Gps

Table 3.5.1

GPS Constellation Status: 1 January 2000 00:00:00.000 GPS-Time

Orb./Plane S/C a e i il u ui +■ M \an (des.) (j Position PKK type Clock (km)_(deg.) (des.) (des.) (des )_

A-l

09

IIA

Ce

26559.3

0.009K

54.0

175.7

32.3

103.0

127.0

-53.0

A-a

25

IIA

Cs

26561 7

0.0078

53.6

173.5

232.9

356.0

71.9

-108.1

A-3

27

IIA

Cs

26559.3

0.0137

53.9

174.7

I9S.3

212.2

1.1

-178.9

A-4

19

II

Rb

'26560.0

0.0053

53.1

172.4

203.6

233.8

12.0

-168.0

A-5

OS

IIA

Kb

26.533.7

0.0086

54.8

178.2

102.1

148.2

152.2

-28.0

B-l

22

IIA

Kb

26553.9

0.0123

53.5

233.7

30.5

278.4

92.6

-87.4

B-2

30

IIA

Cs

26562.8

0.0056

54.1

233,7

83.8

3.5

137.2

-42.8

B-3

02

II

Cs

26561-3

Ü.Ol 94

53.6

232.9

236.7

140.7

24.3

-155,7

B-4

Q5

IIA

Cs

26562.0

0.0019

S3.7

234.0

9.5

38.6

153,3

-26.7

C-l

OS

IIA

Cs

26558.9

0.0068

54.5

297,2

222.1

306.4

170.8

-9.2

0-2

03

IIA

Cs

26361.2

0.0010

54.1

294,8

72.8

207.5

118.6

-61.4

0-3

31

IIA

Cs

26561.7

0.0092

54.6

295.4

45.7

175.0

102.7

-77.3

0-4

07

IIA

Ca

26559.5

0,0109

54.6

295.4

239 7

75.1

53.6

-126.4

D-l

24

IIA

Rb

26501.1

0,0090

56.5

358.4

261.4

325.4

61.7

-118.3

D--2

15

II

Cs

26555.5

0.0073

56.3

0.2

85.8

118.6

139.2

-40.7

D-3

17

II

Cs

26558.9

0 0113

56.4

2.5

167.5

224.5

14.7

-165.3

D-4

04

IIA

Rb

26562.0

0.0053

56.0

357.8

323.0

0.5

78.4

-101.6

D-3

11

IIR

Os

26559 3

0.0029

.53.0

355.2

183.8

101.0

125.8

-54.2

E-l

14

II

Os

26562-1

0.0005

.56.1

59.3

123.5

31.4

155.0

-25.0

E-2

21

II

Os

26553.9

0.0160

55.7

56.9

211.5

130,0

22.5

-157.5

E-3

L0

IIA

Os

26557.3

0.0038

55.8

56.5

353.0

256,6

84.7

-95.3

E-4

23

IIA

Os

26562.3

0.0145

55.9

59.2

249.3

163,6

41.8

-138.2

E-5

16

II

Cs

26562.3

0.0044

55.9

59.5

19.6

355,5

137.2

-42.8

P-l

01

IIA

Cs

26568.4

0.0048

55.0

117.9

238.8

333,0

5,7

-174.4

F-2

2S

HA

Rb

26562.3

0.0116

55.2

116.9

2.1

180.0

106.9

-73.1

F-3

IS

n

Cs

26559.2

0.0076

54.4

114.0

107,0

II 7.9

162.7

-17.4

F-4

23

IIA

Rb

26358.6

0,0073

55.0

115.3

248.2

81.0

56.3

-123.7

F-8

13

IIR

Rb

26558.7

0,0022

55.2

116.5

322.6

244.1

130.7

-41.3

The peculating orbit elements are expresiied in ,12000. PRN is the GPS identifier, Cs denotes cesium and Rb is :;.!S/C Type identified I i Hat el lite design type, and Aan is longitude of the ascending node.

The peculating orbit elements are expresiied in ,12000. PRN is the GPS identifier, Cs denotes cesium and Rb is :;.!S/C Type identified I i Hat el lite design type, and Aan is longitude of the ascending node.

The discussion in this section also applies to the current Russian navigation satellite system, known as GLONASS (Global Navigation Satellite System) and the future European Space Agency GALILEO (planned for operation by 2008).

Both satellite constellations use three orbital planes with about 10 satellites (including spares) in each plane (GALILEO). The GLONASS satellites use a 63° inclination and orbit periods of 11 hours 15 minutes. GALILEO satellites are expected to use a 56° inclination with an orbit period of 14 hours 22 minutes. Each GLONASS satellite broadcasts on a different frequency in the L-band, but GALILEO will have broadcast characteristics similar to GPS.

A Block II GPS satellite is illustrated in Fig. 3.5.1. The transmit antenna is the array shown on the main body of the spacecraft with the helical windings. The large panels on both sides are the solar panels used to generate power. Each satellite carries standard quartz frequency standards, as well as multiple atomic frequency standards (two cesium and two rubidium). In fact, a tunable quartz standard is used to excite the cesium standard, for example, at the natural frequency of 9,192, 631, 770 Hz. It is this frequency that, in fact, defines the SI second.

The carrier frequencies are derived from the frequency standard in use (cesium, rubidium, or quartz), but additional information is superimposed. A simple analogy can be drawn with a common radio where a carrier frequency is used (e.g., 100 MHz) to carry the audio (< 20, 000 Hz). In this example, the transmitter superimposes audio on the carrier, and the receiver extracts the audio signal when the radio is properly tuned to the carrier frequency. In the case of GPS (or GLONASS), the information superimposed on the carrier includes ranging codes and other data necessary to perform the navigation function offered by the satellite constellation.

GPS uses several ranging codes, though they have many similarities. In concept, the ranging codes are generated as pseudo-random noise (PRN). Consider the PRN code to be a series of binary digits (bits)—001101011100—ir example, superimposed on the carrier. Each bit, known in GPS terminology as a chip, has a specific time duration depending on the code. The PRN bit sequence is determined by a documented algorithm. Each bit in the sequence will be transmitted by the satellite at a specific time determined by the satellite clock (which is derived from the frequency standard). Hence, as the receiver extracts the bit sequence from the carrier, it will assign receive times to each bit based on its own clock. With the ability to replicate the PRN code, the receiver will cross-correlate, or align, the received bit sequence with the sequence it is able to generate. Since each bit has a known transmit time, the difference between receive time and transmit time is obtained by this cross-correlation; that is, the quantity — in Eq. (3.3.1) is determined, as well as the individual times, and . Note that the time when each bit in the code is transmitted is determined by the satellite clock, so the time is based on the satellite clock. Similarly, the time when the bit is

Figure 3.5.1: Block II GPS satellite. The satellite solar panels rotate about the axis mounted perpendicular to the main body (spacecraft bus) and the transmit antenna array, shown with the helical windings in the center, is directed toward the Earth's center. The antenna transmit pattern encompasses the visible Earth. A body-ix ed set of axes includes a y axis coincident with the solar panel axes and a z axis directed toward the Earth's center. The spacecraft can present the maximum cross-sectional area of the solar panels to the Sun by rotating the bus about the z axis (yaw) and rotating the solar panels about the y axis.

received, tR, is determined by the clock in the receiver.

The PRN codes currently transmitted by the GPS satellites are:

• C/A (Coarse Acquisition): This code uses 1023 bits and repeats every 1 ms. The algorithm for generating the sequence is described in detail by Hofmann-Wellenhof et al. (1997). Each bit requires about 1 microsec for transmission or about 300 meters in distance. One major purpose of this code is to facilitate acquisition of the P-code, which is a much longer bit sequence. Since the C/A code repeats every millisecond, an ambiguity exists between each millisecond interval. In other words, there is no information about absolute time within the C/A code. Resolving this ambiguity to determine the correct time interval requires additional information (e.g., information broadcast by the GPS satellites about their position).

• P (Precise): This code has a much longer duration of 37 weeks before it repeats. But this long repeat interval is divided into one week segments and each segment is assigned to a specific GPS satellite. Each satellite, in turn, repeats its assigned code each week. The duration for each bit is the equivalent of 30 meters in distance, corresponding to a transmission rate of 10.23 x 106 bits per sec. All information about the P-code is readily available. Most receivers use the C/A code for initial acquisition, then transition to the P-code. Since the P-code within each satellite does not repeat for one week, direct cross-correlation without use of the C/A code is challenging. Direct P-code acquisition is easier if the receiver has an accurate clock.

• Y: This code is generated from the P-code, but a classifed code (W-code) is used to mix with the P-code. This mixing produces an encrypted P-code. When the Y-code is being transmitted, it is said that Anti-Spooing (AS) has been invoked. The terminology arises from the military consideration that an adversary could transmit false P-code signals to confuse, or spoof, a receiver. When AS is used, the classifed Y-code avoids this possibility.

In the GPS satellites known as Block II, including Block IIA and Block IIR, the C/A code is transmitted only on L1 and the P/Y codes are transmitted on both L1 and L2. As a consequence, receivers capable of operating with only C/A are single-frequency receivers. Without the second frequency, the ionosphere correction cannot be made as accurately as measurements obtained with two frequencies, since it must rely on less accurate ionosphere models. Modern dual-frequency receivers are available that may be capable of correlating directly with the Y-code or they may use signal processing techniques, such as cross-correlation of the Y-code on the two frequencies to obtain the ionosphere delay. The method based on advanced signal processing effectively provides a dual-frequency measurement without knowledge of the Y-code. A pseudo-measurement usually is created by adding the measured ionosphere delay to the C/A pseudorange.

Geodetic Marker

Figure 3.5.2: Typical GPS antenna setup. A choke-ring antenna is shown on the left and the antenna set up with a tripod over a geodetic marker is shown on the right. The height of the antenna reference point (ARP) above the geodetic marker is usually made to high accuracy with a geodetic-quality graduated ruler. The antenna phase center locations, denoted by L1 and L2, are separately calibrated.

Geodetic Marker

Figure 3.5.2: Typical GPS antenna setup. A choke-ring antenna is shown on the left and the antenna set up with a tripod over a geodetic marker is shown on the right. The height of the antenna reference point (ARP) above the geodetic marker is usually made to high accuracy with a geodetic-quality graduated ruler. The antenna phase center locations, denoted by L1 and L2, are separately calibrated.

A typical GPS receiver antenna installation is shown in Fig. 3.5.2, which shows a choke-ring antenna on the left. The choke ring is designed to reduce the effects of multipath, a phenomenon that occurs when the incoming GPS signal is refected from nearby objects, such as buildings for a ground receiver. The refected signal travels a longer path to the antenna, thereby introducing another error source into the measured signal. The choke-ring antenna is used for both ground-based and space-borne installations.

The relationship between the measured ranges and the satellite state requires the specific ation, or estimation, of the receiver antenna location. For precision orbit determination, the coordinates of the antenna shown in Fig. 3.5.2 must be known or determined in an appropriate reference frame. Furthermore, the reference point to which those coordinates refer and the specific point to which the range measurements are made are required. The antenna usually is described with a phase center, the point to which range measurements refer. This phase center usually is obtained by empirical testing, including testing in anechoic chambers. Such testing determines the phase center pattern for a particular antenna. Experi ence has shown that such patterns are common to a particular antenna type so that the test results of a subset may be applied to other nontested antennas.

For some antennas, the phase center pattern may be azimuthally symmetric, but may exhibit change as a function of elevation. For precision applications, the characteristics of the phase center variation must be known, as well as the location of the phase center even if it is invariant. Furthermore, in some cases, the coordinates published for a particular antenna may refer to a specific point other than the phase center, usually referred to as the antenna reference point (ARP). In these cases, the correction to the phase center must be separately applied. It is important that the specific point where a priori coordinates for the antenna should be applied is understood. To further complicate matters, the phase center for Li is usually different from the location for L2. As shown in Fig. 3.5.2, the location for the L1 phase center is ¿i with respect to the ARP and the location of the L2 phase center is ¿2.

The precision of GPS pseudorange measurements is receiver dependent, but most modern receivers are at the level of about 1 meter for P-code pseudorange. Note that the combination of two measurements made at different frequencies to remove ionosphere effects will produce a noisier measurement (Eq. 3.4.14). Although the precision of the pseudorange is meter level, the accuracy of the measurement is usually not comparable. For example, pseudorange measurements may be negative because of unsynchronized clocks, a clear indication that a measurement may be precise, but not accurate. Nevertheless, the correction for clock errors can be determined through appropriate estimation strategies and the corrections obtained from them will render the measurement accurate, as well as precise. As a means to control the accuracy of pseudorange measurements, the GPS satellite clocks may be dithered. This dithering produces clock errors that cannot be accounted for without access to Department of Defense classified information. When clock dithering is activated, it is said that Selective Availability (SA) has been invoked. Unclassified techniques to remove SA will be described in Section 3.6, but SA was deactivated in May, 2000.

The pseudorange measurement given by Eq. (3.3.9) can be expanded for either L1 or L2 to give p = p + c(¿ÍR - ¿Ít) + fytrop + ¿Pion + e (3.5.1)

where p is the measured pseudorange, p is the true range between the true transmit time and the true receive time, ¿ír is the receiver clock difference with true time, ¿ít is the transmitter clock difference with true time,

¿ptrop is the troposphere delay,

¿pion is the ionosphere contribution, and e represents remaining errors, such as instrument noise.

Computation of the true range, p, would require knowledge of the true GPS satellite position and the true receiver antenna coordinates, as well as the true transmit and receive times. In practice, these quantities may not be known with high accuracy. In the orbit determination problem, for example, the satellite position may be known a priori with an accuracy of several meters. In this instance, the error term e will represent the error between the true range and the computed range formed from the a priori known position. The receiver ability to measure pseudorange is characterized by the instrument's precision, usually at the meter level.

A more precise GPS measurement is based on the carrier phase. With the previously described atmospheric effects, the usual form of the phase, expressed as range and similar to Eq. (3.5.1), can be obtained from Eq. (3.3.26). For either L1 or L2, it can be shown that

® = p + c(5tR- StT) + \N + ¿Ptrop - ¿Pion + e (3.5.2)

where

$ is the measured phase range for the specifed frequency,

A is the wavelength of the signal (L1 or L2),

NV is the integer phase ambiguity, and the other terms were defined with Eq. (3.5.1).

Note that the raw phase measurement, provided by a receiver consists of the accumulated integer cycles since a reference time, plus the fractional part of a cycle. The measured phase range is

but in some receivers the expression may require $ = — A<^>.

For comparison with pseudorange, the precision of phase range is usually characterized at the several millimeter level. If the GPS receiver is carried on a satellite, the term ¿ptrop is zero and Spion may be sufficiently small to neglect. Even at 1000 km altitude, the ionosphere contribution is at the decimeter level. The phase range from L1 and L2 can be combined to remove the ionosphere contribution using the same approach applied to pseudorange (Hofmann-Wellenhof etal., 1997).

In applications of GPS measurements to the determination of an orbit of a low Earth orbiter (LEO), such as described in Section 3.7, the positions of the GPS satellites must be known or determined. One option is to apply the techniques of estimation described in the following chapters to the determination of the orbits of the GPS satellites using a network of ground stations. In some cases, the GPS satellite orbits may be determined simultaneously with the orbit of a LEO, but in others the GPS satellite orbits may be iX ed to orbits determined by other sources.

The GPS ephemerides can be recreated using information broadcast by the satellites in near real time. These broadcast ephemerides can be generated from 16 parameters (navigation message or ephemeris parameters) based on Keple-rian orbit elements and coefficients of terms that represent time dependency (see Hofmann-Wellenhof et al., 1997) . The set of broadcast parameters applies to a specific interval of time, typically two hours, and new sets of parameters are broadcast automatically by a GPS satellite as the applicable time interval changes. The accuracy of the broadcast ephemerides generally is regarded to be at the 10-meter level. The primary intent is for the broadcast ephemerides to support real-time or near real-time applications. The information used to create the parameters broadcast by the GPS satellites is based on determination of the GPS satellite orbits by the Department of Defense using a set of six monitor stations. These monitor stations record pseudorange and carrier phase measurements between the ground-based receiver and the GPS satellite, which are then used to determine the orbits through a process that makes use of the methodologies in the following chapters. The orbits determined by this process are then extrapolated forward in time and the extrapolated ephemerides are approximated with a model based on the 16 ephemeris parameters. The ephemeris parameters are uploaded to the GPS satellites for broadcast during the appropriate time interval.

Precise GPS ephemerides are available with a latency of about one day or longer. These ephemerides are intended to support applications with high accuracy requirements, such as those related to space geodesy. Depending on the application, the position accuracy of a satellite carrying a GPS receiver may approach the centimeter level, while other applications may require an accuracy of ten meters. Two sources of ephemerides are available: National Imagery and Mapping Agency (NIMA) and the International GPS Service (IGS). In both cases, the respective agency operates a ground network of GPS receivers to support the determination of the GPS orbits. In the case of the IGS, an international collaboration of agencies supports a ground network of 200 receivers, somewhat uniformly distributed around the Earth. Seven Analysis Centers of the IGS use a subset of measurements from these receivers to determine GPS ephemerides and the IGS combines these products into a single official IGS product. The IGS fnal product is available with a latency of two to three weeks with an accuracy expected to be at the decimeter level, but a rapid product is available with a one-day latency.

Satellite-to-Satellite Tracking (SST)

Various forms of satellite-to-satellite tracking (SST) are in use. This terminology usually applies to measurements collected between a pair of satellites, but the common terminology enables identification of the respective satellite altitude. If a GPS receiver is carried on a LEO satellite, then the previously described GPS measurements would be categorized as high-low SST measurements. For some GPS satellites, an inter-satellite range measurement is made, known as cross-link ranging, that would be a high-high SST measurement.

A recent example of low-low SST measurements is represented by the Gravity Recovery And Climate Experiment (GRACE). The SST measurements are primarily used to detect components of the Earth's gravitational field and especially gravity variations associated with redistribution of mass. Two low-altitude satellites are used and each satellite transmits signals at two frequencies in the K-band (24 GHz) and Ka-band (32 GHz), but the actual frequencies used by each satellite are not identical. The satellites have approximately the same 500-km altitude and are in the same orbit plane, but separated in the along-track direction by about 200 km. Each satellite carries a GPS receiver, but these receivers have been mod-ifed to track both the GPS signals and the K-band signals transmitted by the other GRACE satellite.

The GRACE SST measurements in the K-band are similar to GPS one-way measurements of carrier phase made in the L-band. Two K-band measurements are made at different frequencies on each satellite to enable a correction for the ionosphere using the technique discussed in Section 3.4.2. The measurements made and recorded by each GRACE satellite are a form of one-way carrier phase similar to GPS. Each GRACE satellite carries an ultra-stable oscillator as the frequency reference (~4.8 MHz) that is used to generate the transmitted signal and to mix with the signal that arrives from the other satellite. Simply stated, each satellite measures the carrier phase signal it receives from the other satellite relative to the signal that it transmits. In an approach similar to measurement differencing (Section 3.6), the measurements collected on each satellite can be added to obtain a measurement that is proportional to the range between the satellites, while at the same time removing long-term oscillator instability. This form of SST measurement has been termed dual-one-way-ranging. The measurement and instrumentation has been described by Dunn et al. (2003).

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