellites are included in the observed set and the type 0 condition indicates that there is no intersection between observed and predicted set. Table 2


Table 2 and 3 show the classification results for the GPS and GLONASS constellations separately, by using both the original height and the constrained one. The results carried out by constraining the relative height and by adopting the registered one are similar with slight worsening for the first configuration. This can be due to the point cloud surfacing method that doesn’t faithfully reflect the environment morphology. On the other hand, the use of a Digital Terrain Model (DTM) with 3D building models could improve the visibility analysis. In addition, it must be considered that the GNSS test was performed three years later than the lidar survey: possible changes of the urban plane due to the construction or demolition of buildings which might have taken place during this time lapse could have negatively influenced the satellite visibility analysis. The type 1, 2, 3 situations could be considered acceptable because the observed satellites are included (or even coincident for type 1) in the predicted set; according to this, the unacceptable cases are simply type 0 (not satellite in common between predicted and observed sets) and 4 (some observed satellites are not predicted) and the percentage of these types are always about 30-35%. In detail the table 2 shows the results for GPS case with constraint and original height; the proposed planning worked properly in the 67.8 % and 69.6 % of cases respectively. The tables 3 show the same results for the GLONASS, demonstrating that 62.8 % and 65.6 % of cases are acceptable for the two configurations. It could be noticed that the “type 1” and “type 2” are the cases where the algorithm shows the best performance and these cases are more frequent in the constrained height configuration (43.5 % and 28.4 % respectively for GPS, 16.9 % and 15.7 % for GLONASS). The “type 3” case, although herein considered still acceptable, is less significant than previous ones; more “type 3” situations occurred with original height configuration, probably due to an over-estimation of the antenna altitude performed by XSens MTi-G. The percentage of GPS and GLONASS acceptable cases (types 1-3) are comparable, showing that the proposed mission-planner provides suitable results for both constellations. It could be noticed that the percentage of GLONASS types 1 and 2 is lower than GPS case; this occurrence is due to the limitation on the receiver GLONASS channels (only 4) which implies a number of predicted GLONASS satellites larger than the observed one. Finally a comparison between the developed mission-planner and a standard one is carried out for a single epoch to show the actual beneficial of the advanced tool. In figure 14 the sky-plots, predicted at 11:00 29th July 2011 for an observer at Pompei and obtained by the aforesaid mission-planners, are shown. For the considered epoch and position, the GPS and GLONASS observed satellites are respectively 9, 12, 15, 17, 26, 27 and 15. Hence the missionplanner with DSM is able in this case to predict a large part of the visible GPS satellites, only the number 17 is not predicted probably owing to an imperfection of the DSM (the satellite is near the border of the visible area, i.e. the area included in the blue line).




Figure 13 Moreover the only observed GLONASS satellite (i.e. the number 15) is included in the set predicted by the developed mission-planner, but additional five satellites are predicted too; probably these satellites are visible from the antenna but the signals received are in acquisition or tracking phase. The satellites predicted by a standard mission-planner are shown in the right side of figure 14; as expected several satellites not observed are pointed 11 Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.


out as visible, because the presence of obstacles is not considered. For this reason a standard mission-planner always overrate the number of visible satellites. Figure 14

Conclusions In this work, a GNSS planning method for dynamic missions has been proposed. The procedure developed for the satellite visibility prediction has been performed by operating in the ECEF reference system, avoiding transformations that would increase the computational time. The reliability of the results is strongly influenced by the age of the DSM and by the ephemerides: the longer is the lapse of time between these input parameters and the survey date, the worse is the quality of the results. The computing time is directly proportional to the number of epochs to process as well as to the DSM point cloud size. The number of epochs is determined by the number of the path waypoints and by the time span window size. The satellite visibility for a single point can be easily simply obtained by choosing a long time window; on the other hand, by flagging the visible points of DSM for all the azimuth directions, with a prefixed angular resolution, the ground visibility map between DSM points can be achieved.



Table 3


References Ackermann, S. and Troisi, S. (2010). “Una procedura di modellazione automatica degli edifici con dati LIDAR”. Bollettino della SIFET (Società Italiana di Fotogrammetria e Topografia), 2/2010, 9-25. Angrisano, A., Gaglione, S. and Gioia, C. (2012). “RAIM Algorithms for Aided GNSS in Urban Scenario”. Ubiquitous Positioning, Indoor Navigation, and Location Based Service (UPINLBS), IEEE, Washington DC, USA Angrisano, A., Gioia, C., Gaglione, S. and Del Core. G. (2013a). “GNSS Reliability Testing in Signal-Degraded Scenario,” International Journal of Navigation and Observation, vol. 2013, Article ID 870365, 12 pages Angrisano, A., Gaglione, S. and Gioia, C. (2013b). “Performance assessment of aided Global Navigation Satellite System for land navigation” IET Radar, Sonar and Navigation. doi: 0.1049/iet-rsn.2012.0224, in press Cai, C. (2009). “Precise Point Positioning Using Dual-Frequency GPS and GLONASS Measurements”. M.Sc Thesis, Department of Geomatics Engineering, University of Calgary, Canada, UCGE Report No. 20291 Coppa, U., Guarnieri, A., Pirotti, F. and Vettore, A. (2009). “Accuracy enhancement of unmanned helicopter positioning with low-cost system”. Appl. Geomatics, 1(3), 8595. Guth, P. L. (2004). “The Geometry of Line-of-Sight and Weapons Fan Algorithms.” Studies in Military Geography and Geology, Springer Netherlands, 271-285. Han, J.Y. and Li, P.-H. (2010). “Utilizing 3-D topographical information for the quality assessment of a satellite surveying.” Appl. Geomatics, 2(1), 21-32. Han, J.Y., Wu, Y., and Liu, R.Y. (2012). “Determining the optimal site location of GNSS base stations”, Bol.Ciênc. Geod., 18(1): 154-169. Hofmann-Wellenhof, B., Lichtenegger, H. and Collins, J. (2001). “GPS Theory and Practice (5th revised edition).” Springer, Wien. ICD-GLONASS (2008). “Global Navigation Satellite System GLONASS Interface Control Document, version 5.1.” Moscow, Russian Federation. IS-GPS-200 (2004). “Navstar GPS Space Segment/Navigation User Interfaces, Revision D.” ARINC Research Corporation, El Segundo, CA, USA. Leick, A. (2004). “GPS Satellite Surveying, 3rd Edition.” John Wiley & Sons, Inc. Li, R. (1997). “Mobile Mapping: An Emerging Technology for Spatial Data Acquisition.” Photogramm. Eng. Remote Sens., 63(9), 1085-1092. Mikhail, E. M., Bethel, J. S. and McGlone, J. C. (2001). “Introduction to Modern Photogrammetry.” John Wiley & Sons, Inc. Oude Elberink, S. (2009). “Target Graph Matching for Building Reconstruction.” The International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol. XXXVIII, Part 3/W8, 49-54. Parkinson, B. W. (1996). “GPS Error Analysis. In: Global Position System: Theory and Applications, Vol. I.” American institute of Aeronautics and Astronanutics, Inc., 469483. Taylor, G., Li, J., Kidner, D. and Ware, M. (2005). “Surface Modelling for GPS Satellite Visibility.” Web and Wireless Geographical Information Systems, Lecture Notes in Computer Science,Vol. 3833, Springer Berlin / Heidelberg, 281-295.






Tables


Table 1. Waypoint classification conditions, with O = “set of Observed satellites” and P = “set of Predicted satellites” Color

Type

Condition

Green

1

O { P OR O P AND # O { #Channels

Cyan

2

O P AND (# P # O) 2

Yellow

3

O P AND (# P # O) ! 2

Red

4

O P OR > #(O P) # O AND #(O P) # P @

NONE

0

OP

Accepted Manuscript Not Copyedited



Table 2. GPS results


Constrained relative height (10 channels) Original relative height (10 channels)

Type

1

2

3

4

0

Total

%

8.9%

34.6%

24.33%

27.36%

4.81%

100%

#

150

583

410

461

81

1685

%

2.14%

26.23%

41.25%

25.93%

4.45%

100%

#

36

442

695

437

75

1685




Table 3. GLONASS results


Constrained relative height (4 channels)

Original relative height (10 channels)

Type

1

2

3

4

0

Total

%

11.39 %

5.52%

45.93%

11.57%

25.58%

100%

#

192

93

774

195

431

1685

%

9.67 %

5.99%

49.91%

10.15%

24.27%

100%

#

163

101

841

171

409

1685




Figure 1. Flowchart of the proposed method Figure 2. Main software graphical user interface Figure 3. Orbital Propagator Algorithms Figure 4. Mission timeline Planning scheme Figure 5. Satellite Visibility Figure 6. Prime meridian and observer meridian planes Figure 7. Observer meridian plane and observer-satellite plane Figure 8. Intersection between triangulated DSM and satellite-receiver plane Figure 9. DSM profile and obstruction angle for a generic satellite direction Figure 10. Sky plot showing satellite geometry (GPS in blue and GLONASS in red) and a 10 degree resolution obstacle map Figure 11. (a) Novatel FlexPak-G2 series OEMStar GPS/GLONASS receiver. (b) XSens MTi-G GPS/IMU integrated receiver Figure 12. Relative Height waypoint correction Figure 13. Test trajectory colored according to the results of Table 3 Figure 14. Predicted visible satellites with the developed tool (on the left) and a standard mission planning application



List of Figures



List of Tables:



Table 1. Waypoint classification conditions, with O = “set of Observed satellites” and P = “set of Predicted satellites” Table 2. GPS results Table 3. GLONASS results


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Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.

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Accepted Manuscript Not Copyedited Copyright 2013 by the American Society of Civil Engineers J. Surv. Eng.

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