Navigation and orbit computation aspects of the ESA NAVSAT system concept

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Acta Astronautica Vol. 15, No. 4, pp. 195-208, 1987 0094-5767/87 $3.00+0.00

NAVIGATION A N D ORBIT COMPUTATION ASPECTS

OF THE ESA NAVSAT SYSTEM CONCEPTt

K. F. WAKKER, B. A. C. AMBROSIUS, H. LEENMAN and R. NOOMEN

Delft University of Technology, Department of Aerospace Engineering, Kluyverweg I, Delft, The Netherlands

(Received 14 January 1986)

Abstract--The European Space Agency (ESA) presently studies a NAVSAT satellite navigation system concept, which may be considered a civil variant of the U.S. NAVSTAR Global Positioning System (GPS). A user of the NAVSAT system will be able to determine his 3-dimensional position in realtime with an absolute accuracy of better than 10 m, and his velocity with an accuracy of about 10 cm/s. Since 1983 the National Aerospace Laboratory (NLR) and Delft University of Technology (DUT) in The Netherlands are involved in the NAVSAT studies. This paper presents some results of a Study of NAVSAT Control Segment Characteristics. It starts with an introduction of the general concept. Then, the satellite orbit and tracking aspects are discussed and the ranging error budgets and the achievable user positioning accuracy are estimated. Subsequently, a proposed tracking data compression technique is described. The orbit determination of the satellites from the compressed tracking data is discussed in some detail and results are presented of orbit determination and orbit prediction error analyses. The paper concludes with an analysis of a realtime Kalman filter process to improve the orbit information during a satellite pass over a ground station.

l. INTRODUCTION

The use of artificial satellites for purposes of navigation started in late 1957, when investigators at the Johns Hopkins Applied Physics Laboratory began radio tracking of the first earth satellite S P U T N I K 1. Their investigations led to a demonstration that the entire satellite orbit could be determined by means of measurements on the doppler frequency shift of the satellite's radio signals as received during passes over ground stations. The navigation satellite system concept was born, when it was realized that, as a consequence, a radio receiver's unknown position could be determined from the same type of doppler measurements if the satellite's orbit is known. This basic concept has led to the T R A N S I T navigation system[l], consisting of 5 or 6 satellites in circular polar orbits at an altitude of about 1100 km, and a ground segment consisting of 4 tracking stations located in the U.S.A. This passive all-weather navigation system has been in continuous use by the U.S. Navy since 1963 and was released for civil use in 1967. It is estimated that in the early 1980's the total number of users reached 10,000.

The nominal mean waiting time between

T R A N S I T satellite passes amounts to about 1.5 h for a user at the equator, decreasing to less than 1 h for users at latitudes of more than 50deg North or South. The system provides 2-dimensional navigation accuracy to better than 10 m, while for land survey and geodetic positioning accuracies of better than 1 m

1"Paper IAF-85-262 presented at the 36th Congress of the International Astronautical Federation, Stockholm, Sweden, 7-12 October 1985.

are achieved. This, however, requires the processing of observations acquired during 30-50 satellite passes over the same fixed receiver. In the 1960's, it became obvious that an accurate 3-dimensional realtime and global satellite navigation system had much to offer to all types of military users. These characteristics could not be provided by the T R A N S I T system and various alternative concepts were studied in the U.S.A. This ultimately has led to the development of the NAVSTAR Global Positioning System (GPS). This GPS system[2] is designed to provide instantaneous positioning for military operations on land, at sea and in the air. The system is expected to be fully operational in 1988 and will consist then of 18 active satellites, distributed over 6 orbit planes, each plane inclined at 55 deg to the earth's equator and mutually separated by 60 deg of right ascension of their ascending node. The orbit altitude is about 20,180 km, which corresponds to an orbital period of 12 h; the 3 co-orbiting satellites are separated by 120deg of geocentric angle. The satellites operate fully autono- mously, but periodically require ground contact to refresh the user navigation message consisting of satellite ephemeris and clock error parameters, all- satellite almanacs, etc. The satellites broadcast two coherent L-band frequency radio signals, time- controlled by synchronized onboard atomic clocks. The navigation signals are jam-resistant and the full accuracy of the system is only available to authorized users capable to decipher the precise pseudo-random noise code used by the satellites. The user determines his position and clock offset by taking pseudo-range measurements to 4 satellites. From the doppler shift of the carrier signal he may also determine his instantaneous velocity. The global 3-dimensional 195

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196 K . F . WAKKER et al.

instantaneous navigation accuracy of an authorized user will be better than 15 m in position and within 10cm/s in velocity. The GPS ground segment will eventually consist of 6-12 stations. At the moment, there are 6 first-generation satellites operational. These are used for testing purposes during the concept validation and full-scale engineering development phase.

For civil applications, GPS has a number of draw- backs. First, because it is a military system, it most probably will not be available in its full-accuracy version to most civil users. Instead, they have to accept a degraded accuracy level of about 100 m, which rules out many potential applications. Further- more, high-quality receivers will be expensive; one reason being the special transmission techniques applied in GPS, which were developed to meet the military requirements for communications security and invulnerability to jamming. In addition, the system is completely under political control of the U.S.A., and may switch to special encrypted trans- missions during periods of severe political or military tension, making the system useless for a general user. The question then arises: would it be possible to develop a civil variant of GPS under international management, offering to all users a very high precision, not artificially degraded, position determination capability at much lower costs? This question has led to the NAVSAT concept, presently being studied by the European Space Agency (ESA)[3].

2. THE NAVSAT CONCEPT

The NAVSAT satellite navigation system concept is based on a number of considerations aiming at a simplification of the GPS design. It was realized that the satellites themselves can be simplified if the requirement of autonomous operation is dropped, which implies that the satellites must be under continuous control of ground stations distributed over cooperating countries. As a consequence, all satellites only have to carry simple, highly-reliable, transparent transponders, so that most of the complexity has been transferred to the ground segment. Since protec- tion of the downlink signals against deliberate jamming is no longer required, the signal structure can be much simpler, thereby reducing the complexity and costs of the navigation receivers. Instead of the GPS approach of transmitting continuous signals and channel sharing by code-division multiple access (CDMA), NAVSAT will use 133ms burst signals with time-division multiple access (TDMA) channel sharing. Each 1.8 s T D M A frame contains 12 slots, each slot corresponding to one satellite, whereby antipodal satellites will share the same time slot. The use of TDMA has some important advantages, such as the fact that the receiver does not need to know which satellite is in view, so that no almanac message is required, and that the average satellite power

requirements are lower. The ground segment, however, will be relatively complicated and expensive. In the present concept, the space segment consists of 24 satellites encircling the earth in 20,000 km altitude circular orbits, inclined at 55deg to the equator. The satellites are uniformly distributed over 3 orbit planes, which are separated by 120 deg in their right ascension of the ascending node. So, in contrast to the GPS system, in the NAVSAT concept each orbit plane contains 8 satellites with a geocentric position angle of 45 deg between successive satellites. In this orbit configuration, 6 or 7 satellites will be visible from any point on earth for 96% of the time, while for 74% of the time 8 or 9 satellites will be in view.

A number of studies have already been performed for ESA on the feasibility of the NAVSAT concept, on the details of the ground and space segments and on the development of overall system simulation software. In this paper, only some results will be presented of a recent study on the NAVSAT Control Segment Characteristics performed under ESA contract by the National Aerospace Laboratory (NLR) and the Section Orbital Mechanics of Delft Univer- ity's Department of Aerospace Engineering[4,5]. The paper will concentrate on the orbit and tracking aspects of the satellites, and on the user positioning accuracy which may be expected from the NAVSAT system.

In the Dutch study it is assumed that the ground segment (Fig. 1) will consist of 6 so-called Regional Centers (RC) or uplink stations, distributed over the Earth such that each satellite is visible from at least one station at all times, and a Mission Center (MC). The overall ground segment will perform a number of complex tasks. First, the MC has to provide the coordination between the uplink stations for assign- ment and handover of satellite control from one RC to another. In principle, an RC can control a satellite as long as it is more than 5deg above the local horizon. An RC will acquire two-way ranging data on all satellites that are under its control as long as these satellites are at an elevation of more than 20deg. The tracking data will be compressed into so-called normal points and transmitted to the MC. Each RC will also acquire one-way ranging data on all satellites that are visible but not controlled from that RC. These measurements will also be transmitted in a compressed form to the MC, where they will be used, in combination with the two-way data, to determine the clock errors at the RCs[4,5]. The MC will process the tracking data for the orbit determination of all satellites and will generate orbit predictions for each of the satellites spanning a period of about 1 week. A special set of parameters representing these predicted orbits will be sent by the MC to the RCs. At each RC the two-way tracking data acquired during a single pass will be used to improve the orbit prediction generated by the MC, and this improved orbit will be sent to the next RC, where it

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The ESA NAVSAT system concept 197

PACE I

SEGMENT

TE :;,SsTALS '"

CONTROL

[

USER

SEGMENT

(CI SIGNAL IN THE C BAND |~5 GHz) ILl SIGNAL IN THE L BAND (1.56 GHz} IS) SIGNAL IN THE S BAND (2.2 GHz)

~ ~ ~ ~ R A N G I N G D A T A

~TIME DIFFERENCE ESTIMATES \PASS REPORT

/

.A. SCNEOO'E

\

/

OREIT.REO,~,O. \ \

/

T,.E STNC.RONI.ATION \

\

' ORBIT REFINEMENT Ill "

MC MISSION CENTRE

RC REGIONAL CENTRE (i: UP TO 61

Fig. 1. The NAVSAT system elements (top) and the ground control segment data flows (bottom)[4].

will be used to determine a set of parameters accurately representing the satellite ephemeris during the satellite's pass over that RC. These parameters will be included in the navigation message transmitted by the RC and relayed by the satellite to the user.

3. ORBIT AND TRACKING

The osculating orbital elements and their epoch for the single N A V S A T satellite which was selected for most of the orbital analyses are listed in Table 1. Because all satellites move in similar orbits, the results of these analyses will be generally applicable to all satellites. The preliminary network of RCs, which also act as tracking stations, consists of stations at Hawaii, Kourou (French Guiana), Libreville (Gabon), Orroral (Australia), Porto Alegre (Brazil) and Sri Lanka. It is assumed that an RC controlling a satellite acquires two-way range measurements to that satellite during the appropriate time slot in each T D M A frame. The ranging is performed on the uplink C-band frequency and one or two downlink L-band frequencies, depending on the ultimate system design. To enable an accurate modeling of the ionospheric propagation delays on both the uplink

and downlink signals, at least two coherent downlink frequencies are required. One of these will be the primary L-band frequency, but instead of a second- ary L-band signal, possibly the S-band telemetry signal may be utilized to provide the necessary information. The minimum elevation for tracking purposes was set at 20 deg, in order to prevent cor-

Table 1. The adopted values of the osculating elements and derived parameters* of the single NAVSAT satellite orbit

Epoch 95/3/21

O h 0= 0 s UT

Semi-major axis (km) 26561

Eccentricity 0.0

Inclination (deg) 55.0

R.a. ascending node (deg) 45

rate of change (deg/day) -0.039

Argument of perigee (deg) 0

rate of change (deg/day) 0.022

Mean anomaly (deg) 0

rate

of change (deg/day) 722.073

Altitude (km) 20184

Nodal period (min) 717.91

Revolutions per day 2.0

Equat. spacing daily tracks (km) 2.39

Local solar time at ascending node (h) 15.00

*The derived parameters are computed on basis of the

mean

orbital elements. The altitude is relative to a spherical earth with a

radius

of 6375 km.

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Fig. 2. The visibility masks at a cut-off elevation of 6 Regional

ruption of the measurements by too large unmodeled atmospheric propagation effects. Of course, adequate radio contact for transmitting navigation messages to the satellite and for communication between the RCs is possible down Co an elevation of 5 deg. Figure 2 shows the visibility contours of the RCs for a 20 deg and a 5 deg cut-off elevation. For the 20 deg cut-off elevation the region between 55 deg North and 55 deg South is obviously not completely covered, indicating that the high-quality tracking data will not be available continuously. For a cut-off elevation of 5 deg the coverage is complete, which is essential because of the requirement that each satellite should always be

20 deg (top) or 5 deg (bottom) for the network of Centers.

under control of a ground station. Some statistics of the view periods of the satellite with the orbit parameters listed in Table 1 are summarized in Table 2. This view period is defined as that part of a satellite pass over a ground station during which the satellite is above a specified cut-off elevation for that particular station. The case of the 20 deg minimum elevation refers to the tracking coverage of the network. So, for tracking the average view period is about 5.8 h. The single satellite considered can be tracked for about 98% of the time, while for about 35% of the time it can be tracked from 2 or 3 stations simultaneously. The column for a 5 deg cut-off elevation refers to the

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T h e E S A N A V S A T s y s t e m c o n c e p t 199

Table 2. Summary of the view periods of the single NAVSAT satellite from the 6 Regional Centers during a 1-day time interval Cut-off elevation (deg)

20 5

Total number of passes 6 6

Maximum view period (min) 500 605

Average (min) 347 406

Percentage total visibilitay time 98.3 100

Maximum non-visible period (min) 20 0

Average (min) 12.5 0

Periods with simult, visibility

from 2 Regional Centers* 4 7

Average duration (min) 84 87

Periods with simult, visibility

from 3 Regional Centers* 1 3

Average duration (min) 165 132

Percentage simult, visibility time 34.7 69.8

*Only periods > 5 min.

view periods during which an RC can transmit a navigation message to a user through that satellite. This period is on the average about 6.8 h. For this minimum elevation the satellite is continuously visible from at least 1 station and for about 70% of the time from 2 or 3 stations simultaneously.

4. RANGING ERROR BUDGETS

An RC will acquire two-way ranging data during the periods that it controls a satellite. These data are subsequently transmitted to the central MC, where they are combined with tracking data from the other RCs and processed to determine and predict the satellite orbits (Section 7). They are also processed in realtime at the RCs themselves using a Kalman filter to improve the predicted orbit (Section 8). So, these measurements play a vital role in the generation of the navigation messages for the user. To allow time synchronization between RCs, each RC also takes one-way range measurements to those satellites which are visible but not under control of that particular RC[4,5]. A user of the system, on the other hand, can only acquire one-way pseudo-range measurements.

Data on at least 4 NAVSATs are then sufficient to determine his quasi-instantaneous position.

For tracking, the ranging signal path is from RC to satellite and back to the same RC, while for user navigation ranging errors are introduced along the signal path from RC to the satellite to the user. For both communication links error budgets can be made up, which will differ because of the different ranging concepts applied, the quality differences between a receiver at the RC and a user's receiver, and the feasibility of modeling various error sources more

accurately at an RC. Detailed analyses have led to the

error budgets listed in Table 3, which are intended

to represent the state-of-the-art in technology and atmospheric signal propagation modeling for the mid 1990's. For a discussion on the magnitude of the various error contributions the reader is referred to[5]. The error budgets listed indicate that the rms overall tracking error at an RC will be about 0.6 m. A user will be able to measure a pseudo-range with an rms accuracy of about 3.3 m. The major con- tributors to the user's overall ranging errors are: RC timing errors, satellite ephemeris errors, atmospheric refraction errors and errors introduced by the user's receiver itself. When it is realized that the quality of the user equipment and of the atmospheric refraction models will probably improve significantly during the operational phase of the NAVSAT system, it will be clear that, to exploit the full capabilities of the system, the NAVSAT ground segment should be designed in accordance with the highest precision standards. This means that time synchronization between the RCs as well as satellite orbit prediction should be performed with an extreme precision.

5. USER POSITIONING ACCURACY

In the NAVSAT concept, a user calculates his position using pseudo-range measurements to all visible satellites. In principle, it is sufficient to process

Table 3. Estimated equivalent ranging error budget for a Regional Center (left) and a user of the NAVSAT system (right)

Error source Rms error (m) Error source Rms error (m)

Transmitter Control segment

group delay 0.3 group delay 0.3

clock error 0 clock error 0.9

Space segment Space segment

ephemeris 0 ephemeris 1.5

group delay 0.2 group delay 0.2

Atmospheric refraction Atmospheric refraction

troposphere 0.05 troposphere, uplink 0.05

ionosphere 0.1 troposphere, downlink 0.8

ionosphere, uplink 0.1

ionosphere, downlink 0.5

Receiver User segment

dynamics 0 dynamics "] 1.5

range noise 0.2 pseudo-range noise _d

clock noise 0 clock noise 1.0

computation noise 0.2 computation noise 1.0

quantization 0.2 quantization 0.5

group delay 0.3 group delay 1.0

multipath 0 multipath 1.0

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200 K.F. WAKKER et al.

4 (quasi-)simultaneous observations to obtain an instantaneous position fix. This was a basic design philosophy behind the NAVSTAR/GPS concept, which was optimized by requiring that the 4 satellites providing the best geometry would be selected from the constellation of satellites actually visible at any time. Theoretically, the best geometry occurs when 1 of the satellites is at the user's zenith and the other 3 are low above the horizon and separated by 120 deg in azimuth. Due to the T D M A channel sharing and the application of a strong continuous wave (CW) carrier signal, the NAVSAT concept makes it easier to design user equipment that allows the user to navigate on all visible satellites, and this may improve the positioning accuracy as will be demonstrated below.

In satellite navigation error analyses, it has proven to be practical to express the navigation error as the product of a User Equivalent Range Error (UERE) and a Dilution Of Precision (DOP) factor. The UERE is defined as the uncorrelated portion of the errors in the pseudo-range observations to the various satellites, and may, according to Table 3, be set equal to 3.3 m for a user of the NAVSAT system. The DOP factors are unequivocally determined by the geometric relationship between the user's position and the position of the satellites used for the navigation. A number of DOP factors may be identified depending on the particular component of the navigation accuracy matrix considered. In this paper, only the GDOP factor will be discussed, dealing with the overall positioning accuracy in a 4-dimensional space-time system. A small value of GDOP indicates

a good geometry of the satellites that are used for the positioning, and will result in small errors in the position and time-offset fixes.

The position geometry of all satellites relative to a user will change continuously with time. For NAVSAT type orbits, the time history of this geometry does not only depend on the number of orbit planes and the number of satellites in each plane, but also on the phase staggering. This staggering can be described as follows. The phase staggering is tp deg if at the time that a satellite in one orbit plane is over the equator, a satellite in the adjacent plane with a larger right ascension of the ascending node is at an in-orbit angle of q~ deg North, while another satellite in the other adjacent plane is at an in-orbit angle of q3 deg South. For the NAVSAT system a preliminary staggering of 30 deg was adopted.

A typical example of the continuously changing position geometry of the 24 NAVSATs relative to a specific user is shown in Fig. 3. This Figure indicates which satellites are visible as a function of time during one day for a user at 0deg latitude and longitude. The visible satellites are indicated by the symbol + ; the satellites constituting the best 4-satellite geometry by ~). Figure 4 shows the variation of GDOP during a 1-day period at 2-min intervals for a user at 0 deg latitude and longitude and a user at 80 deg latitude and 0 deg longitude. A 5 deg minimum elevation mask was applied. Both Figures consist of 2 plots: one for the case where the positioning is based on all visible satellites (bottom) and a second one for the case that only the 4 satellites providing the best geometry are used (top). The

Time NAVSAT s a t e l l i t e number

( h r ) i 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 0 @ + + @ + @ + + i @ @ + + @ + @ + + + 2 @ + @ @ + + + + @ 3 + + + @ + @ @ @ + + 4 @ + + @ + @ + @ + 5 @ + @ + + + + + @ @ 6 @ + + + + @ + @ @ 7 @ + @ @ @ + + + + + 8 @ + @ + @ + + + 9 + + + + + @ @ + g @ i0 + + @ + @ @ + + @ ii @ @ + + + + + + @ @ 12 + @ + @ + + + @ @ 13 + + @ @ @ + @ + + + 14 + @ @ @ + + @ + + 15 + + + @ + @ + @ @ + 16 @ + + @ + @ + @ + 17 @ + @ + + + + + @ @ 18 @ + + + @ + + @ @ 19 @ + @ + + @ @ + + + 20 @ + @ + + @ @ + + 21 + + + @ + + @ @ + @ 22 + + @ + @ @ @ + + 23 @ + + @ + + + @ + @ 24 @ + + @ + + @ + g

Fig. 3. The time history of the NAVSAT satellites visible for a user at 0 deg latitude and 0 deg longitude during a 1-day period. The results hold for a 30 deg phase staggering. The visible satellites are indicated

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The ESA NAVSAT system concept S I I I I I 201 I I I I I 5 I I I I I ~ qm wl ~ ,m em ,m ~m ,m '~ o i I I I I 21t0 riB0 720 960 1200 ltlqO TIME tHIN} 5 l I I I I g 0 ,li4t~,i I : '~ I ~ I : " lii, l l l i l i : : I ... t I I t 5 I I I I' I • • • ~ i • • • i I • • • I i / 1 ,i " "I I • " ;I I" ° °t / / 2qO riB0 720 960 1200 lqttO

TIME (MINI

Fig. 4. Daily variation of the GDOPs for a satellite phase staggering of 30 deg and a user at 0 deg longitude and 0 deg latitude (left) or 80 deg latitude (fight). The upper plots hold for the 4-best-satellites configur-

ation, the plots below for the configuration of all visible satellites. GDOP obviously varies strongly with time and geo-

graphical position. Analyses described in[5] have demonstrated that for a user navigating on all visible satellites GDOP may vary between 1.5 and 3 during a day. When he uses only the best 4 satellites GDOP ranges from 2.2 to 4.2. When a GDOP rms value of 2.2 is adopted for the case that all visible satellites are tracked and the UERE is assumed to be 3.3 m, the overall rms user navigation position error turns out to be about 7 m. This may be considered a represen- tative value for a user anywhere on earth.

6. TRACKING DATA COMPRESSION

All NAVSAT orbit computations will start from the tracking data providing information on a satellite's true motion. In the present NAVSAT concept, the RCs acquire two-way range measurements on each satellite which at that moment is under control of that particular RC. The measurements are assumed to be acquired at a rate of 1 measurement per 1.8 s (Section 2), which yields a total of about 11,600 measurements for an average tracking period per pass of 347 min. The information contained in these data will be utilized at the MC to determine, in retrospect, the actual orbits of the satellites and to predict those orbits further ahead. These predicted orbits will serve as the basis for the generation of the

ephemeris information to be included in the user navigation message. At the RC itself, the tracking data may be used to improve the predicted orbits in semi-realtime (Section 8). The transmission of the full set of tracking data acquired during all passes over all RCs to the MC would put a heavy burden on the communication links. From the orbit determination point of view, the transmission of such large sets is also completely unnecessary, since, in principle only 10 to 20 well-distributed good-quality observations per pass are required. Therefore, in[5] a technique is proposed in which the original tracking data for each pass are compressed into a small number of quasi- observations, such that the full information content of the original measurements is preserved.

This technique takes advantage of the fact that the motion of a satellite is a smooth process, that does not lead to significant high-frequency variations in the satellite's state-vector during a pass over an RC. This means that the series of range measurements of a complete pass can be approximated by a relatively smooth function. Only a small number of synthetic observations derived from that function, as well as their corresponding statistical information, have to be transmitted to the MC. It was demonstrated in[5] that this kind of data compression can be accom- plished by fitting a 10th to 14th degree polynomial to the squares of the range measurements. For tracking

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time spans of up to 200 min, a polynomial o f degree 10 is sufficient; for longer periods the degree must be raised by 2 for each additional 200 min.

The fitting function is evaluated at specially selected times and subsequently these values and the deviation of the true observations from the fitted polynomial are used to generate so-called normal points and the variances o f these synthetic observations. Such normal points have the property that, in principle, they are uncorrelated, so that the full information content can be represented by the time of each normal point, and the synthetic range and its standard deviation at that time. So, for a polynomial o f degree 12, which leads to 13 normal points, a total o f only 39 quantities has to be transmitted. C o m - paring this to the n u m b e r o f original measurements it is clear that by this technique a data compression factor of 600 or so is realized.

It is shown in[5] that, irrespective of the presence of realistic dynamic model errors, the orbits computed from the created normal points very closely resemble the orbits computed from the full-rate measurements. The m a x i m u m differences over a period of 2 days were found to be less than 10cm, which is completely negligible for the orbit determination o f the N A V S A T satellites.

7. ORBIT COMPUTATION ACCURACY In the equivalent error budget for a pseudo-range measurement taken by a user o f the N A V S A T system, a value o f 1.5m was adopted for the contribution of the satellite ephemeris error (Table 3). F r o m a simple geometrical analysis it can be found that a 1.5 m rms ephemeris error contribution to the U E R E can be reached if the rms orbit errors remain below 1.1 m in the radial satellite position c o m p o n e n t and below 3.6 m for the cross-track and along-track position components. The overall orbit c o m p u t a t i o n scheme should therefore be designed such that these high orbit accuracy requirements can be met. It was found that this is a very critical aspect in the N A V S A T concept, and therefore a large part of[5]

is devoted to the analysis of the achievable orbit accuracies.

At the M C the normal points received from all RCs are combined for each satellite into data arcs of suitable length, which are then processed to determine the best fitting orbit for each individual satellite. In general, the orbit determination accuracy is dependent on the accuracy o f the measurement and dynamic models used in the orbit computations, the accuracy and spatial distribution of the tracking data and the length of the data arc. F o r very short arcs the measurement parameters, such as the atmospheric refraction models, may be the d o m i n a n t error source, while the effects of dynamic parameters, such as the solar radiation pressure, will become d o m i n a n t for longer arcs.

The estimated orbit forms the basis for an orbit prediction over a period of a few days after the time of the last observation processed. Suitable parameters describing the predicted orbits of all satellites are subsequently transmitted to the RCs, where they are used to compute a reference orbit for each satellite during each pass over those stations. It will be clear that the orbit prediction starts from a state-vector derived from the orbit determination, and that the accuracy of the predicted orbit is dependent on the accuracy of this initial state-vector, the accuracy of the dynamic models applied in the orbit prediction and the length of the prediction interval. In general, the orbit prediction errors will steadily increase with time. In[5] the details of orbit determination and prediction error analyses are discussed and results are presented for tracking data arcs of 1, 2 and 5 days, each followed by a 5-day orbit prediction period. Here, only some results are summarized for the case of a 2-day orbit determination period which was found to give the best results.

A summary of the adopted measurement and dynamic error models is given in Table 4. It is emphasized that in order to ease the interpretation of the orbit determination results, in the simulations only the orbit state at epoch was considered a solve- for parameter. In reality, in addition to this epoch

Table 4. Error parameters for the orbit determination and prediction error analysis

Estimated parameters

Unadjusted measurement errors

Unadjusted dynamic errors

Number of error parameters

• orbit state at epoch

• station coordinates--10 cm in each local X, Y, Z • pole position--0.002 arcsec in Xp, Yp

• station tidal uplift--10% of the effect • measurement noise---5 cm

• measurement bias---30 cm; randomly assigned to 50% of the stations

• tropospheric refraction--3% of the effect; randomly assigned to 50% of the stations per day • ionospheric refraction--2% of the effect at 1.6 GHz • gravity field--40% of the difference between the GEM-9 and

GEM-L2 models, both truncated at degree and order 15

• gravitational parameter--4).01 ppm

• earth and ocean tides--10% of the k 2 solid-earth effect *direct solar radiation--l%, 11% or 3% of the effect • albedo radiation--20% of the effect

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The ESA NAVSAT system concept 203 Table 5. Contributions of the individual error sources to the orbit errors for an arc consisting of a 2-day orbit determination period followed

by a 5-day orbit prediction. Listed are the rms values of the radial/cross-track/along-track position errors in centimeters Days

1 and 2 Day 3 Day 4 Day 5 Day 6 Day 7

Error source determination p r e d i c t i o n p r e d i c t i o n p r e d i c t i o n p r e d i c t i o n prediction

Gravity field 3/7/12 7/12/60 11/15/153 1 4 / 1 9 / 2 9 0 1 8 / 2 3 / 4 7 1 22/27/695

Gravit. parameter 7/30/27 7/30/67 7/30/112 7/30/157 7/30/203 7/30/249

Direct solar radiation 30/24/62 110/26/251 213/26/477 318/26/710 423/26/945 529/26/1181

Albedo radiation 0/0/1 1/1/8 1/1/21 1/1/40 2/1/65 2/1/96

Earth and ocean tides 0/1/0 0/2/2 0/3/4 0/4/6 0/4/8 0/5/9

Pole position I/7/9 1/7/10 1/7/18 1/7/27 1/7/36 1/7/46

Station coordinates 4/30/26 4/30/43 4/30/62 4/30/83 4/30/104 4/30/126

Station tidal uplift 0/1/2 0/1/3 0/1/5 0/I/6 0/1/7 0/1/9

Tropospheric refraction 2/19/I 1 2/19/28 2/19/46 2/19/65 2/19/83 2/19/101

Ionospheric refraction 4/36/26 4/36/71 4/36/115 4/36/159 4/36/204 4/36/248

Measurement noise 0/3/4 0/3/7 0/3/10 0/3/14 0/3/17 0/3/21

Range bias 4/48/21 4/48/47 4/48/77 4/48/107 4/48/138 4/48/168

Overall(rss) 32/80/82 111/82/285 213/82/538 318/83/814 424/84/1113 530/85/1437

state-vector always a n u m b e r o f other parameters, like force scaling factors, etc., will be solved for to achieve the best orbital fit. To approximate this actual practice with the simpler a p p r o a c h adopted for the simulations, the solar radiation pressure model error was valued such that it represents a residual error after the adjustment o f a radiation pressure scaling factor during the processing of the tracking data. F o r the orbit predictions and for the 1-day orbit determination the residual solar radiation pressure error was assumed to equal 3% of the modeled solar radiation pressure. F o r a 2-day' orbit determination arc (the only one for which results are presented in this paper), the residual error was set at 1.5% of the modeled solar radiation pressure; for the 5-day arc an error level of 1% was adopted. All simulations were performed for a N A V S A T satellite having a solar radiation reflection coefficient of 1.2 and a cross- sectional area-to-mass ratio o f 0.01 m2/kg. It was assumed that the satellite was in an orbit with the parameters listed in Table 1.

Table 5 presents a summary o f the contributions of all error sources to the errors in the satellite's radial, cross-track and along-track position components. The first c o l u m n lists the rms o f the errors in the position components during the 2-day orbit determination period; the next 5 columns list the rms orbit errors for each consecutive day of the prediction interval. T o compress the large a m o u n t o f information available, the contributions of various individual error parameters belonging to the same class o f error sources were combined in an rss sense. So, for example, the listed contribution o f the station coordi- nate errors is the rss o f the contributions of all individual errors in the 18 station position components. Similarly, the tropospheric refraction model

error contribution is the rss o f 8 separate

contributions o f the r a n d o m l y selected daily error parameters per station.

The Table clearly reveals that the solar radiation pressure model produces the largest radial and along- track errors during the orbit determination and in the orbit prediction as well. In the orbit determination phase, errors in the earth's gravitational parameter,

the modeling of ionospheric refraction, station coordinates and measurement biases also cause significant orbit errors. During the subsequent 5-day orbit prediction period, the contributions of various error sources to the radial and along-track position components grow significantly.

The evolution of the errors in the satellite position components, generally, will show a secular trend upon which various types of periodic variations are superimposed. It is the secular trends that d o m i n a t e the growth o f the orbit errors with time. T o visualize this increase with time, the daily rms errors in the position components m a y be represented by a s m o o t h fitted curve. In Fig. 5 such time-histories o f the smoothed errors in the radial and along-track position components due to a few specific error sources are plotted for the 5-day orbit prediction period. The curves for the measurement error contributions refer to the propagation into the orbit prediction o f the contributions o f all types of measurement errors in the orbit determination phase to the errors in the state-vector from which the orbit prediction starts. The figures clearly underline the importance o f deriv- ing accurate models for the solar radiation pressure acting on the N A V S A T satellites. To keep the model errors small, the satellites should preferably be designed such that the variations in their surface geometry are as small as possible when viewed from different directions, and that the surface reflection characteristics are as uniform as possible.

Table 5 and Fig. 5 indicate that the daily rms overall radial error increases from 0.3 m in the orbit determination phase to more than 5 m after 5 days o f orbit prediction; the daily rms along-track error increases from 0.8 m to more than 14 m in the same period. This corresponds to error growth rates of about 1 m / d a y and 3 m / d a y in the radial and along- track directions, respectively. In the cross-track direction the daily rms orbit error remains constant at about 0.8 m over the whole period. The errors occur- ring after 5 days o f orbit prediction will obviously yield a m u c h larger ephemeris error contribution than the 1.5 m assumed in Section 4 for the user ranging error budget. As a consequence, orbit errors may A.A. 15/4--B

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I I I I / 0 = G R R V I T T F I E L D / A = G R R V I T R T I O N A L PARAMETER 7 " + - SOLAR R R D I R T I O N / X = RLBEDO RADIRTION ~ " : SOLID ERRTH T I D E S / 0 ~ 204 K.F. WAKKER et al. lqqO 2880 q320 5760 7200 TIME (?IIN) 0 = G R R V I T T F I E L D = G R A V I T R T I O N R L PARAMETER + = SOLAR R A D I A T I O N X = ALBEDO R A D I A T I O N / = S O L I D EARTH T I D E S f = MEASUREMENT O ~ :" -'" - , - , , , O lqq0 2B80 q320 5760 7200 TIME (MIN) Fig. 5. The variation of the smoothed daily rms radial (left) and along-track (right) position component errors during the 5-day prediction period following the 2-day tracking data arc, due to measurement model

errors and some individual types of dynamic model errors. become a major error source which will seriously

degrade the user positioning accuracy, unless shorter orbit prediction intervals of about 1 day are applied. Such short prediction periods, however, might pose serious problems with respect to the time-contraints of the orbit computation efforts at the MC and the communications between the MC and the RCs. Therefore, a strategy was developed, in which the MC generates orbit predictions only once every week and the RCs improve these predicted reference orbits using their own tracking data.

8. SEMI-REALTIME ORBIT I M P R O V E M E N T

When a NAVSAT satellite is under control of an RC, that station acquires high-precision two-way dual-frequency range measurements of the satellite. In principle, these measurements can be used to improve the orbit of the satellites. Such an orbit refinement process will actually be based on the minimization of the differences between the actual range measurements and their computed counter- parts, which follow from the predicted ephemeris and the known position of the tracking antenna. For a number of operational reasons, it would be advan- tageous to perform a semi-realtime orbit improvement. This requirement quite naturally leads to the selection of an extended Kalman filter process. The application of this process to the NAVSAT orbit improvement is discussed extensively in[5] and the results of numerical experiments are given there.

The basic scheme proposed in[5] is that during a satellite pass over an RC that RC processes its own

two-way ranging data with a Kalman filter technique. Before that RC hands over the control of the satellite to the next RC, it transmits the last best estimate of the satellite's state and its covariance matrix to that next RC. There, this information can be used during the transition phase, in which both RCs view the same satellite, to generate improved ephemerides, from which the navigation message to be sent out by that RC will be derived. During the pass over that RC again a local Kalman filter process will be applied to improve the orbit and, just as during the transition from the first to the second RC, the final estimate from the filter is transmitted to the third RC. By transmitting both the final estimate of the state- vector and the state covariance matrix to a next RC, all information in the measurements that has gradually accumulated during one pass becomes available to the filter process at the next RC. As that next RC will, generally, view the orbit from a different angle than the previous RC, its range measurements may provide additional information for those position and velocity components which could not be determined too accurately from the measurements of the previous RC. Thus, successive passes over different RCs may gradually lead to state estimates with the highest possible accuracy in all directions. This accuracy, in fact, is limited only by the accuracy of the measurement and dynamic models applied in the orbit computations. In principle, this sequence of local orbit improvements could lead to a stable around- the-world Kalman filter orbit estimation process for all satellites. However, the complexity of the computations that would have to be performed in real-

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Fig. 6. The ground track of the NAVSAT satellite used for the Kalman filter simulations. Indicated are the 6 segments corresponding to the measurement taking periods of the different Regional Centers.

time is so large that it probably would render this solution impractical. Therefore, a more appropriate approach is to perform the complex computations off-line at the MC and to distribute accurate predicted reference orbits to be used by the local Kalman filters. This also provides a safeguard against the occurrence of filter divergence which would otherwise be difficult to detect.

In one of the numerical experiments oti5 ] the around-the-world scheme has been simulated. The bssic approach was to generate simulated range observations for all passes of a single NAVSAT satellite over the RCs during a l-day period. All observations below a 20 deg cut-off elevation for each station were eliminated. A further restriction was that in case of overlap a pass was considered ended when the satellite moved closer to the next RC than it was to the RC controlling it up to that time. Figure 6 shows the visibility masks of the RCs for a cut-off elevation of 20 deg, and, plotted along the ground track of the satellite, the 6 segments corresponding to the measurement taking periods of the different RCs. The sequence starts with the satellite under control of Kourou. Subsequent data taking occurs during passes over the RCs at Porto Alegre, Libreville, Sri Lanka, Orroral and Hawaii.

The simulated observations were generated with the GEM-9 gravity model, truncated at degree and order 6, while the observations were processed with the GEM-9 gravity model truncated at degree and order 3. The purpose of the difference between the two models is to simulate the errors in the full dynamic model which will be used in real orbit computations. In this way, an error level correspond-

ing to unmodeled accelerations of the order of 0.1/~m/s 2 was simulated. The noise level of the measurements was set at 0.6 m. It should be realized that, in contrast to the real-world situation, by this simulation approach the true orbit of the satellite is known. This is the orbit corresponding to the GEM-9 model truncated at degree and order 6. So, when the results of the Kalman filter are compared to this true orbit, the differences indicate the accuracy of the estimated orbit.

Figures 7 and 8 show the evolution of the errors in the radial and along-track satellite position components during the 6 passes. The two thin solid lines in all plots are mirror images of each other and represent the computed standard deviations of the radial and along-track position estimates. The thick irregular broken lines indicate the true position estimate errors. The initial satellite position vector just before the first measurement at Kourou was given an offset of 5 m in the along-track direction, 2 m cross track and I m in the radial direction. These numbers correspond more or less to the errors accumulated after a 1-day orbit prediction (Section 7). The figures demonstrate that already during the first pass over Kourou the orbit errors converge to a level which is well below the initial state error in that direction, and so do the standard deviations. During the passes over Porto Alegre and Libreville the errors increase some- what, indicating that the dynamic model error contributions build up more quickly than the measurements can counteract them. During the transition from Libreville to Sri Lanka, a jump in the errors as well as in the standard deviations takes place, empha- sizing the importance of the continuously changing

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206 K . F . WAKKER et al. :it % - I NAVSRT T O q l 7 6 2 . 1 2 5 0 NJO T I H E I M I N ) o o g t~ 0 ¸ o= N L - ! NRVSRT T O q l T S 2 . ~ s g q HJO J

6

1

122 1 6 3 TIME t H I N ) z % g w 0 g N

|

- I NRVSRT T O ¼ | 7 6 2 . 3 9 1 7 MJ0 " - , - ' V % ' . . " ~ " - . s , . ~ % g == "J 0 g o. - 1 NRVSRT T O q l T S 2 . q O 5 q HJO

;~ ¢o Io~ I,o ]),, ; . . .

T I H [ )HIM) TIME t H I N )

z %

g

! -

-NRYSAT T O q 1 7 6 2 . 7 1 8 8 M J0 ~'~,%IT T O q i T 6 2 , g 3 B 1 MJO

zu

%

~ . . .

TIME (HIM) T I H E t H I N )

Fig. 7. The evolution of the radial position error and the computed standard deviation during the 6 successive passes over Kourou (left top), Porto Alegre (right top), Libreville (left center), Sri Lanka (right

center), Orroral (left bottom) and Hawaii (right bottom).

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z o

©

- 1

NR¥SRT 10 ' 1 7 6 2 . 1 2 5 0 flJO o 1 z o i ° 1 NAVSAT T O , 1 7 6 2 . 2 6 9 ' HJO T I N ( t H I N ) T I N [ t H I N ) 163 I lc o o = t o - I NRYSRT 10 , 1 7 6 2 . 3 9 1 7 MJD T o , 1 " / 6 2 . , I 1 5 , HJO l NRVSRT o ~ O . a . '7 o - 1

;s

;0

I0~

1,0

;,,

~,3

T I H E t H I N ) T I N E t H I N ) 3 , 2 1 ]c o 0 L - I NAYSRT T O , 1 7 6 2 . 7 1 1 1 8 NJO 1 . NRVSRT T o q 1 7 6 2 . 9 3 6 1 N J ° o ~ 0

"

136 ~o,

' r l . E m l m 'fiNe reiN)

Fig. 8. The evolution of the along-track position error and the computed standard deviation during the 6 successive passes over Kourou (left top), Porto Alegre (right top), LibreviUe (left center), Sri Lanka (right

center), Orroral (left bottom) and Hawaii (right bottom).

2 7 2

tracking geometry. Thereafter, it looks as if the process has stabilized. For the cross-track position component similar results were obtained in[5].

As a conclusion it may be stated that the Kalman filter continuous orbit update scheme probably will perform a vital task in the NAVSAT system operations. Provided that there are no large systematic errors in the measurements, the filter will be capable of enhancing the accuracy of the ephemerides in the navigation message to a level that will satisfy the

1.5 m U E R E requirement. The precise way of how such an orbit improvement mode should be imple- mented in an operational system needs further investigations. Some possibilities are already described in[5].

9 . C O N C L U S I O N S

The study on the NAVSAT ground segment characteristics has demonstrated that it is feasible to

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208 K . F . WAKKER et al. develop an efficient and flexible operations scheme

for the tracking o f the 24 satellites, the transmission and processing of the tracking data, the orbit computation, the distribution o f orbit information and the transmission of navigation messages. At the 6 RCs, which perform the continuous tracking o f the satellites and the uplinking of user navigation messages, special attention should be given to the compression of tracking data and the local semi-realtime orbit improvement when a satellite passes over an RC. The requirement of having precise orbits o f the satellites a few days in advance implies that the satellites should be designed such that the solar radiation pressure can be modeled as accurately as possible. A l t h o u g h some aspects have to be in- vestigated in more detail, the present study has proven that the accuracy o f the orbit computations will satisfy the requirements specified by the user positioning accuracy goals and that the ESA N A V S A T concept may be an attractive civil alternative for the U S military N A V S T A R / G P S system. Acknowledgements--The authors wish to give special thanks to H. J. D. Piersma, T. van der Ploeg and E. J. O. Scbrama for their contributions to the part of the study performed by Delft University of Technology (DUT). They also acknowledge the many fruitful discussions with L. J. M. Joosten, O. B. M. Pietersen and H. F. A. Roefs of the

National Aerospace Laboratory (NLR). The study was carried out under ESA contract 5501/83/F/RD, with DUT acting as subcontractor of the NLR. The ESA and NLR study managers were H. Laue and H. F. A. Roefs, respectively. We thank both organizations for the approval to publish some results of our analyses.

REFERENCES

1. T. A. Stansell, The TRANSIT Navigation Satellite System. Magnavox, Torrance, Calif. (1978).

2, Various authors, GPS special issue, Navigation, Vol. 25, No. 2, summer (1978).

3. C. Rosetti, Prospects for NAVSAT--A future worldwide civil navigation satellite system, ESA Bulletin, no. 30, May 1982, pp. 54-59; also: NAVSAT, a worldwide civil satellite navigation system, 34th IAF congress, paper IAF-83-90, Budapest, October (1983). 4. L. J. M. Joosten, P. J. de Pagter, O. B. M. Pietersen,

J. J. Renes and H. F. A. Roefs, Study of NAVSAT control segment characteristics, Part 1: Elements of a control segment concept, National Aerospace Labora- tory, Report NLR TR 84086 L part 1, Amsterdam (1984).

5. K. F. Wakker, B. A. C. Ambrosius, H. Leenman, R. Noomen, H. J. D. Piersma, T. van der Ploeg and E. J. O. Schrama, Study of NAVSAT control segment

characteristics, Part 2: Orbit computation aspects,

National Aerospace Laboratory and Delft University of Technology, Report NLR 84086 L part 2, Amsterdam and Delft (1984).