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GPS-Based Geodesy Tracking: Technology Prospects for the Year 2000 W. G. Melbourne Jet Propulsion Laboratory California Institute of Technology Pasadena, California 91109 INTRODUCTION The twenty-first century is a scant dozen years away, too near for many landmark advances in technology, yet long enough for a few surprises to emerge. To put it into focus one need only look backwards 12 years to the way things were in 1976, the year of our bicentennial. The Navstar/Global Positioning System (GPS) program had already been underway for two years. Meanwhile, we are still awaiting the launch of the first Block II satellite, which will mark the onset of the GPS operational phase. Of course, history is laden with inaccurate predictions of future technology trends based on current knowledge. My message is really ambivalent. Don't expect too much progress in the decade of the 1990s; on the other hand, do expect some surprises because technology often advances in quantum jumps. In the case of GPS, the evidence today unmistakably suggests future trends for high accuracy geodesy and Earth satellite tracking. Given the current performance of GPS, particularly on regional baselines, one can say that GPS has arrived. Its attributes of high accuracy and relatively low cost make it the geodetic technique of choice in the l990s for most of the regional deformation studies that require high temporal and spatial resolutions. It has even greater potential for the future. I would like to discuss this potential in terms of: a. future accuracies of GPS geodetic systems, b. future costs for data acquisition equipment, operations and data analysis, and c. future applications in ground and satellite geodesy. PROSPECTS FOR MILLIMETER ACCURACIES IN GPS-BASED GEODESY What are the limiting error sources today for GPS systems and what are the prospects for their improvement? I think that we should take our cues on these questions from experience with VLBI. The horizontal accuracy from Mark VLBI III systems ranges from around 1/2 - 1 cm on regional baselines to 1 - 1-1/2 cm on transcontinental baselines (Clark et al., 1987; see chapter by Rogers) the vertical accuracy is about a factor of 2-3 worse because of tropospheric water vapor errors and limitations of observational geometry, i.e., one cannot observe below 124

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125 one's horizon. Roughly the same ratio between horizontal and vertical appears to hold in GPS accuracies. However, there is some suggestion that the more robust observation scenario with GPS systems, in which GPS satellite and ground receiver clock instabilities are isolated to prevent possible corruption of baseline estimates, yields better accuracies in the vertical component than are obtained with VLBI. Today's evidence (Blewitt et al., 1988) supports the position that GPS horizontal accuracies are comparable to VLBI accuracies on regional baselines. For example, Figure 1 shows the agreement between GPS and VLBI-determined baselines over a range of lengths up to 2000 km for several measurement campaigns spanning 1985-1988. Centimeter-level agreement is the norm for regional baselines. On transcontinental baselines, GPS systems are not quite as accurate as VLBI because of current limitations in the control of GPS reference system errors, which should be remedied in the near future with stronger GPS fiducial and/or global tracking networks. The principal errors limiting GPS performance today arise from: a. mix-modeling and/or mix-calibrating the propagation media, b. antenna multipath, c. antenna phase center variability, and d. reference system errors including the terrestrial reference frame, limitations in alignment with VLBI and SLR frames, and the GPS satellite ephemerides. I will now summarize the present status of these error sources and try to estimate their future course in the 1990s. To reach the millimeter level will also require dealing with error sources that are presently masked by these ''tall poles'' cited above. For example, seasonal environmental effects such as ground water variability can certainly affect the height of monuments at the millimeter level in certain soil conditions. Ocean loading is another. GPS satellite multipath will have to be dealt with on longer baselines. I will mainly focus on the current limitations and the prospects for improving them. PROPAGATION MEDIA Tropospheric water vapor is the major error source for VLBI and GPS systems. Small errors can arise from mix-modeling or mix-calibrating the troposphere and the ionosphere. Dry Troposphere. The total zenith delay of the dry troposphere is about 2 m and is readily determined barometrically to a precision of about 1 mm using standard atmosphere models. Departures from hydrostatic equilibrium of the dry component of the troposphere leads to zenith delay mix-modeling that can amount to a few millimeters in certain dynamical conditions. For baselines longer than the correlation length of these departures from hydrostatic equilibrium, differential delay errors will translate into comparable errors in the horizontal

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126 components and into larger errors in the vertical component. Bender (1987) has discussed the potential error arising from the dry component of the troposphere. To reach 1 mm accuracy it may be necessary to utilize synoptic meteorological data under some conditions; improved mapping functions may be required to transfer from the zenith to line- of-sight delays. Ionosphere. There are small departures from the standard dual band plasma frequency correction for group delay and phase advance through the ionosphere. Also, for equatorial and high latitude observations, particularly those made during very high solar activity, ionospheric scintillations can be troublesome. The rapid phase variations and concomitant signal amplitude in the L-band carriers induces tracking errors in-the tracking loops of some receivers and even loss of lock; on the other hand, some receivers of more recent design are capable of tracking signal frequency accelerations of up to several g's, even in adverse signal conditions, without significant error at the millimeter level. Code-tracking receivers definitely have a big advantage over codeless receivers in weakened and highly variable signal conditions. Consequently, this aspect of the ionospheric problem is likely to improve greatly, even with the high solar activities expected in the early l990s, with the advanced receiver designs expected by then. The other aspect is the departure from the dual frequency correction resulting from ionospheric density gradients and from the small corrections in ionospheric refractivity due to the presence of the geomagnetic field. These effects, which depend on the third and higher degrees in carrier frequency, can amount to several millimeters at low elevations during high ionospheric activity. Another error contribution arises from the residual LCP component of the GPS signal which is about a factor of four below the RCP component. The propagation velocities of the RCP and LCP waves differ slightly in a plasma containing a magnetic field. The rejection of the LCP component by GPS antennas is not complete, typically 10-20 db lower (in power). As a result errors relative to the dual band correction up to a few millimeters can result. Additional modeling based on the dual frequency correction may be required to reach the millimeter level (Clynch and Renfro, 1982~. Water Vapor. Water vapor zenith delays range from 5 cm in dry and cold conditions, upwards to 50 cm in tropical conditions. Water vapor is not in hydrostatic equilibrium. As a result, in situ meteorological measurements to infer total water vapor delay can be in error by as much as 100% of the actual delay; they have fallen into disrepute. Currently, stochastic modeling and water vapor radiometry-based calibration are the only viable techniques for dealing with water vapor. Using the best technology currently available, mix-modeling and/or mis- calibrating the differential water vapor delay at the geodetic sites results in expected horizontal baseline errors that range from a few millimeters to perhaps a centimeter depending on the strategies used, on the local meteorological conditions, and on the length of the baseline (Elgered et al., 19881. At these error levels the correlation length

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127 for water vapor is well below 100 km for many regions (Treuhaft and Lanyi, 1987~. For the vertical component these error levels should be increased by a factor of three. State-of-the-art water vapor radiometers have a stability over several hours of about lK in measuring sky temperature (Jannsen, 1985~. This translates into an accuracy in zenith delay of about 0.5 cm. Short period stability can be somewhat better but this is less important for baseline accuracy than long period stability. Assuming the WVR error can be characterized as a random walk process with an expected error accumulation of 0.5 cm after four hours of tracking, one obtains about 3 mm as the expected error in the horizontal baseline components. A meteorologically benign region, such as the relatively dry western U.S. or even a tropical area with a uniform marine layer, would be characterized by low temporal and spatial variability in water vapor delay. For these regions, an equally successful approach is to stochastically model the tropospheric zenith delay as a piecewise constant random walk or as a first order Gauss-Markov process. The values of the constants in this time series are adjusted in a batch- sequential least squares process in which both the transition from one value to the next and the length of time over which the vertical delay is held fixed are a priori constrained by the stochastic model. By judicious choice of the values of the parameters in the stochastic model, one can obtain baseline repeatabilities that are competitive with those obtained with WAR calibrations (Herring et al., 1989; Tralli et al., 1988~. Whether this approach will prevail in less benign tropospheric conditions with high spatial and temporal gradients such as those sometimes prevailing at Kokee Park, Kauai is undetermined. A general consensus remains elusive on strategies for dealing with the water vapor problem toward achieving 1 mm horizontal baseline accuracy. A major reason for this is that the variability of water vapor delay, both spatially and temporally, is not well understood as a function of locale, season and current meteorological conditions. Of particular concern is the spectral power of the variability at periods of roughly a half hour and longer; these are the components that can partially mimic the signatures of the geodetic parameters in the tracking data and thus corrupt their estimates. Continuously operating arrays of GPS receivers, to be discussed later, offer some promise in developing a data base that should enable one to quantify the spectral properties of water vapor variability and to develop strategies for exploiting this knowledge. Pushing the WVR-based methodology to yield l mm horizontal baseline accuracies will~be a major technological challenge. To achieve this, the current dual channel WAR will have to be expanded to several channels and the sky temperature measurement accuracies improved to O.1K, a tough requirement. Current WAR system temperatures are several hundred Kelvins. Future W7R's using HEMT technology will probably achieve around NOOK, thus, the precision requirement will be around 0.1%. However, the accuracy requirement of O.1K is more stringent

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128 requiring corresponding instrumental and calibration stability over several hours. Further, the retrieval algorithms for inversion of the measured sky temperatures to the water vapor-induced path delay, which involve similar but different integral equations along the line-of- sight, will have to be greatly improved over current algorithms; they are likely to become highly dependent on the region and the local meteorology. Also, mapping functions to map WVR line-of-sight delays to the local vertical or to the GPS directions will need further development. To achieve millimeter-level performance by WVR calibration is going to be very expensive in the short term. Current W7R's cost around $125K and that price is likely to go up unless major strides are made in solid state digital RF systems; that is an ambitious undertaking today at these relatively high frequencies (20-60 GHz). However, if present development trends persist in microwave monolithic integrated circuits (MMIC technology), the mid-l99Os may see virtually all-digital W7R's including digital sampling at these RF frequencies enclosed in a highly stable oven that occupies a volume of less than 106 cm; in addition to costing an order of magnitude less than current designs, it would also promise an order of magnitude improvement in instrumental stability. Using a phased array antenna for sky coverage would also improve performance and reduce cost. Nevertheless, the cost trend for the WAR is likely to move opposite to that of the GPS receiver technology in the early 1990s; the current factor of two in their relative unit cost is likely to grow to ten. Unless their costs can be reduced by an order of magnitude, WAR systems will not be affordable in large numbers and would be concentrated mainly at VLBI fiducial and other sites where the highest accuracy is sought. While it may be theoretically possible for GPS-based geodetic systems to achieve millimeter horizontal baseline accuracies with major capital outlays, as a practical matter we may be mostly limited to accuracies attainable with the stochastic modeling approach. Stochastic modeling will reach an impasse at some accuracy level. The short period (t OCR for page 124
129 ANTENNA MULTIPATH Antenna multipath refers to the perturbation of the received signal due to the presence of reflective objects in the vicinity of the antenna. These spurious signals are characterized by additional delay and usually smaller amplitude relative to the direct signal, and they contain phase shifts. They combine interferometrically with the main signal to cause phase and amplitude variations; these are processed by the receiver and manifest themselves in the measurements as carrier phase and group delay errors. Thus, both the carrier phase and the pseudorange measurements are corrupted by multipath, although in fundamentally different ways. Their manifestation also depends on the signal processing architecture of the receiver. Carrier Phase Multipath. Carrier phase multipath depends on the signal processing scheme used to recover the carrier. For receivers using a half chip early/late gate correlation approach multipath can arise from objects up to distances of 450 m for C/A-based recovery and 45 m for P- code-based recovery. Figure 2 gives an example of multipath in carrier phase measurements. Here, the plots are the post-fit smoothed residuals of double-differenced carrier phase measurements of two GPS satellites from two ground receivers. Ionospheric effects have been eliminated with dual band measurements. The residuals are shown for two separate diurnal passes (an arbitrary vertical offset and the siderial period adjustment in the abscissa are included for illustrative convenience). The ground receivers were TI-4100s with the standard TI-4100 antenna. The RMS variation about zero mean is around 1-1/2 cm. Notice the high degree of diurnal repeatability; the cross correlation function peaks strongly for a zero time lag. Multipath in the carrier phase measurements will certainly have to be dealt with if 1 mm baseline accuracies are sought. It is the long period spectral components of multipath variability, hence, reflections from nearby objects, i.e., roughly 1/2 hour and longer, for which one needs to be concerned. The shorter period components will tend to average out over several hours of observations and will have little corrupting influence on the baseline estimates. The high degree of diurnal repeatability in multipath suggests that a major fraction of it could be calibrated out by building up an empirical template from a number of successive passes.: But one would be vulnerable to 1. The Navstar/GPS Joint Program Office has recently announced that it is considering raising the GPS satellite altitudes about 50 km, which would increase their period by two (2) minutes. This would cause the ground tracks to drift westward 1 degree per day; thus, exact daily repeatability would no longer hold and would be replaced with an annual repetition. Near exact repeatability might occur at intermediate intervals but it would involve different satellites. Although this adjustment breaks an undesirable resonance and results in improved station keeping; however, it would be unfortunate for those wishing to calibrate diurnal multipath effects.

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130 environmental changes around the antenna site during the intervening periods between revisitations with a GPS receiver; these could lead to different multipath signatures and hence, to multipath-induced baseline errors that are different on the two visitations. Thus, short-term baseline repeatability over a few days might be an optimistic measure of long-term repeatability spanning several years of site revisitations. These considerations also lead one to require standardization and configuration control of antenna/backplane assemblies over a span of years because of internal multipath in these systems. Counting on common mode error cancellations is a dangerous game when the outcome depends on the stability of two big numbers that are differenced! Pseudorange Multipath Errors. Multipath error in the pseudorange depends on the dispersive character of the multipath effects across the power spectrum of the pseudorange PRN code. Pseudorange measurements are made by matching local models of the ranging code generated at the receiver with codes being received from the GPS satellite. In general, the received signal is a combination of direct and reflected signals with different delays, phases and amplitudes. The effect of this combined input is to distort the shape of the correlation function between the model and received signals. This shape distortion maps into error in determining the point of maximum correlation and this mapping function will depend on the particular correlation scheme used by the receiver. As an example, for a half chip early/late gate scheme, a peak error of ~5 ns occurs when a multipath signal is present with an amplitude of 0.1 and an additional delay of ~0.5 chip (1 P-code chip = 97 us) relative to the direct signal. Because the effective "wavelength" of P-code pseudorange is two orders of magnitude greater than the carrier wavelengths, the pseudorange mulipath error is typically a factor of 100 greater than carrier phase multipath error. An important exception is the case where the reflecting objects are within 1 carrier wavelength of the receiving antenna. In this case, the carrier phase multipath is reduced by less than order of magnitude relative to pseudorange multipath. Figure 3 illustrates P-code pseudorange multipath effects for a typical environment using a TI-4100 antenna. The integration time for the points in this figure is two minutes; thus, thermal noise is an insignificant contributor to these residuals. Successive daily plots will attest to these residuals being primarily multipath-induced. RMS levels for P-code pseudorange typically are in the 1-2 m range for TI- 4100 measurements; in some cases they are worse, even causing loss of lock; in some cases they are better but rarely, if ever, are they below 50 cm. Multipath errors need not be anywhere near as high as those in Figure 3. With proper care in preparing a site with low multipath environment and with use of advanced antennas and, most importantly, backplane designs, multipath can be reduced by over an order of magnitude. Figure 4 shows the multipath level in a recent experiment

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131 using a Rogue receiver which has a Dorne & Margolin antenna coupled with a choke ring backplane designed at JPL (see insert on Figure 4~. These results are from a single receiver tracking a single GPS satellite whose elevation with time is also shown. Here, the residuals are plotted in the form of two-minute points, the nominal output rate of the Rogue receiver, and also as half-hour running average points. The ordinate on this plot is the linear combination of P:, L: and L2 that eliminates both the ionospheric and range delays, where P: is the L1 pseudorange and L: and L2 are the carrier phase measurements, all expressed in range units. This linear combination should be constant with time; variations are measures of multipath, which for this combination is strongly dominated by that on P:. Also shown are two bands pertaining to performance specifications that we have placed on our antenna/backplane development effort. These specifications can in part be described by the requirement: multipath spectral power shall not cause P-code pseudorange residuals to exceed 30 cm for all periods of five minutes or less, nor exceed 5 cm for all periods of 30 minutes or longer. The latter condition is the most stringent one and the most relevant to baseline recovery accuracy. Except for very low elevations this test amply satisfied our long period multipath requirement. Future innovations on this design are likely to further improve these results. The particular test shown in Figure 4 demonstrates two points: (1) dramatic improvements in multipath can be achieved, so that smoothed P- code pseudorange accuracies below 5 cm appear feasible, and (2) high frequency multipath, which tends to originate from more distant objects, can be averaged down to relatively low levels. The very high repeatability of these residuals on a daily basis (with peak cross- correlation values well over 90% for this particular experiment) also suggests an approach for calibrating multipath effects in a stable environment. The Utility of Pseudorange. A brief digression on the value of high accuracy pseudorange would seem to be in order. Most GPS practitioners make little use of the P-code pseudorange for high accuracy applications. The reasons for this have been, (a) its relatively coarse (meter-level) accuracy, primarily because of multipath and partly because the architecture of the TI-4100 receiver, the standard of the 1980s, through its multiplexing and baseband processing design, resulted in effectively SNR-limited P-code performance, and (b) the uncertain future availability of the P-code on the Block II satellites through possible actuation of the anti-spoofing (AS) function. Receiver manufacturers have exploited that uncertainty by developing systems for the civilian market that avoid use of the P-code, using instead the C/A code to recover L: and various nonlinear detection schemes (e.g., Costas loops, signal squaring, delay and multiply, code enhanced squaring) to recover the second harmonic of L2 and in some cases P1, Pa, L1-L2 and P1- P2. Codeless recovery pays a price in the form of higher SNR-driven measurement errors, which is particularly significant for the P-code, and higher thresholds for signal detection and tracking the L2 carrier. However, receivers of the late 1980s and the l990s are and will achieve nearly an order of magnitude improvement in SNR performance through elimination of multiplexing, use of the P-code, use of double sideband

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132 in-phase and quadrature processing, lower system temperatures, and elimination of interchannel biases through all-digital processing. Moreover, the average received signal strength (C/No) of the P-code modulation from the Block II satellites may be about 3 db higher. The DoD has progressively relaxed and/or clarified its position on the operation of AS over the last several years; its current announced position is that, except in times of national emergency, AS will be off except for periods of test and training which would be scheduled relatively infrequently and announced in advance. The DoD policy on Selective Availability (SA) is another matter to be discussed later; but SA does not normally render inoperative the P-code tracking functions of receivers without decryption capability. However, receivers without decryption capability (i.e., without the so-called W-chip and the crypto-keyed information), regardless of whether they are P-code trackers or not, would not be able to recover the corrections to SA in real-time. The discussion earlier suggests that 5 cm differential P-code pseudorange accuracies or better on 30-minute averages will be attainable for receiver and antenna/backplane systems that are well- designed and well-sited, and that it will be largely available to civilian users. Of what use is this capability given the already very high accuracy of carrier phase data which would easily be accurate to sub-millimeter levels if it were not limited by multipath and the troposphere? A number of applications come to mind. 1. Tracking GPS satellites with dual band carrier phase and 5 cm pseudorange would yield highly accurate global ephemerides obtained with far less tracking per pass than is required today. As a rough estimate, 5 cm is about 1 part in 108 on a baseline between two tracking stations 5000 km apart. If the effect of the satellite multipath on baselines of this length can be controlled or calibrated to 5 cm or better, one would expect to obtain ephemerides from a global network of GPS tracking stations that surpass 20 cm in accuracy, a factor of 5-10 better than today. 2. Carrier phase data that are phase connected, i.e., that have no cycle dropouts, provide range change information to nearly perfect accuracy but cannot measure absolute range unless the cycle ambiguities are resolved. Pseudorange measures absolute range but cannot compete with carrier phase in measuring range change. This suggests a synergistic approach (Hatch, 1982~. By combining these data types one can map a whole time series of pseudorange observations to a common epoch with nearly perfect accuracy using the continuous and phase connected carrier phase observations. Thus, all of the pseudorange observations made over a span of hours can be brought to bear on a single time point and their errors thereby averaged down. For that epoch, geometric positioning is accomplished with an effective ranging accuracy that should be far better than the accuracy of the individual

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133 pseudorange points. This quasi-geometric point positioning approach will have major applicability to tracking from dynamical platforms such as ocean platforms and buoys, aircraft and spacecraft, and in kinematic ground tracking. It will also be used for high accuracy orbit determination of future Earth satellite missions such as TOPEX/Poseidon which will carry a GPS flight-rated receiver (Yunck et al., 1985~. This approach obviates the need for extensive dynamical models to generate the motion of the user platform. 3. It is well known that accurate pseudorange improves the accuracy of baseline determinations, particularly the east-west component (for most regions except very high latitudes) (Melbourne, 1985~. Coarse pseudorange accuracy, e.g., 100 m, provides sufficient accuracy in clock synchronization so that negligible error is introduced in the ephemeris look-up epoch. From that level down to 1 m little improvement is realized. However, for pseudorange accuracy below a carrier wavelength, baseline accuracy typically improves by factors of 1 to 5, depending on the component and the situation. This is because with carrier phase data alone, the baseline estimation process must include the carrier cycle ambiguities or biases which can typically be estimated to an accuracy of about 1/2 carrier wavelength or better. In those situations where it is not possible to exploit the integer character of the cycle ambiguities and hence to fix their values, introducing pseudorange with an accuracy that is comparable to or better than the a posterior) cycle ambiguity accuracy adds significant information bearing on their values; it aids in breaking the high correlations that tend to prevail between the biases and the eastern component of the baseline. Figure 5 gives an example of the effect of introducing pseudorange into the estimation process with increasing accuracy ranging from no pseudorange to carrier range, the latter being the case where the cycle ambiguities are exactly known. 4. Pseudorange can also greatly assist in resolving the carrier cycle ambiguities. Cycle ambiguity resolution strategies without highly accurate pseudorange have had moderate success for well designed networks that contain a range of different baseline lengths. These techniques have been applied to networks up to about 1000 km in extent (Blewitt, 1989; Dong and Bock, 1989~. But these schemes usually have not been able to correctly fix 100% of the cycle ambiguity integers in any given measurement session mainly because of ionospheric delay and ephemeris errors. Aiding the ambiguity resolution process with accurate pseudorange would virtually assure a 100% success rate at all baseline lengths. It can be shown (Melbourne, 1982) that the cycle ambiguity integers for L1 and L2 are given by the expressions: (1) nigh = 4.091*P: - 3.091*P2 - L: (2) next = 5.091*P~ - 4.91*P2 - L2 where L and P are the carrier phase (module 2~) and P-code pseudorange measurements, respectively, all expressed in range units; and ~ is the

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134 carrier wavelength. Here, n, P and L may be considered as residuals, and/or as singly or doubly differenced. In the absence of measurement errors the left hand side of these equations are constants with time for a series of phase-connected carrier phase observations and P-code measurements. This suggests reducing the effect of measurement errors by averaging this system over an entire pass to obtain an ensemble mean for (n:,n21; short period measurement errors (including multipath) will average out, but long period effects will likely remain. If the long period effects are sufficiently low, the ensemble mean should lie close to an integer doublet and hence can be fixed. However, it can be shown that for a greater than 95% confidence level of picking the correct integer values for (n',n2), the standard deviation of the ensemble mean must be less than 1/4 in each component; inspection of the above system of equations reveals that this is rather ambitious, requiring that the residual systematic pseudorange errors and averaged down multipath errors must in aggregate be no larger than about 1 cm. Nevertheless, Figure 4 suggests that the Rogue receiver/antenna system came close to achieving this goal in that particular experiment. The ordinate of Figure 4 is merely the linear combination of Equations (1) and (2) that eliminates P2. There exists a similar plot for the combination eliminating P: and it shows comparable performance. One can infer from these two plots that the uncertainties in the ensemble means for the double differenced versions of n: and n2 (for white Gaussian distributed errors) would be around 1/3 for this experiment, close but not quite close enough. Short of an all-out direct assault on the cycle ambiguity problem as described above, to what other use could accurate pseudorange be made? Even if the pseudorange measurement accuracy were not quite sufficient to reliably resolve ambiguities, it certainly would provide a narrow bound on their possible integer values. This information should improve the efficiency of current carrier cycle ambiguity resolution techniques. Also, most techniques first try to fix the value of the difference, n~- n2, the so-called wide lane cycle integer. This corresponds to a wavelength of 86 cm and is therefore relatively easier to resolve. Without P. and P2 the uncertainty in the differential ionospheric delay limits the reliability of this fixing to baselines or a maximum length that depends on solar activity, time of day, elevation angles of the GPS satellites, and geographical location. About 200-300 km appears to be a typical upper limit for campaigns that have been conducted in the continental U.S., Mexico and Central America. For receivers that do not use the P-code to recover L2, but rather, alternative nonlinear techniques that recover the second harmonic of L2, a wide lane ambiguity length of only 43 cm results, which is twice as vulnerable to ionospheric mix-modeling. With the P-code pseudorange the wide lane ambiguity can be fixed with very high reliability quite independent of baseline length (Blewitt, 19891. The above cycle ambiguity equations can be combined to yield (3) n:-n2 = 0.00652*P: - 0.00509*P2 - Lo + L2

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167 ~ Y U] lo: CC O 0 2 c/) F Z LL O Z Z , Y C: ~ 6 z tar O ~ F - A: ~ z m ~r O 1,LI J Z cn rNc ~~"'$ ~ ~. ~1~ ~ f.~{ B' ~\ ~ ~ ~ ! -`i W , ~ ~1 1 o o o o a) o UJ ~n 2 LU Co cn 0 _ a: ~ o o Z ~ Q Z ~ o ~ cn lL Z- 8 o c, c~ z Z ~ o _ ~ __ 1 L~ ~ cn o X J ~ ~ > O ~ ~ Z O O O 1` 1 ~ o ::: U. o a) ,~ . ~ a LL O cn X LU ~ o co oD c) . . ~ - ~ c~ o ~ ~ o cn a) {:5) Q y O ~ a) Ct '~ 3 - o ro~ (D ~n o Z ~n ~o o cn . _ C ~ o _ ~ o J ~ _ a) O Q Q ~0 CO a . _ CS) o a o a z

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168 ~I ~1 1 ~ 80 c' - LL He 111 En LL o LL ' ' I I T r r 70 60 50 40 30 20 10 COVARIANCE ASSUMPTIONS \ \ 18 GPS CONSTELLATION 2 DEN BASELINES (3 cm) 3 NON-DSN SITES (1 0 cm) PSEUDORANGE (5 cm) CARRIER PHASE (0.5 cm) RANDOM-WALK ZENITH TROP \ \ \ \ _, ~ 5cm O I ~I ~I I I ~ I I I I L I I I I 0 6 12 18 24 30 TRACKING ARC LENGTH (hrs) Figure 7. Predicted Accuracy Versus Tracking Time for Recovery of Geocentric Offset in Reference Frame Using Full 21-Satellite Block 11 Constellation and a 12-Station Global Tracking Network. See [30] for Additional Covariance Assumptions

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169 BROAD COVERAGE IMPROVES SHORT-TERM GPS ORBIT DETERMINAT10N SERVES AS AN INTERMEDIATE OBSERVING POINT BETWEEN WIDELY SEPARATED RECEIVERS EXTENDS VERTICAL VIEWING GEOMETRY REDUCES SENSITIVITY TO TROPOSPHERE , LEO/ / ~ J / / Figure 8. Utility of LEO in enhancing accuracies of baselines and GPS ephemerides using a global tracking network. GPS Or

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170 Rogue GPS Receiver Architecture Signal Flow (L1-C/A only) ICY . B.P Fiber B.P liter _ >' DIGITAL BASE BAND DATA L-BAND RF data - _ DOWN- CONVERTER AC'C'=~.AOI~ 11 1~C~11~1 i ~: I'm 1 ~_ DSP BOARD === _ ~ ~ Cos 0 _ ~ ~ Sin0 ~ _ _ F Gen 1 1~l~ Satellite B Satellite A ~~ =~ ~ D , a, 1 11 ~ Hey. ~ 1 thy ~./A A. ~ IN 1/4 ACCUM. CH IP ~VMX BUS ~ | SATELLITE CPU BOARD (68020) _ ~ ~.j: ~_ ~ ~ ~ : . REAL TIME CLOCK BOARD . .. : NON-VOLATILE RAM BOARD . SERIA :'U ~ ~ ::~1 r:5 '~-D . ~ :::,:::.,.~7 ~ \/ME-BUS | HOST CPU BOAR[) (68020) TO USER Fig. 9a). Rogue GPS Receiver Architecture. Only the C/A signal processing is shown. In actuality there are five processing streams for C/A, L1, L2, Pi, and P2.

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171 ~ROGUE TO TURBO ROGUE AFTER C)OWN-CONVERTER ~ _ _ _ ~11~11T DIGITAL SIGNAL PROCESOR _ _ ~ .' ~ _ _ ,___ ~ . ~ _ _ DIGITAL SIGNAL PROCESOR 11111 Weight : ~ 30 kg Size : - 0.16 m 3 Power :~ 250 W Cost : ~ $80 k it_ ~ IlIt =~ Ill! _ ..' .''.'2...2..."'. ...... ...... .... ...... ~ .... ...... ..... ...... . .... . . :: L I I . , TURBO-ROGUE Weight : ~1 0 kg Size :~0.02m3 Power :~25W Cost : ~ $15 k Fig. 9b). The Rogue to Turbo-Rogue Transition utilizing the DFE chip for RF down conversion to baseband digital sampling and the turbo-chip for baseband signal processing. ... ~

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172 n 1 | PREAMP | TYPICAL ANALOG DOWN CONVERSION _ FILTER | NARROW | ~ FILTER ~ ~ it' - ., 1 T . ~-- -l SYNTH ES IZE R | ~ r - ~1 _ SAMPLER SYNTHESIZER 1 600 MHz BW FILTER 600 MHz BW@ LBAND __ ~- 20 MBS SAMPLED DATA TO BASEBAND PROCE' NOR ., ANALOG VS. DIGITAL APPROACH DIGITAL FRONT END _ . rim ~ | CHIP ~ FREQUENCY REFERENCE Figure 10. Functional Schematic of an Analog Front End for RF Down-Conversion to Baseband, A/D Conversion, and Digital Sampling. Digital Front End Eliminates Analog Components that are Expensive and Sources of Error. /

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173 ANALOG RF IN - 0.1 TO 8000 MHz 600 MHz BANDWIDTH SAMPLE R A N D A D ONVERTER (ANALOG ! -:~ SAMPLE RATE SYNTH E SIZER (ANALOG AND DIGITAL) DIGITAL SINK X FILTER AND DATA RATE RE SUCTION _ (D IG ITAL) ~ :~'~2'~ PROD E f CONTROL . ~ ~(DIGITAL' ~ REFERENCE FREQUENCY TO 2C0 MHz SET-UP PRESENTLY (JAN 1 989) BEING DESIGNED AND ;6 SIMULATED a) . ~ . ~ ~ ................... ..... ~ . .......................... DIGITAL BASEBAND O 10 - 600 MEGA SAMPLES 4 TO 1 0 BIT QUADRATURE SAMPLES SELECTABLE COMPLETED DESIGN PRELIMINARY FA3RlCATION IN PROCESS - mom b) Figure 11. a) Functional Layout of Digital Front End Chip for Converting RF Analog to Baseband Digital Samples. by Photo of Completed Sections of the DEE Chip.

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174 ~ -- ~.-~;~ Or, stat ~ ons `Th, ee Is ~' ~ e'-~`v' =~w,-`edi GAG - ~4 I ,- ~t ~ 0~ Add: AN OF ~ GLOE!~L | ~.~tF=rr,at~ ones Cavern ng 1_ IFS Tract..nc~ System arid C:ompe'- i In:: i ^1 Beat i u.ns--ALE. T .~01 } ousted p' ~.~-~ ~.se~ ~r;e ve~-t;~. ~ availabie pri or ~el a~ ~ ve vel c:c:it. es ~ T:e tfJ ' ,`wr ti a~ +~,~ 0 E,; i ~ i r;g t~ydr oger; ~:i E; i `~ ~ i r, ~ wa ~ er- `~ap c.r- ~ ad ~ omet er ~ lOue, at i or`a 1 ~d`~ant a.~e .~Jet wor ~ Er,L'=r,. emer, ~ Stat i c,-'s--EiF S or. l y c =~-~ i de t-`c~mocenec~`s ~ gI ot~1 di stri b~ on ~ Er~har, _e n7~tc`=i ~ ~ ,; ~ i ~ ~ y cs Geo~,~t ~ ~ ca1 ~tr-e. '~t! ~ c~ r~ed~nda~-,cy ~nd sy~tem ~ el ~=bil ity ~ F ~ ate tector'~ cs ~ '-, new areas Low Eart:~-, Ori--, tina Soacecraft 5F ~ Trac t: ~ ng lAet wor ~ Cer~ter Fur~ t i c~n: Oper at ~ c~ns ~' i mp ~ ementat ~ c:~r' Coo' d~ nat~ ooer-"ti o~-,s Data Col ~ ect ~ on ar,~ t.- ansmi ssi ur~-- GF=* l~eteorolcigiccil ~ W'vn' rloct`, rea1-t~rre E.~-~dcast . echemeri des, etc . -Lime ~,~-,i. {:or-~ng of r;etwort oerformar~ce Rea' Conf i c~urat ~ on a'-id f ac: ~ 1 i t ~ es ~c: ntr~-~l :~ _ =cista~ni;-,g er~g~neeri'~y "i~d m~i~atenance Ei-,at; l e per f or mance 2~nd co`~f i gur- at i c~n ~tandar d~ =vs~ e~, des;~ a', a'~d r esearc~i . _ ~ F:esoon~i ~e to Comoutatic:~r-~1 Ce;~ter . , _ . Fr-act:, ca1 geodesy f User s ~i.S-'g product, of the Compc~tational Center- as they star~d) Cor~ti,-,~s t}per~t.~ '~~o .Res~,~.~1 ~ Nor,i tc~s-ed ~ays (~PlfAi Ne~ wol t-s ~1~;~:~> s~ ale' Re`erence f, ame ~i~ t~etwee7, pre-~,; i st: i ng netwc'~ t tJ ~F~/'~'LElfSLR ci te staL~ ~ i u blos-:i tor ~ rlg `~f ~fO3- ~r,i c: u~) i f ~ L:~ Def csr IrS~t] c:n s-IGar- ol =~i ~ ~:c;~r' ]~ ~ es ~ Fr-e- a.~d oost-se~ `_,nic: =~ - , r~ a~;-,itor ~:g 7~-~ - e~ser~-. Ji ~ ~ U~ i r~o ~'ract ~ cai ~rs ar:~ i, =;i"-~t,~ t]~r~~- ~ ^~:e t,-~e ~;-~Cte u~ , 0 Eng i nees~ i ng app 1 i Lat i on5 c;~ Seaf ~ oc:~r aead esy Dyn a~n i c ,oos ~ t i c~-' i ng 0 Frec~ si on na~i gat ~ or' u t~=pp] ~,~ . . . . .. .. . ~us~ on; User s: the Comouf 2~t i s~na1 ~er't er == t ~ ~ it~: `d _? '~ ~ ~;li; .~ ~v ~ ~r;;-y a:]j~-~. =~:~,~ w~ tt,~ pr~r~ct~ ::if th~ Corr,p,ut~t~c~r~ ~enter- i:~ic^~;,~ c,~ t.;~ictf;~t' ^~_;~ct(::v reci~, remer~-= G~ for~ resear- ct ar;,' .~= i ot; i,~-il =,1 '.=i ai~ ; ~ . ..t- o~;-` ~ -- clL~ ur-, I3^ agr-a~' to'~ ~r, vFt~ 8~tT=} t~c[;irig S~'j~ elrl

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175 T NTEF<~4AT ~ f'~L'f' ~-F'D~SORED T ~ ~ t: ~ 1, `] ~ S ~ _ i ~ to I ~C3fl~l3Ll ~ It i ~l L~.r! ~ - ~ Boar ~ Fc7r~ 1 tat ' ~. 'God Redip. __ ~|~IL`~I'L~.' orals-`' Reid er )~1~_~ t fit ~ U'~=l ~ ~I~l in en Limo ~ ~ <-a t ~ or ~ =~ 1 Herr i: e. - ~ or OF ~ ~ -~ h enter ~ ci e is-, Re'~rer.ce Frc'.~e ,_~-;~-~1 Fur,i-ti Brie: Off-' or,; d^~ quay itv .or,t:~;j' ~ ~L,; Or-, a,~d d~stributior~ c; F~rc-~mete. esti that i An-' E;x,;stem desi Or ar~'d Beset.- t:~ ~ Tr~~.i,~~ data ,ur-~du~ts +~r Netwc:'rf; ~e -`ter lo, 0 ~ U ~ ~ 3 So ~ c~t i c~n s ~4cc~ ~ate wFS ---te} 1 ~ te ept~em=r ~ des ,'~. ~! F'~m-~Ocrr' or better Tr~c'.ir~g stat ic~r-' loc^tior,~. s;ite ~p~cif i :: infor~n~tic~n lEr - c [; ~ ~ ~ ~ =t ~t i ;;:~, . ~ e l oc ~. t ~ e~ ' F: 1 ~ ~ ~ '~ ec t c:,n i Gewc=~-,tr i~ he, er,~ e ~r a,~.e o Eartl-, orienta' ton (pol~r `~'uti or ~ 1}11-}17~ r a+~:, GI ;~1 so] ut ~ c,;-~s ~r~d f u1 ~ c~c,~ ar ~ ar-~e r ch ~ ved dat~ ~ Hi gl~' ctetcsl ~ ty ~Fa norroa, pc'~ r,ts ;a Raw tr-opospher e ca i br- at i on dat~ 0 Der ~ed tr-opc; ~,~-~er i~ path! de1 ~y c: c~rr ect ~ or~= IEF OCR for page 124
176 1.0 4 0.01 9 4 2 0.001 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 1 1 6 t / / ~ , , 3 _ AN/ / _ 2 / / ~(n)/csk(n) 0.1 4: / =o 3t / / ~ Pr / / ~ 1 1/1 1 1 1 1 1 ~ 1 1 1 1 1 1, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 1 000.0 100.0 10.0 AN (cm) 1.0 0.1 0.01 Figure 13. Predicted Gravity Recovery from GP-B Using a TOPEX/Poseidon Class GPS Flight Receiver in Conjunction with a GPS Global Tracking System. Mission Duration is 6 Months. aLn) is Based on Combined Tracking and A Priori Kaula Model Information. ok~n) is Based on Kaula Model.

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176 1.0 4 0.01 9 4 2 0.001 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1, 1 1 6 t / / ~ , , 3 _ AN/ / _ 2 / / ~(n)/csk(n) 0.1 4: / =o 3t / / ~ Pr / / ~ 1 1/1 1 1 1 1 1 ~ 1 1 1 1 1 1, 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 10 20 30 40 50 60 70 1 000.0 100.0 10.0 AN (cm) 1.0 0.1 0.01 Figure 13. Predicted Gravity Recovery from GP-B Using a TOPEX/Poseidon Class GPS Flight Receiver in Conjunction with a GPS Global Tracking System. Mission Duration is 6 Months. aLn) is Based on Combined Tracking and A Priori Kaula Model Information. ok~n) is Based on Kaula Model.