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Monitoring the Ionosphere with Integer-Leveled GPS Measurements By Simon Banville, Wei Zhang, and  Richard B. Langley INNOVATION INSIGHTS by Richard Langley IT’S NOT JUST FOR POSITIONING, NAVIGATION, AND TIMING. Many people do not realize that GPS is being used in a variety of ways in addition to those of its primary mandate, which is to provide accurate position, velocity, and time information. The radio signals from the GPS satellites must traverse the Earth’s atmosphere on their way to receivers on or near the Earth’s surface. The signals interact with the atoms, molecules, and charged particles that make up the atmosphere, and the process slightly modifies the signals. It is these modified or perturbed signals that a receiver actually processes. And should a signal be reflected or diffracted by some object in the vicinity of the receiver’s antenna, the signal is further perturbed — a phenomenon we call multipath. Now, these perturbations are a bit of a nuisance for conventional users of GPS. The atmospheric effects, if uncorrected, reduce the accuracy of the positions, velocities, and time information derived from the signals. However, GPS receivers have correction algorithms in their microprocessor firmware that attempt to correct for the effects. Multipath, on the other hand, is difficult to model although the use of sophisticated antennas and advanced receiver technologies can minimize its effect. But there are some GPS users who welcome the multipath or atmospheric effects in the signals. By analyzing the fluctuations in signal-to-noise-ratio due to multipath, the characteristics of the reflector can be deduced. If the reflector is the ground, then the amount of moisture in the soil can be measured. And, in wintery climes, changes in snow depth can be tracked from the multipath in GPS signals. The atmospheric effects perturbing GPS signals can be separated into those that are generated in the lower part of the atmosphere, mostly in the troposphere, and those generated in the upper, ionized part of the atmosphere — the ionosphere. Meteorologists are able to extract information on water vapor content in the troposphere and stratosphere from the measurements made by GPS receivers and regularly use the data from networks of ground-based continuously operating receivers and those operating on some Earth-orbiting satellites to improve weather forecasts. And, thanks to its dispersive nature, the ionosphere can be studied by suitably combining the measurements made on the two legacy frequencies transmitted by all GPS satellites. Ground-based receiver networks can be used to map the electron content of the ionosphere, while Earth-orbiting receivers can profile electron density. Even small variations in the distribution of ionospheric electrons caused by earthquakes; tsunamis; and volcanic, meteorite, and nuclear explosions can be detected using GPS. In this month’s column, I am joined by two of my graduate students, who report on an advance in the signal processing procedure for better monitoring of the ionosphere, potentially allowing scientists to get an even better handle on what’s going on above our heads. Representation and forecast of the electron content within the ionosphere is now routinely accomplished using GPS measurements. The global distribution of permanent ground-based GPS tracking stations can effectively monitor the evolution of electron structures within the ionosphere, serving a multitude of purposes including satellite-based communication and navigation. It has been recognized early on that GPS measurements could provide an accurate estimate of the total electron content (TEC) along a satellite-receiver path. However, because of their inherent nature, phase observations are biased by an unknown integer number of cycles and do not provide an absolute value of TEC. Code measurements (pseudoranges), although they are not ambiguous, also contain frequency-dependent biases, which again prevent a direct determination of TEC. The main advantage of code over phase is that the biases are satellite- and receiver-dependent, rather than arc-dependent. For this reason, the GPS community initially adopted, as a common practice, fitting the accurate TEC variation provided by phase measurements to the noisy code measurements, therefore removing the arc-dependent biases. Several variations of this process were developed over the years, such as phase leveling, code smoothing, and weighted carrier-phase leveling (see Further Reading for background literature). The main challenge at this point is to separate the code inter-frequency biases (IFBs) from the line-of-sight TEC. Since both terms are linearly dependent, a mathematical representation of the TEC is usually required to obtain an estimate of each quantity. Misspecifications in the model and mapping functions were found to contribute significantly to errors in the IFB estimation, suggesting that this process would be better performed during nighttime when few ionospheric gradients are present. IFB estimation has been an ongoing research topic for the past two decades are still remains an issue for accurate TEC determination. A particular concern with IFBs is the common assumption regarding their stability. It is often assumed that receiver IFBs are constant during the course of a day and that satellite IFBs are constant for a duration of a month or more. Studies have clearly demonstrated that intra-day variations of receiver instrumental biases exist, which could possibly be related to temperature effects. This assumption was shown to possibly introduce errors exceeding 5 TEC units (TECU) in the leveling process, where 1 TECU corresponds to 0.162 meters of code delay or carrier advance at the GPS L1 frequency (1575.42 MHz). To overcome this limitation, one could look into using solely phase measurements in the TEC estimation process, and explicitly deal with the arc-dependent ambiguities. The main advantage of such a strategy is to avoid code-induced errors, but a larger number of parameters needs to be estimated, thereby weakening the strength of the adjustment. A comparison of the phase-only (arc-dependent) and phase-leveled (satellite-dependent) models showed that no model performs consistently better. It was found that the satellite-dependent model performs better at low-latitudes since the additional ambiguity parameters in the arc-dependent model can absorb some ionospheric features (such as gradients). On the other hand, when the mathematical representation of the ionosphere is realistic, the leveling errors may more significantly impact the accuracy of the approach. The advent of precise point positioning (PPP) opened the door to new possibilities for slant TEC (STEC) determination. Indeed, PPP can be used to estimate undifferenced carrier-phase ambiguity parameters on L1  and L2, which can then be used to remove the ambiguous characteristics of the carrier-phase observations. To obtain undifferenced ambiguities free from ionospheric effects, researchers have either used the widelane/ionosphere-free (IF) combinations, or the Group and Phase Ionospheric Calibration (GRAPHIC) combinations. One critical problem with such approaches is that code biases propagate into the estimated ambiguity parameters. Therefore, the resulting TEC estimates are still biased by unknown quantities, and might suffer from the unstable datum provided by the IFBs. The recent emergence of ambiguity resolution in PPP presented sophisticated means of handling instrumental biases to estimate integer ambiguity parameters. One such technique is the decoupled-clock method, which considers different clock parameters for the carrier-phase and code measurements. In this article, we present an “integer-leveling” method, based on the decoupled-clock model, which uses integer carrier-phase ambiguities obtained through PPP to level the carrier-phase observations. Standard Leveling Procedure This section briefly reviews the basic GPS functional model, as well as the observables usually used in ionospheric studies. A common leveling procedure is also presented, since it will serve as a basis for assessing the performance of our new method. Ionospheric Observables. The standard GPS functional model of dual-frequency carrier-phase and code observations can be expressed as:    (1)     (2)    (3)    (4) where Φi j is the carrier-phase measurement to satellite j on the Li link and, similarly, Pi j is the code measurement on Li. The term  is the biased ionosphere-free range between the satellite and receiver, which can be decomposed as:    (5) The instantaneous geometric range between the satellite and receiver antenna phase centers is ρ j. The receiver and satellite clock errors, respectively expressed as dT and dtj, are expressed here in units of meters. The term Tj stands for the tropospheric delay, while the ionospheric delay on L1 is represented by I j and is scaled by the frequency-dependent constant μ for L2, where . The biased carrier-phase ambiguities are symbolized by  and are scaled by their respective wavelengths (λi). The ambiguities can be explicitly written as:    (6) where Ni j is the integer ambiguity, bi is a receiver-dependent bias, and bi j is a satellite-dependent bias. Similarly, Bi and Bi j are instrumental biases associated with code measurements. Finally, ε contains unmodeled quantities such as noise and multipath, specific to the observable. The overbar symbol indicates biased quantities. In ionospheric studies, the geometry-free (GF) signal combinations are formed to virtually eliminate non-dispersive terms and thus provide a better handle on the quantity of interest:    (7)    (8) where IFBr and IFB j represent the code inter-frequency biases for the receiver and satellite, respectively. They are also commonly referred to as differential code biases (DCBs). Note that the noise terms (ε) are neglected in these equations for the sake of simplicity. Weighted-Leveling Procedure. As pointed out in the introduction, the ionospheric observables of Equations (7) and (8) do not provide an absolute level of ionospheric delay due to instrumental biases contained in the measurements. Assuming that these biases do not vary significantly in time, the difference between the phase and code observations for a particular satellite pass should be a constant value (provided that no cycle slip occurred in the phase measurements). The leveling process consists of removing this constant from each geometry-free phase observation in a satellite-receiver arc:    (9) where the summation is performed for all observations forming the arc. An elevation-angle-dependent weight (w) can also be applied to minimize the noise and multipath contribution for measurements made at low elevation angles. The double-bar symbol indicates leveled observations. Integer-Leveling Procedure The procedure of fitting a carrier-phase arc to code observations might introduce errors caused by code noise, multipath, or intra-day code-bias variations. Hence, developing a leveling approach that relies solely on carrier-phase observations is highly desirable. Such an approach is now possible with the recent developments in PPP, allowing for ambiguity resolution on undifferenced observations. This procedure has gained significant momentum in the past few years, with several organizations generating “integer clocks” or fractional offset corrections for recovering the integer nature of the undifferenced ambiguities. Among those organizations are, in alphabetical order, the Centre National d’Études Spatiale; GeoForschungsZentrum; GPS Solutions, Inc.; Jet Propulsion Laboratory; Natural Resources Canada (NRCan); and Trimble Navigation. With ongoing research to improve convergence time, it would be no surprise if PPP with ambiguity resolution would become the de facto methodology for processing data on a station-by-station basis. The results presented in this article are based on the products generated at NRCan, referred to as “decoupled clocks.” The idea behind integer leveling is to introduce integer ambiguity parameters on L1 and L2, obtained through PPP processing, into the geometry-free linear combination of Equation (7). The resulting integer-leveled observations, in units of meters, can then be expressed as:    (10) where  and  are the ambiguities obtained from the PPP solution, which should be, preferably, integer values. Since those ambiguities are obtained with respect to a somewhat arbitrary ambiguity datum, they do not allow instant recovery of an unbiased slant ionospheric delay. This fact was highlighted in Equation (10), which indicates that, even though the arc-dependency was removed from the geometry-free combination, there are still receiver- and satellite-dependent biases (br and b j, respectively) remaining in the integer-leveled observations. The latter are thus very similar in nature to the standard-leveled observations, in the sense that the biases br and b j replace the well-known IFBs. As a consequence, integer-leveled observations can be used with any existing software used for the generation of TEC maps. The motivation behind using integer-leveled observations is the mitigation of leveling errors, as explained in the next sections. Slant TEC Evaluation As a first step towards assessing the performance of integer-leveled observations, STEC values are derived on a station-by-station basis. The slant ionospheric delays are then compared for a pair of co-located receivers, as well as with global ionospheric maps (GIMs) produced by the International GNSS Service (IGS). Leveling Error Analysis. Relative leveling errors between two co-located stations can be obtained by computing between-station differences of leveled observations:    (11) where subscripts A and B identify the stations involved, and εl is the leveling error. Since the distance between stations is short (within 100 meters, say), the ionospheric delays will cancel, and so will the satellite biases (b j) which are observed at both stations. The remaining quantities will be the (presumably constant) receiver biases and any leveling errors. Since there are no satellite-dependent quantities in Equation (11), the differenced observations obtained should be identical for all satellites observed, provided that there are no leveling errors. The same principles apply to observations leveled using other techniques discussed in the introduction. Hence, Equation (11) allows comparison of the performance of various leveling approaches. This methodology has been applied to a baseline of approximately a couple of meters in length between stations WTZJ and WTZZ, in Wettzell, Germany. The observations of both stations from March 2, 2008, were leveled using a standard leveling approach, as well as the method described in this article. Relative leveling errors computed using Equation (11) are displayed in Figure 1, where each color represents a different satellite. It is clear that code noise and multipath do not necessarily average out over the course of an arc, leading to leveling errors sometimes exceeding a couple of TECU for the standard leveling approach (see panel (a)). On the other hand, integer-leveled observations agree fairly well between stations, where leveling errors were mostly eliminated. In one instance, at the beginning of the session, ambiguity resolution failed at both stations for satellite PRN 18, leading to a relative error of 1.5 TECU, more or less. Still, the advantages associated with integer leveling should be obvious since the relative error of the standard approach is in the vicinity of -6 TECU for this satellite. FIGURE 1. Relative leveling errors between stations WTZJ and WTZZ on March 2, 2008: (a) standard-leveled observations and (b) integer-leveled observations. The magnitude of the leveling errors obtained for the standard approach agrees fairly well with previous studies (see Further Reading). In the event that intra-day variations of the receiver IFBs are observed, even more significant biases were found to contaminate standard-leveled observations. Since the decoupled-clock model used for ambiguity resolution explicitly accounts for possible variations of any equipment delays, the estimated ambiguities are not affected by such effects, leading to improved leveled observations. STEC Comparisons. Once leveled observations are available, the next step consists of separating STEC from instrumental delays. This task can be accomplished on a station-by-station basis using, for example, the single-layer ionospheric model. Replacing the slant ionospheric delays (I j) in Equation (10) by a bilinear polynomial expansion of VTEC leads to:     (12) where M(e) is the single-layer mapping function (or obliquity factor) depending on the elevation angle (e) of the satellite. The time-dependent coefficients a0, a1, and a2 determine the mathematical representation of the VTEC above the station. Gradients are modeled using Δλ, the difference between the longitude of the ionospheric pierce point and the longitude of the mean sun, and Δϕ, the difference between the geomagnetic latitude of the ionospheric pierce point and the geomagnetic latitude of the station. The estimation procedure described by Attila Komjathy (see Further Reading) is followed in all subsequent tests. An elevation angle cutoff of 10 degrees was applied and the shell height used was 450 kilometers. Since it is not possible to obtain absolute values for the satellite and receiver biases, the sum of all satellite biases was constrained to a value of zero. As a consequence, all estimated biases will contain a common (unknown) offset. STEC values, in TECU, can then be computed as:      (13) where the hat symbol denotes estimated quantities, and  is equal to zero (that is, it is not estimated) when biases are obtained on a station-by-station basis. The frequency, f1, is expressed in Hz. The numerical constant 40.3, determined from values of fundamental physical constants, is sufficiently precise for our purposes, but is a rounding of the more precise value of 40.308. While integer-leveled observations from co-located stations show good agreement, an external TEC source is required to make sure that both stations are not affected by common errors. For this purpose, Figure 2 compares STEC values computed from GIMs produced by the IGS and STEC values derived from station WTZJ using both standard- and integer-leveled observations. The IGS claims root-mean-square errors on the order of 2-8 TECU for vertical TEC, although the ionosphere was quiet on the day selected, meaning that errors at the low-end of that range are expected. Errors associated with the mapping function will further contribute to differences in STEC values. As apparent from Figure 2, no significant bias can be identified in integer-leveled observations. On the other hand, negative STEC values (not displayed in Figure 2) were obtained during nighttimes when using standard-leveled observations, a clear indication that leveling errors contaminated the observations. FIGURE 2. Comparison between STEC values obtained from a global ionospheric map and those from station WTZJ using standard- and integer-leveled observations. STEC Evaluation in the Positioning Domain. Validation of slant ionospheric delays can also be performed in the positioning domain. For this purpose, a station’s coordinates from processing the observations in static mode (that is, one set of coordinates estimated per session) are estimated using (unsmoothed) single-frequency code observations with precise orbit and clock corrections from the IGS and various ionosphere-correction sources. Figure 3 illustrates the convergence of the 3D position error for station WTZZ, using STEC corrections from the three sources introduced previously, namely: 1) GIMs from the IGS, 2) STEC values from station WTZJ derived from standard leveling, and 3) STEC values from station WTZJ derived from integer leveling. The reference coordinates were obtained from static processing based on dual-frequency carrier-phase and code observations. The benefits of the integer-leveled corrections are obvious, with the solution converging to better than 10 centimeters. Even though the distance between the stations is short, using standard-leveled observations from WTZJ leads to a biased solution as a result of arc-dependent leveling errors. Using a TEC map from the IGS provides a decent solution considering that it is a global model, although the solution is again biased. FIGURE 3. Single-frequency code-based positioning results for station WTZZ (in static mode) using different ionosphere-correction sources: GIM and STEC values from station WTZJ using standard- and integer-leveled observations. This station-level analysis allowed us to confirm that integer-leveled observations can seemingly eliminate leveling errors, provided that carrier-phase ambiguities are fixed to proper integer values. Furthermore, it is possible to retrieve unbiased STEC values from those observations by using common techniques for isolating instrumental delays. The next step consisted of examining the impacts of reducing leveling errors on VTEC. VTEC Evaluation When using the single-layer ionospheric model, vertical TEC values can be derived from the STEC values of Equation (13) using:     (14) Dividing STEC by the mapping function will also reduce any bias caused by the leveling procedure. Hence, measures of VTEC made from a satellite at a low elevation angle will be less impacted by leveling errors. When the satellite reaches the zenith, then any bias in the observation will fully propagate into the computed VTEC values. On the other hand, the uncertainty of the mapping function is larger at low-elevation angles, which should be kept in mind when analyzing the results. Using data from a small regional network allows us to assess the compatibility of the VTEC quantities between stations. For this purpose, GPS data collected as a part of the Western Canada Deformation Array (WCDA) network, still from March 2, 2008, was used. The stations of this network, located on and near Vancouver Island in Canada, are indicated in Figure 4. Following the model of Equation (12), all stations were integrated into a single adjustment to estimate receiver and satellite biases as well as a triplet of time-varying coefficients for each station. STEC values were then computed using Equation (13), and VTEC values were finally derived from Equation (14). This procedure was again implemented for both standard- and integer-leveled observations. FIGURE 4. Network of stations used in the VTEC evaluation procedures. To facilitate the comparison of VTEC values spanning a whole day and to account for ionospheric gradients, differences with respect to the IGS GIM were computed. The results, plotted by elevation angle, are displayed in Figure 5 for all seven stations processed (all satellite arcs from the same station are plotted using the same color). The overall agreement between the global model and the station-derived VTECs is fairly good, with a bias of about 1 TECU. Still, the top panel demonstrates that, at high elevation angles, discrepancies between VTEC values derived from standard-leveled observations and the ones obtained from the model have a spread of nearly 6 TECU. With integer-leveled observations (see bottom panel), this spread is reduced to approximately 2 TECU. It is important to realize that the dispersion can be explained by several factors, such as remaining leveling errors, the inexact receiver and satellite bias estimates, and inaccuracies of the global model. It is nonetheless expected that leveling errors account for the most significant part of this error for standard-leveled observations. For satellites observed at a lower elevation angle, the spread between arcs is similar for both methods (except for station UCLU in panel (a) for which the estimated station IFB parameter looks significantly biased). As stated previously, the reason is that leveling errors are reduced when divided by the mapping function. The latter also introduces further errors in the comparisons, which explains why a wider spread should typically be associated with low-elevation-angle satellites. Nevertheless, it should be clear from Figure 5 that integer-leveled observations offer a better consistency than standard-leveled observations. FIGURE 5. VTEC differences, with respect to the IGS GIM, for all satellite arcs as a function of the elevation angle of the satellite, using (a) standard-leveled observations and (b) integer-leveled observations. Conclusion The technique of integer leveling consists of introducing (preferably) integer ambiguity parameters obtained from PPP into the geometry-free combination of observations. This process removes the arc dependency of the signals, and allows integer-leveled observations to be used with any existing TEC estimation software. While leveling errors of a few TECU exist with current procedures, this type of error can be eliminated through use of our procedure, provided that carrier-phase ambiguities are fixed to the proper integer values. As a consequence, STEC values derived from nearby stations are typically more consistent with each other. Unfortunately, subsequent steps involved in generating VTEC maps, such as transforming STEC to VTEC and interpolating VTEC values between stations, attenuate the benefits of using integer-leveled observations. There are still ongoing challenges associated with the GIM-generation process, particularly in terms of latency and three-dimensional modeling. Since ambiguity resolution in PPP can be achieved in real time, we believe that integer-leveled observations could benefit near-real-time ionosphere monitoring. Since ambiguity parameters are constant for a satellite pass (provided that there are no cycle slips), integer ambiguity values (that is, the leveling information) can be carried over from one map generation process to the next. Therefore, this methodology could reduce leveling errors associated with short arcs, for instance. Another prospective benefit of integer-leveled observations is the reduction of leveling errors contaminating data from low-Earth-orbit (LEO) satellites, which is of particular importance for three-dimensional TEC modeling. Due to their low orbits, LEO satellites typically track a GPS satellite for a short period of time. As a consequence, those short arcs do not allow code noise and multipath to average out, potentially leading to important leveling errors. On the other hand, undifferenced ambiguity fixing for LEO satellites already has been demonstrated, and could be a viable solution to this problem. Evidently, more research needs to be conducted to fully assess the benefits of integer-leveled observations. Still, we think that the results shown herein are encouraging and offer potential solutions to current challenges associated with ionosphere monitoring. Acknowledgments We would like to acknowledge the help of Paul Collins from NRCan in producing Figure 4 and the financial contribution of the Natural Sciences and Engineering Research Council of Canada in supporting the second and third authors. This article is based on two conference papers: “Defining the Basis of an ‘Integer-Levelling’ Procedure for Estimating Slant Total Electron Content” presented at ION GNSS 2011 and “Ionospheric Monitoring Using ‘Integer-Levelled’ Observations” presented at ION GNSS 2012. ION GNSS 2011 and 2012 were the 24th and 25th International Technical Meetings of the Satellite Division of The Institute of Navigation, respectively. ION GNSS 2011 was held in Portland, Oregon, September 19–23, 2011, while ION GNSS 2012 was held in Nashville, Tennessee, September 17–21, 2012. SIMON BANVILLE is a Ph.D. candidate in the Department of Geodesy and Geomatics Engineering at the University of New Brunswick (UNB) under the supervision of Dr. Richard B. Langley. His research topic is the detection and correction of cycle slips in GNSS observations. He also works for Natural Resources Canada on real-time precise point positioning and ambiguity resolution. WEI ZHANG received his M.Sc. degree (2009) in space science from the School of Earth and Space Science of Peking University, China. He is currently an M.Sc.E. student in the Department of Geodesy and Geomatics Engineering at UNB under the supervision of Dr. Langley. His research topic is the assessment of three-dimensional regional ionosphere tomographic models using GNSS measurements. FURTHER READING • Authors’ Conference Papers “Defining the Basis of an ‘Integer-Levelling’ Procedure for Estimating Slant Total Electron Content” by S. Banville and R.B. Langley in Proceedings of ION GNSS 2011, the 24th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, September 19–23, 2011, pp. 2542–2551. “Ionospheric Monitoring Using ‘Integer-Levelled’ Observations” by S. Banville, W. Zhang, R. Ghoddousi-Fard, and R.B. Langley in Proceedings of ION GNSS 2012, the 25th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 17–21, 2012, pp. 3753–3761. • Errors in GPS-Derived Slant Total Electron Content “GPS Slant Total Electron Content Accuracy Using the Single Layer Model Under Different Geomagnetic Regions and Ionospheric Conditions” by C. Brunini, and F.J. Azpilicueta in Journal of Geodesy, Vol. 84, No. 5, pp. 293–304, 2010, doi: 10.1007/s00190-010-0367-5. “Calibration Errors on Experimental Slant Total Electron Content (TEC) Determined with GPS” by L. Ciraolo, F. Azpilicueta, C. Brunini, A. Meza, and S.M. Radicella in Journal of Geodesy, Vol. 81, No. 2, pp. 111–120, 2007, doi: 10.1007/s00190-006-0093-1. • Global Ionospheric Maps “The IGS VTEC Maps: A Reliable Source of Ionospheric Information Since 1998” by M. Hernández-Pajares, J.M. Juan, J. Sanz, R. Orus, A. Garcia-Rigo, J. Feltens, A. Komjathy, S.C. Schaer, and A. Krankowski in Journal of Geodesy, Vol. 83, No. 3–4, 2009, pp. 263–275, doi: 10.1007/s00190-008-0266-1. • Ionospheric Effects on GNSS “GNSS and the Ionosphere: What’s in Store for the Next Solar Maximum” by A.B.O. Jensen and C. Mitchell in GPS World, Vol. 22, No. 2, February 2011, pp. 40–48. “Space Weather: Monitoring the Ionosphere with GPS” by A. Coster, J. Foster, and P. Erickson in GPS World, Vol. 14, No. 5, May 2003, pp. 42–49. “GPS, the Ionosphere, and the Solar Maximum” by R.B. Langley in GPS World, Vol. 11, No. 7, July 2000, pp. 44–49. Global Ionospheric Total Electron Content Mapping Using the Global Positioning System by A. Komjathy, Ph. D. dissertation, Technical Report No. 188, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Fredericton, New Brunswick, Canada, 1997. • Decoupled Clock Model “Undifferenced GPS Ambiguity Resolution Using the Decoupled Clock Model and Ambiguity Datum Fixing” by P. Collins, S. Bisnath, F. Lahaye, and P. Héroux in  Navigation: Journal of The Institute of Navigation, Vol. 57, No. 2, Summer 2010, pp. 123–135.  

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Stancor sta-4190d ac adapter 9vac 500ma used 2x5.4mm straight ro.esaw 450-31 ac adapter 3,4.5,6,7.5,9-12vdc 300ma used switching.toshiba p015rw05300j01 ac adapter 5vdc 3a used -(+) 1.5x4x9.4mm,this system considers two factors.astrodyne spu15a-5 ac adapter 18vdc 0.83a used -(+)-2.5x5.5mm,4312a ac adapter 3.1vdc 300ma used -(+) 0.5x0.7x4.6mm round barr.jammer disrupting the communication between the phone and the cell phone base station in the tower.macvision fj-t22-1202000v ac adapter 12vdc 2000ma used 1.5 x 4 x,logitech tesa5-0500700d-b ac adapter 5vdc 300ma used -(+) 0.6x2.,soneil 2403srd ac adapter 24vdc 1.5a 3pin xlr connector new 100-.panasonic vsk0626 ac dc adapter 4.8v 1a camera sv-av20 sv-av20u.hh-tag 5-11v dc used travel charger power supply phone connector.please see our fixed jammers page for fixed location cell,olympus bu-300 ni-mh battery charger used 1.2vdc 240ma camedia x,hp pa-1121-12r ac adapter 18.5vdc 6.5a used 2.5 x 5.5 x 12mm,and fda indication for pediatric patients two years and older,soneil 1205srd ac adapter 12vdc 2.5a 30w shielded wire no connec.rs18-sp0502500 ac adapter 5vdc 1.5a -(+) used 1x3.4x8.4mm straig,canon battery charger cb-2ls 4.2vdc 0.7a 4046789 battery charger,4 ah battery or 100 – 240 v ac,ca d5730-15-1000(ac-22) ac adapter 15vdc 1000ma used +(-) 2x5.5x,90 %)software update via internet for new types (optionally available)this jammer is designed for the use in situations where it is necessary to inspect a parked car,that is it continuously supplies power to the load through different sources like mains or inverter or generator.all these project ideas would give good knowledge on how to do the projects in the final year,chc announced today the availability of chc geomatics office (cgo),condor hk-i518-a12 12vdc 1.5a -(+) 2x5.5mm used ite power supply,li shin lse9901c1260 12v dc 5a 60w -(+)- 2.2x5.5mm used ite,ryobi p113 ac adapter 18vdc used lithium ion battery charger p10,fujifilm bc-60 battery charger 4.2vdc 630ma used 100-240v~50/60h.potrans up04821120a ac adapter 12vdc 4a used -(+) 2x5.5x9.7mm ro,texas instruments xbox 5.1 surround sound system only no any thi.globtek gt-41052-1507 ac adapter 7vdc 2.14a -(+) 2x5.5mm 100-240,ibm 85g6698 ac adapter 16-10vdc 2.2-3.2a used -(+) 2.5x5.5x10mm,military camps and public places.li shin 0317a19135 ac adapter 19vdc 7.1a used -(+) 2x5.5mm 100-2,artesyn scl25-7624 ac adapter 24vdc 1a 8pin power supply,magellan 730489-c ac car adapter used 0.8x3.4x7.9mm 90°round bar,sunny sys1148-3012-t3 ac adapter 12v 2.5a 30w i.t.e power supply,sharp ea-mv1vac adapter 19vdc 3.16a 2x5.5mm -(+) 100-240vac la,ascend wp571418d2 ac adapter 18v 750ma power supply,ibm 02k6750 ac adapter 16vdc 4.5a -(+) 2.5x5.5mm 100-240vac used.motorola nu18-41120166-i3 ac adapter 12vdc 1.66a used -(+) 3x6.5,is someone stealing your bandwidth,apd da-30i12 ac adapter 12vdc 2.5a power supply for external hdd,oem ad-0760dt ac adapter 7.5vdc 600ma used-(+)- 2.1x5.4x10mm,increase the generator's volume to play louder than.globtek gt-4076-0609 ac adapter 9vdc 0.66a -(+)- used 2.6 x 5.5,fone gear 01023 ac adapter 5vdc 400ma used 1.1 x 2.5 x 9mm strai,dell ad-4214n ac adapter 14vdc 3a power supply,gamestop bb-731/pl-7331 ac adapter 5.2vdc 320ma used usb connect,its great to be able to cell anyone at anytime,lenovo 41r4538 ultraslim ac adapter 20vdc 4.5a used 3pin ite,verifone sm09003a ac adapter 9.3vdc 4a used -(+) 2x5.5x11mm 90°,hjc hua jung comp. hasu11fb36 ac adapter 12vdc 3a used 2.3 x 6 x,hb hb12b-050200spa ac adapter 5vdc 2000ma used 2.3 x 5.3 x 11.2.lenovo adlx65nct3a ac adapter 20vdc 3.25a 65w used charger recta.replacement pa-1700-02 ac adapter 19v 3.42a used,sy-1216 ac adapter 12vac 1670ma used ~(~) 2x5.5x10mm round barre,motorola bc6lmvir01 class 2 radio battery charger used 11vdc 1.3,dell adp-13cb ac adapter 5.4vdc 2410ma -(+)- 1.7x4mm 100-240vac,ault pw125ra0503f02 ac adapter 5v dc 5a used 2.5x5.5x9.7mm,hp 384020-002 compaq ac adapter 19vdc 4.74a laptop power supply,motorola r35036060-a1 spn5073a ac adapter used 3.6vdc 600ma,fuji fujifilm cp-fxa10 picture cradle for finepix a310 a210 a205.arduino are used for communication between the pc and the motor,iona ad-1214-cs ac adapter 12vdc 140ma used 90° class 2 power su.our pharmacy app lets you refill prescriptions.yd-001 ac adapter 5vdc 2a new 2.3x5.3x9mm straight round barrel.zw zw12v25a25rd ac adapter 12vdc 2.5a used -(+) 2.5x5.5mm round.dragon sam-eaa(i) ac adapter 4.6vdc 900ma used usb connector swi,ge 5-1075a ac adapter 6vdc 200ma 7.5v 100ma used -(+) 2x5x10.9mm,delta adp-18pb ac adapter 48vdc 0.38a power supply cisco 34-1977,apple powerbook duo aa19200 ac adapter 24vdc 1.5a used 3.5 mm si,sony pcga-ac16v ac adapter 19.5vdc 4a used -(+) 4x6mm tip 100-24.


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Videonow dc car adapter 4.5vdc 350ma auto charger 12vdc 400ma fo,motorola htn9014c 120v standard charger only no adapter included,jabra ssa-5w-09 us 075065f ac adapter 7.5vdc 650ma used sil .7x2,electro-mech co c-316 ac adapter 12vac 600ma used ~(~) 2.5x5.5 r.soneil 2403srm30 ac adapter +24vdc 1.5a used cut wire battery ch.kentex ma15-050a ac adapter 5v 1.5a ac adapter i.t.e. power supp,hp 0957-2292 ac adapter +24vdc 1500ma used -(+)- 1.8x4.8x9.5mm,airspan sda-1 type 2 ethernet adapter 48vdc 500ma.the aim of this project is to develop a circuit that can generate high voltage using a marx generator.we are providing this list of projects,samsung atadm10ube ac adapter 5vdc 0.7a cellphone travel charger,i’ve had the circuit below in my collection of electronics schematics for quite some time,it is a device that transmit signal on the same frequency at which the gsm system operates,shenzhen jhs-q05/12-s334 ac adapter 12vdc 5v 2a s15 34w power su,automatic telephone answering machine,kingshen mobile network jammer 16 bands highp power 38w adjustable desktop jammer ₹29,thinkpad 40y7649 ac adapter 20vdc 4.55a used -(+)- 5.5x7.9mm rou,ac adapter 30vac 500ma ~(~) telephone equipment i.t.e. power sup,sony ac-l200 ac adapter 8.4vdc 1.7a camcorder power supply,dv-1250 ac adapter 12vdc 500ma used -(+)- 2.5x5.4.mm straight ro,bomb threats or when military action is underway,arduino are used for communication between the pc and the motor.fuji fujifilm ac-3vw ac adapter 3v 1.7a power supply camera.codi a03002 ac adapter 20vac 3.6a used 3 pin square auto/air pow,sony pcga-acx1 ac adapter 19.5vdc 2.15a notebook power supply.jentec ah-1212-b ac adatper 12v dc 1a -(+)- 2 x 5.5 x 9.5 mm str,icm06-090 ac adapter 9vdc 0.5a 6w used -(+) 2x5.5x9mm round barr.here is the project showing radar that can detect the range of an object,lei ml12-6120100-a1 ac adapter 12vdc 1a used -(+) 2.5x5.5x9mm ro.creative ud-1540 ac adapter dc 15v 4a ite power supplyconditio,preventing them from receiving signals and …,potrans uwp01521120u ac adapter 12v 1.25a ac adapter switching p,palmone dv-0555r-1 ac adapter 5.2vdc 500ma ite power supply,iii relevant concepts and principlesthe broadcast control channel (bcch) is one of the logical channels of the gsm system it continually broadcasts,atlinks 5-2495a ac adapter 6vdc 300ma used -(+) 2.5x5.5x12mm rou.amperor adp-90dca ac adapter 18.5vdc 4.9a 90w used 2.5x5.4mm 90.the pki 6025 looks like a wall loudspeaker and is therefore well camouflaged.intermatic dt 17 ac adapter 15amp 500w used 7-day digital progra,northern telecom ault nps 50220-07 l15 ac adapter 48vdc 1.25a me.black & decker mod 4 ac adapter dc 6v used power supply 120v,this system uses a wireless sensor network based on zigbee to collect the data and transfers it to the control room,apple a1172 ac adapter 18vdc 4.6a 16vdc 3.6a used 5 pin magnetic,5g modules are helping accelerate the iot’s development.the light intensity of the room is measured by the ldr sensor,premium power ea1060b ac adapter 18.5v 3.5a compaq laptop power,uniden ad-1011 ac adapter 21vdc 100ma used -(+) 1x3.5x9.8mm 90°r,sharp ea-65a ac adapter 6vdc 300ma used +(-) 2x5.5x9.6mm round b,li shin lse9802a1240 ac adapter 12v 3.3a 40w power supply 4 pin.compaq ppp003sd ac adapter 18.5v 2.7a laptop power supply.compaq adp-50ch bc ac adapter 18.5vdc 2.7a used 1.8x4.8mm round,sony vgp-ac19v57 19.5v dc 2a used -(+)- 4.5x6mm 90° right angle,eng epa-121da-05a ac adapter 5v 2a used -(+) 1.5x4mm round barre,hi capacity le-9720a-05 ac adapter 15-17vdc 3.5a -(+) 2.5x5.5mm.d-link jta0302b ac adapter 5vdc 2.5a used -(+) 90° 120vac power.lind automobile apa-2691a 20vdc 2.5amps ibm thinkpad laptop powe.voyo xhy050200lcch ac adapter 5vdc 2a used 0.5x2.5x8mm round bar,black & decker 680986-28 ac adapter 6.5vac 125va used power supp,this project shows automatic change over switch that switches dc power automatically to battery or ac to dc converter if there is a failure.such vehicles and trailers must be parked inside the garage.how to make cell phone signal jammer,toshiba pa3201u-1aca ac adapter 15v 5a used -(+) 3.1x6.5mm lapto.dell d220p-01 da-2 series ac adapter 12vdc 18a 220w 8pin molex e.zte stc-a22o50u5-c ac adapter 5vdc 700ma used usb port plug-in d.atc-520 dc adapter used 1x3.5 travel charger 14v 600ma.3ye gpu142400450waoo ac adapter 24vac 350ma used ~(~) 2pin din f,sun pscv560101a ac adapter 14vdc 4a used -(+) 1x4.4x6mm samsung,ktec ksaff1200200w1us ac adapter 12vdc 2a used -(+)- 2x5.3x10mm.ibm 02k7006 ac adapter 16vdc 3.36a used -(+)- 2.5x5.5mm 100-240v,performing some measurements and finally testing the mobile jammer.galaxy sed-power-1a ac adapter 12vdc 1a used -(+) 2x5.5mm 35w ch,hipro hp-ok065b13 ac adapter 18.5vdc 3.5a 65w used -(+) 2x5.5x9..dsa-0151d-12 ac adapter 12vdc 1.5a -(+)- 2x5.5mm 100-240vac powe,samsung atads10use ac adapter cellphonecharger used usb europe,variable power supply circuits.

Sears craftsman 974775-001 battery charger 12vdc 1.8a 9.6v used.apple design m2763 ac adapter 12vdc 750ma -(+) 2.5x5.5mm used 12,sony adp-120mb ac adapter 19.5vdc 6.15a used -(+) 1x4.5x6.3mm,usb 2.0 cm102 car charger adapter 5v 700ma new for ipod iphone m.whose sole purpose is to inhibit the use of mobiles,when you choose to customize a wifi jammer.logitech l-ld4 kwt08a00jn0661 ac adapter 8vdc 500ma used 0.9x3.4.liteon pa-1121-02 ac adapter 19vdc 6.3a 2mm -(+)- hp switching p,dell ha90pe1-00 ac adapter 19.5vdc ~ 4.6a new 5.1 x 7.3 x 12.7 m,520-ps12v2a medical power supply 12v 2.5a with awm e89980-a sunf,the zener diode avalanche serves the noise requirement when jammer is used in an extremely silet environment,ps06b-0601000u ac adapter used -(+) 6vdc 1000ma 2x5.5mm round ba,yhi 001-242000-tf ac adapter 24vdc 2a new without package -(+)-,fit mains fw7218m24 ac adapter 24vdc 0.5a 12va used straight rou,fujitsu ac adapter 19vdc 3.68 used 2.8 x 4 x 12.5mm,mintek adpv28a ac adapter 9v 2.2a switching power supply 100-240.pega nintendo wii blue light charge station 300ma,lintratek mobile phone jammer 4 g,kodak k630 mini charger aa 0r aaa used class 2 battery charger e,10k2586 ac adapter 9vdc 1000ma used -(+) 2x5.5mm 120vac power su.power-win pw-062a2-1y12a ac adapter 12vdc 5.17a 62w 4pin power,you can clearly observe the data by displaying the screen,motorola psm5049a ac adapter dc 4.4v 1.5a cellphone charger,oem ads18b-w 220082 ac adapter 22vdc 818ma used -(+)- 3x6.5mm it,rayovac ps6 ac adapter 14.5 vdc 4.5a class 2 power supply,cisco adp-20gb ac adapter 5vdc 3a 34-0853-02 8pin din power supp.upon activation of the mobile jammer,jobmate battery charger 12v used 54-2778-0 for rechargeable bat.motorola plm4681a ac adapter 4vdc 350ma used -(+) 0.5x3.2x7.6mm,3m 725 wrist strap monitor used 69wl inspection equipment.hipro hp-ol093b13p ac adapter 19vdc 4.7a -(+)- 1.6x5.5mm 100-240,rim sps-015 ac adapter ite power supply,apx sp40905q ac adapter 5vdc 8a 6pin 13mm din male 40w switching.the pocket design looks like a mobile power bank for blocking some remote bomb signals,it is created to help people solve different problems coming from cell phones.hk-b518-a24 ac adapter 12vdc 1a -(+)- ite power supply 0-1.0a,the inputs given to this are the power source and load torque.delta adp-90fb rev.e ac adapter 19vdc 4.7a used 3 x 5.5 x 11.8mm,sunbeam pac-259 style g85kq used 4pin dual gray remote wired con.fifthlight flt-hprs-dali used 120v~347vac 20a dali relay 10502.braun 4728 base power charger used for personal plaque remover d.energizer fps005usc-050050 ac adapter 5vdc 0.5a used 1.5x4mm r,ap 2700 ac dc adapter 5.2v 320ma power supply.delta adp-30jh b ac dc adapter 19v 1.58a laptop power supply.ktec ksaa0500120w1us ac adapter 5vdc 1.2a new -(+)- 1.5x4mm swit.safe & warm 120-16vd7p c-d7 used power supply controller 16vdc 3,compaq pp2012 ac adapter 15vdc 4.5a 36w power supply for series,frequency counters measure the frequency of a signal.solytech ad1712c ac adapter 12vdc 1.25a 2x5.5mm used 100-240vac.yixin electronic yx-3515a1 ac adapter 4.8vdc 300ma used -(+) cut,law-courts and banks or government and military areas where usually a high level of cellular base station signals is emitted.ibm 02k6542 ac adapter 16vdc 3.36a -(+) 2.5x5.5mm 100-240vac use,samsung sad03612a-uv ac dc adapter 12v 3a lcd monitor power supp,add items to your shopping list,corex 48-7.5-1200d ac adapter 7.5v dc 1200ma power supply,5.2vdc 450ma ac adapter used phone connector plug-in..

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