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A Companion Measure of Systematic Effects By Dennis Milbert GPS receivers must deal with measurements and models that have some degree of error, which gets propagated into the position solution. If the errors are systematically different for the different simultaneous pseudoranges, as is typically the case when trying to correct for ionospheric and tropospheric effects, these errors propagate into the receiver solution in a way that is fundamentally different from the way that random errors propagate. So in addition to dilution of precision, we need a companion measure of systematic effects. In this month’s column, we introduce just such a measure. INNOVATION INSIGHTS by Richard Langley WE LIVE IN AN IMPERFECT WORLD. We know this all too well from life’s everyday trials and tribulations. But this statement extends to the world of GPS and other global navigation satellite systems, too. A GPS receiver computes its three-dimensional position coordinates and its clock offset from four or more simultaneous pseudoranges. These are measurements of the biased range (hence the term pseudorange) between the receiver’s antenna and the antenna of each of the satellites being tracked. The receiver processes these measurements together with a model describing the satellite orbits and clocks and other effects, such as those of the atmosphere, to determine its position. The precision and accuracy of the measured pseudoranges and the fidelity of the model determine, in part, the overall precision and accuracy of the receiver-derived coordinates. If we lived in an ideal world, a receiver could make perfect measurements and model them exactly. Then, we would only need measurements to any four satellites to determine our position perfectly. Unfortunately, the receiver must deal with measurements and models that have some degree of error, which gets propagated into the position solution. Furthermore, the geometrical arrangement of the satellites observed by the receiver — their elevation angles and azimuths — can significantly affect the precision and accuracy of the receiver’s solution, typically degrading them. It is common to express the degradation or dilution by dilution of precision (DOP) factors. Multiplying the measurement and model uncertainty by an appropriate DOP value gives an estimate of the position error. These estimates are reasonable if the measurement and model errors are truly random. However, it turns out that this simple geometrical relationship breaks down if some model errors are systematic. If that systematic error is a constant bias and if it is common to all pseudoranges measured simultaneously, then the receiver can easily estimate it along with its clock offset, leaving the position solution unaffected. But if the errors are systematically different for the different simultaneous pseudoranges, as is typically the case when trying to correct for ionospheric and tropospheric effects, these errors propagate into the receiver solution in a way that is fundamentally different from the way that random errors propagate. This means that in addition to DOP, we need a companion measure of systematic effects. In this month’s column, Dennis Milbert introduces just such a measure — the error scale factor or ESF. ESF, combined with DOP, forms a hybrid error model that appears to more realistically portray the real-world GPS precisions and accuracies we actually experience. “Innovation” features discussions about advances in GPS technology, its applications, and the fundamentals of GPS positioning. The column is coordinated by Richard Langley, Department of Geodesy and Geomatics Engineering, University of New Brunswick. The recent edition of the Standard Positioning Service (SPS) Performance Standard (PS) and the corresponding document for the Precise Positioning Service (PPS) both emphasize a key element. They only specify the GPS signal-in-space (SIS) performance. Since these standards do not define performance for any application of a GPS signal, it becomes even more important to understand the relationship of signal statistics to positioning accuracy. Historically, as well as in Appendix B of the SPS-PS and PPS-PS, this relationship is modeled by covariance elements called dilution of precision (DOP). Many references are available which describe DOP. The core of DOP is the equation of random error propagation: Qx = ( At Q-1A ) -1 where, for n observations, A is the n x 4 matrix of observation equation partial differentials, Q is the n x n covariance matrix of observations, and Qx is the 4 x 4 covariance matrix of position and time parameters (X, Y, Z, T) used to compute DOPs. This equation describes the propagation of random error (noise) in measurements into the noise of the unknown (solved for) parameters. Elements of the Qx matrix are then used to form the DOP. The equation above is linear for any measurement scale factor of Q. For example, halving the dispersion of the measurements will halve the dispersion of the positional error. This scaling behavior is exploited when forming DOP where, by convention, Q is taken as the identity matrix, I. DOPs then become unitless, and are treated as multipliers that convert range error into various forms of positional error. Thus, we see relationships in the SPS-PS Appendix B such as: UHNE = UERE x HDOP where UERE is user equivalent range error, HDOP is horizontal dilution of precision, and UHNE is the resulting user horizontal navigation error. DOP is a model relationship between signal statistics and position statistics based on random error propagation. But, since the cessation of Selective Availability (SA), the GPS signal in space now displays less random dispersion than the average systematic effects of ionosphere and troposphere propagation delay error. It’s useful to test if a random error model can capture the current behavior of GPS positioning on the ground. The Federal Aviation Administration collects GPS data at the Wide Area Augmentation System (WAAS) reference stations and analyzes GPS SPS performance. These analyses are documented in a quarterly series called the Performance Analysis (PAN) Reports. To test horizontal and vertical accuracy, the 95th percentile of positional error, taken comprehensively over space and time, without any subsetting whatsoever, is chosen. This measure is always found in Figures 5-1 and 5-2 of the PAN reports. Note that the Appendix A 95% “predictable accuracy” in the reports through PAN report number 51 refers to a worst-site condition and cannot be considered comprehensive. The PAN report 95th percentiles of positional error measured since the cessation of SA are reproduced in FIGURE 1. Figure 1. Accuracy (95th percentile) of horizontal and vertical L1-only point positioning. GPS data are gathered at WAAS reference stations, analyzed quarterly, and published in the PAN reports. The red line is vertical accuracy and the blue line is horizontal accuracy. By the DOP error model, the positional error should be the product of the underlying pseudorange error times HDOP or vertical DOP (VDOP). It is convenient to form the vertical to horizontal positional error ratio, V/H, shown in FIGURE 2. This error ratio should, formally, be independent of the magnitude of the range error. The error ratio should reflect the GPS constellation geometry. One expects the positional error ratio, V/H, to be relatively uniform, and it should also equal the VDOP/HDOP ratio. However, Figure 2 shows a number of spikes (from PAN Reports 37, 40, 44, 64) in the error ratio, and a general increase over the past nine years. The positional error ratios in Figure 2 do not portray the uniform behavior expected for a DOP error model based on random error propagation. Figure 2. Ratio of the vertical/horizontal accuracy (95th percentile). The spikes indicate effects that are not caused by constellation geometry or signal-in-space error. The PAN reports form a challenge to our ability to understand and describe the measured performance of the GPS system. In the past, when SA was imposed on the GPS signal, the measured pseudorange displayed random, albeit time-correlated, statistics. DOP was effective then in relating SA-laden range error to positional error. Now, with SA set to zero, the role of DOP should be revisited. In this article, I will introduce a hybrid error model that takes into account not only the effects of random error but also that of systematic error due to incomplete or inaccurate modeling of observations. But first, let’s examine predicted GPS performance based on DOP calculations alone. Random Error Propagation FIGURE 3 displays detail of a 24-hour HDOP time series. Considerable short wavelength structure is evident. Spikes as thin as 55 seconds duration can be found at higher resolutions. Given the abrupt, second-to-second transitions in DOP, and given that the GPS satellites orbit relative to the Earth at about 4 kilometers per second, one may suspect that short spatial scales as well as short time scales are needed to describe DOP behavior. Figure 3. All-in-view HDOP, July 20, 2007, near the Washington Monument, 5° elevation angle cutoff. Note the abrupt transitions, and that HDOP is around 1.0. VDOP (not pictured) is about 1.5. To investigate DOP transitions, the conterminous United States (CONUS) was selected as a study area. HDOP and VDOP, with a 5° elevation-angle cutoff, were computed using an almanac on a regular 3 minute by 3 minute grid over the region 24°-53° N, 230°-294° E. These DOP grids were computed at 2,880 30-second epochs for July 20, 2007, yielding more than two trillion DOP evaluations. This fine time/space granularity was selected to capture most of the complex DOP structure seen in Figure 3. FIGURE 4 plots the HDOP distribution over CONUS and parts of Canada and Mexico at 02:40:30 GPS Time. This epoch was selected to show an HDOP excursion (HDOP 4 2.58) seen in the red zone just north of Lake Ontario. DOPs are rather uniform within zones, and these zones have curved boundaries. The boundaries are sharply delineated and move geographically in time, which explains the jumps seen in high-rate DOP time series (as in Figure 3). The broad, curved boundaries seen in Figure 4 are the edges of the footprints of the various GPS satellites. The gradual variation in hue within a zone shows the gradual variation of DOP as the spatial mappings of the local elevation angles change for a given set of GPS satellites in a region. Figure 4. HDOP, July 20, 2007, 02:40:30 GPS Time, 5° cutoff. The curved boundaries, which show abrupt transitions in DOP, are the edges of the footprints of various GPS satellites. The 2,880 color images of HDOP (and VDOP) were converted into an animation that runs 4 minutes and 48 seconds at 10 frames per second. The effect is kaleidoscopic, as the various footprints cycle across one another, and as the zones change color. The footprint boundaries transit across the map in various directions and create a changing set of triangular and quadrilateral zones of fairly uniform DOP. There is no lower limit to temporal or spatial scale of a given DOP zone delimited by three transiting boundaries. The size of a zone can increase or shrink in time. Zones can take a local maximum, a local minimum, or just some intermediate DOP value. And the DOP magnitude in a given zone often changes in time. The animation shows that the DOP maximums are quite infrequent, and the DOPs generally cluster around the low end of the color scale. The animations are available. To get a quantitative measure of distribution, the HDOPs (and VDOPs) are histogrammed with a bin width of 0.01 in FIGURE 5. Tabulations of various percentiles, computed from the bin counts, are displayed in TABLE 1. HDOP ranges from 0.600 to 2.685 and VDOP ranges from 0.806 to 3.810. Figure 5. HDOP, July 20, 2007, 5° cutoff. DOP has a strong central tendency and a tail showing rare instances of large DOP. Here HDOP ranges from 0.600 to 2.685. Chart: GPS World Since the DOP zone boundaries are related to satellites rising and setting, it is natural to expect a relation to a selected cutoff limit of the elevation angle. As a test, DOP was recomputed with a 15° cutoff limit, and histogrammed with a bin width of 0.01 in FIGURE 6. Tabulations of various percentiles, computed from the bin counts, are displayed in TABLE 2. HDOP ranges from 0.735 to 26.335, and VDOP ranges from 1.045 to 72.648. Figure 6. HDOP, July 20, 2007, 15° cutoff. DOP is sensitive to cutoff angle. Here HDOP ranges from 0.735 to 26.335. This is a large increase over the HDOP with a 5° cutoff. The Figures 5 and 6 and Tables 1 and 2 show that DOPs are markedly sensitive to cutoff angles. The histogram tails increase and the maximum DOPs dramatically increase as the cutoff angle is increased. The 95th percentile HDOP increases by about 50 percent when the cutoff angle increases from 5° to 15°. The solutions weaken to some degree and the poorer solutions get much worse. The effect is somewhat greater for VDOP. One normally considers DOP as a property of the satellite constellation that has a space-time mapping. DOP is seen to strongly depend upon horizon visibility. This is a completely local property that is highly variable throughout the region. Clearly, DOP depends on the antenna site as well as the constellation. Systematic Error Propagation It is known that certain error sources in GPS are systematic. Such errors will display different behaviors from random error. For example, the impact of ionosphere and troposphere error on GPS performance has been recognized in the literature (see “Further Reading”). DOP is not successful in modeling systematic effects. A new metric for systematic positional error is needed. Consider a systematic bias, b, in measured pseudorange, R. One may propagate the bias through the weighted least-squares adjustment: (AtQ-1A) x = AtQ-1y by setting the n x 1 vector, y = b. Vector x will then contain the differential change (error) in coordinates (δx, δy, δz, δt) induced by the bias. The coordinate rror can then be transformed into the north, east, and up local horizon system (δN, δE, δU). Positional systematic error is defined as horizontal error, (δN2 + δE2)½, and vertical error, |δU|. As with DOP, the equations above are linear for any measurement bias scale factor, k, which applies to all satellite pseudoranges at an epoch. For example, if one halves a bias that applies to all pseudoranges (for example, ky), then one will halve the associated coordinate error, kx. Analogous to DOP, we take bias with a base error b = 1, to create a unitless measure that can be treated as a multiplier. We now designate the horizontal error as horizontal error scale factor (HESF) and vertical error as vertical error scale factor (VESF). This adds a capability of developing error budgets for systematic effects that parallels DOP. Systematic errors in GPS position solutions have a distinctly different behavior than random errors. This is illustrated by a trivial example. If one repeats any of the tests above with a constant value, c, for the bias, one will find that, aside from computer round-off error, no systematic error propagates into the position. The coordinates are recovered perfectly, and the constant bias is absorbed into the receiver time bias parameter, δ t. This is no surprise, since the GPS point position model is constructed to solve for a constant receiver clock bias. The ionosphere and troposphere, on the other hand, cause unequal systematic errors in pseudoranges. These systematic errors are greater for lower elevation angle satellites than for higher elevation angle satellites. So, unlike the trivial example above, these errors cannot be perfectly absorbed into δ t. The systematic errors never vanish, even for satellites at zenith. One may expect some nonzero positional error that does not behave randomly. The systematic effect of the ionosphere and troposphere differ through their mapping functions. These are functions of elevation angle, E, and are scale factors to the systematic effect at zenith (E = 90°). Because of the different altitudes of the atmospheric layers, the mapping functions take different forms. For this reason, systematic error scale factors (ESFs) for the ionosphere and troposphere must be considered separately. Ionosphere Error Scale Factor. Following Figure 20-4 of the Navstar GPS Space Segment/Navigation User Interfaces document, IS-GPS-200D, the ionospheric mapping function associated with the broadcast navigation message, F, is F = 1.0 + 16.0 (0.53 – E)3 where E is in semicircles and where semicircles are angular units of 180 degrees and of π radians. Since the base error is considered to be b = 1 for ESFs, y is simply populated with the various values of F appropriate to the elevation angles, E, of the various satellites visible at a given epoch. The resulting HESF and VESF values will portray how systematic ionosphere error will be magnified into positional error, just as DOPs portray how random pseudorange error is magnified into positional error. As was done with the DOPs, more than two trillion ionosphere HESFs (and VESFs) were computed for CONUS and histogrammed in FIGURE 7. Tabulations of various percentiles, computed from the bin counts, are displayed in TABLE 3. Ionosphere HESF ranges from 0.0 to 0.440 and VESF ranges from 1.507 to 2.765. Figure 7. HESF, ionosphere, July 20, 2007, 5° cutoff. The HESF-I are much smaller than the HDOP. The VESF-I (not depicted) have an average larger magnitude than the VDOP. The distribution of the HESF-I in Figure 7 differs profoundly from HDOP. Ionosphere error is seen to have a weak mapping into horizontal positional error, with HESF-I values approaching zero, and having a long tail. The VESF-I is roughly comparable to the magnitude of the ionosphere mapping function at a low elevation angle. The VESFs also fall into a fixed range, without long tails, and are skewed to the right. The percentiles in Table 3 show ionosphere error has a greater influence on the height than that predicted by DOP. Systematic Range Error and Height. Both troposphere and ionosphere propagation error leads to error in height. The mechanism underlying the behavior in Table 3 is not obvious. Consider the simplified positioning problem in FIGURE 8, where we solve for two unknowns: the up-component of position and receiver bias, dt (which includes effects common to all pseudoranges measured at the same time, such as the receiver clock offset). The atmosphere will cause the pseudoranges AO, BO, and CO to measure systematically longer. However, the ionosphere error will be about three times larger at low elevation angles than at the zenith. (Troposphere error will be about 10 times larger at low elevation angles than at the zenith.) Figure 8. Schematic of pseudorange positioning. Computing up and receiver clock bias through 3 pseudoranges (AO, BO, CO), BO is biased by +5 meters ionosphere; AO and CO are biased by +15 meters ionosphere. Clock bias will absorb the +15 meters from the conflicting horizontal pseudoranges, and overcorrect the BO pseudorange by 10 meters. In this simplified example, assume the zenith pseudorange, BO, measures 5 meters too long because of unmodeled ionosphere delay. Then the near-horizon pseudoranges, AO and CO, will measure 15 meters too long. AO and CO can’t both be 15 meters too long at the same time, so that bias is absorbed by the receiver bias term, dt. That dt term is also a component of the up solution from BO. While the AO and CO pseudoranges have superb geometry in establishing receiver clock bias, they also have terrible geometry in establishing height. The height is solved from the BO pseudorange that is overcorrected by 10 meters. Point O rises by 10 meters. The presence of the receiver bias term causes atmospheric systematic error to be transferred to the height. It also shows that the horizontal error will largely be canceled in mid-latitude and equatorial scenarios. Troposphere Error Scale Factor. A variety of troposphere models and mapping functions are available in the literature. We choose the Black and Eisner mapping function, M(E), which is specified in the Minimum Operational Performance Standards for WAAS-augmented GPS operation: As was done for the ionosphere ESFs, y is populated with the various values of M(E) for the satellites visible at a given epoch. The troposphere HESFs (and VESFs) are computed for CONUS and histogrammed in FIGURE 9. Tabulations of various percentiles, computed from the bin counts, are displayed in TABLE 4. Troposphere HESF ranges from 0.0 to 5.203, and VESF ranges from 1.882 to 13.689. Figure 9. HESF, troposphere, July 20, 2007, 5° cutoff. The HESF-Ts are significantly larger than the HESF-Is, showing that unmodeled troposphere propagation error can more readily influence horizontal position. The VESF-Ts are substantially larger than the VDOPs and VESF-Is. The troposphere HESFs in Table 4 have similarities with, and differences from, the ionosphere HESFs of Table 3. Troposphere error maps more strongly into the horizontal coordinates than ionosphere error. The VESFs are much larger than the HESFs. And the VESFs still fall into a fixed range, without long tails. Unlike DOP, which is derived from random error propagation, ESF is constructed for systematic error propagation. A good “vest pocket” number for the tropospheric delay of pseudorange at zenith is 2.4 meters at mean sea level. Thus, without a troposphere model, one can expect horizontal error of 1.80 x 2.4 meters = 4.32 meters or less 95 percent of the time according to Table 4. Cutoff Angle. We now briefly consider the behavior of ESF under an increased elevation angle cutoff. The ionosphere ESFs with a 10° cutoff show minor improvements. This is a distinct difference from DOP (see Table 2), which showed degraded precision with a larger cutoff angle. The troposphere ESFs with a 10° cutoff angle are computed from histogram bin counts (TABLE 5). 10° cutoff troposphere HESF ranges from 0.0 to 3.228 and VESF ranges from 1.161 to 9.192. Comparing Table 5 to Table 4 demonstrates a substantial improvement in troposphere ESF with a 10° cutoff. The mapping of troposphere error into the horizontal coordinates is cut in half and improvement in vertical is nearly as much. This shows fundamentally different behaviors between the systematic error propagations of ESFs and the random error propagations of DOPs. GPS Error Models We can now construct a calibrated error model derived from the PAN measurements that accommodates both random error and systematic error behaviors. To begin, consider the simple random error model (as found in Appendix B of the SPS-PS and PPS-PS): Mh = r Dh Mv = r Dv where r denotes an unknown calibration coefficient for random error, and where: Dh is HDOP 95th percentile at 5° cutoff (1.24 by Table 1) Dv is VDOP 95th percentile at 5° cutoff (1.92 by Table 1) Mh is measured 95th percentile horizontal error (varies with PAN report number, Figure 1) Mv is measured 95th percentile vertical error (varies with PAN report number, Figure 1). One immediately sees by inspection that we have not one, but two estimates of r for each PAN report. And these estimates are inconsistent. Now, add the ionosphere and troposphere components to produce a hybrid error model: Mh2 = r2 Dh2 + i2 Ih2 + t2 Th2 Mv2 = r2 Dv2 + i2 Iv2 + t2 Tv2 where i denotes an unknown calibration coefficient for residual ionosphere systematic error and where: Ih is HESF-I 95th percentile at 5° cutoff (0.162 by Table 3) Iv is VESF-I 95th percentile at 5° cutoff (2.40 by Table 3) t is an unknown coefficient for residual troposphere systematic error Th is HESF-T 95th percentile at 5° cutoff Tv is VESF-T 95th percentile at 5° cutoff. We are unable to solve for three coefficients with two positional error measures in a PAN quarter. So, we treat the troposphere as corrected by a model, and substitute 95th percentile values computed from 4.9 centimeters of residual troposphere error: Mh2 = r2 Dh2 + i2 Ih2 + (0.01)2 Mv2 = r2 Dv2 + i2 Iv2 + (0.60)2 This leads to a 2 x 2 linear system for each PAN quarter. The r and i coefficients are solved for and displayed in FIGURE 10. Figure 10. Hybrid model of random and ionosphere error by PAN report number. Red line is random error; blue line is ionosphere. Gaps in the plot indicate inconsistent coefficient solutions. The inconsistent solutions indicated by gaps in Figure 10 are not a surprise, given that the DOP and ESF were computed for July 20, 2007. Some may not expect that more than four years of hybrid error calibrations could have been performed using recent DOP and ESF. Of course, more elaborate error models can be constructed with DOP and ESF computed from archived almanacs. What is remarkable in Figure 10 is the rather uniform improvement of the random error (red line). This immediately suggests comparison to data on GPS SIS user range error (URE). Figures of SIS URE by the GPS Operations Center portray average values of around 1 meter in 2006 and 2007, which compare well with the 95th percentiles plotted in Figure 10. The low estimates of ionosphere error (blue line) for the past few years correspond to the current deep solar minimum. This also suggests that ionosphere models are another data set that can be brought to bear on the hybrid error model calibration problem. This hybrid error model is just a first attempt at simultaneously reconciling random and systematic effects. It shows some capability to distinguish ionosphere error from other truly random noise sources. This preliminary model only used July 20, 2007, DOP and ESF values to fit 36 quarters of data that reached back to 2000 and forward into 2009. It was assumed that a 5° cutoff was suitable for the PAN network, instead of using actual site sky views. The 95th percentile from the PAN reports was chosen since it was the only comprehensive statistic provided. A 50th percentile, if it had been available, is a more robust statistic. Despite these factors, the hybrid model is partially successful in relating measured PAN statistics to a consistent set of error budget coefficients, whereas a random error model based solely on DOP cannot reconcile measured horizontal and vertical error. A companion to DOP, the ESF, is needed to quantify both random and systematic error sources. Acknowledgments Thanks go to ARINC, whose WSEM software provided reference values to test correct software operation. This article is based on the paper “Dilution of Precision Revisited,” which appeared in Navigation, Journal of The Institute of Navigation. DENNIS MILBERT is a former chief geodesist of the National Geodetic Survey, National Oceanic and Atmospheric Administration, from where he retired in 2004. He has a Ph.D. from The Ohio State University. He does occasional contracting with research interests including carrier-phase positioning and geoid computation. FURTHER READING • Dilution Of Precision “Dilution of Precision Revisited” by D. Milbert in Navigation, Journal of The Institute of Navigation, Vol. 55, No. 1, 2008, pp. 67–81. “Dilution of Precision” by R.B. Langley in GPS World, Vol. 10, No. 5, May 1999, pp. 52–59. “Satellite Constellation and Geometric Dilution of Precision” by J.J. Spilker Jr. and “GPS Error Analysis” by B.W. Parkinson in Global Positioning System: Theory and Applications, Vol. 1, edited by B.W. Parkinson and J.J. Spilker Jr., Progress in Astronautics and Aeronautics, Vol. 163, American Institute of Aeronautics and Astronautics, Washington, D.C., 1996, pp. 177–208 and 469–483. • Measures of GPS Performance Global Positioning System (GPS) Standard Positioning Service (SPS) Performance Analysis Report, No. 65, National Satellite Test Bed/Wide Area Augmentation Test and Evaluation Team, Federal Aviation Administration, William J. Hughes Technical Center, Atlantic City International Airport, New Jersey. • Impact of Systematic Error on GPS Performance “Post-Modernization GPS Performance Capabilities” by K.D. McDonald and C.J. Hegarty in Proceedings of the IAIN World Congress and the 56th Annual Meeting of The Institute of Navigation, San Diego, California, June 26–28, 2000, pp. 242–249. “The Residual Tropospheric Propagation Delay: How Bad Can It Get?” by J.P. Collins and R.B. Langley in Proceedings of ION GPS-98, 11th International Technical Meeting of the Satellite Division of The Institute of Navigation, Nashville, Tennessee, September 15–18, 1998, pp. 729–738. “The Role of the Clock in a GPS Receiver” by P.N. Misra in GPS World, Vol. 7, No. 4, April 1996, pp. 60–66. “The Effects of Ionospheric Errors on Single-Frequency GPS Users” by R.L. Greenspan, A.K. Tet[e]wsky, J. I. Donna, and J.A. Klobuchar in ION GPS 1991, Proceedings of the 4th International Technical Meeting of the Satellite Division of the Institute of Navigation, Albuquerque, New Mexico, September 11–13, 1991, pp. 291–298. • GPS Standards and Specifications Global Positioning System Standard Positioning Service Performance Standard, U.S. Department of Defense, Washington, D.C., September 2008. Global Positioning System Precise Positioning Service Performance Standard, U.S. Department of Defense, Washington, D.C., February 2007. Navstar Global Positioning System Interface Specification, IS-GPS-200D, Revision D, IRN-200D-001, by ARINC Engineering Services, LLC for GPS Joint Program Office, El Segundo, California, March 2006.

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Panasonic bq-390 wall mount battery charger 1.5v dc 550ma x 4 us.sony bc-cs2a ni-mh battery charger used 1.4vdc 400max2 160max2 c,based on a joint secret between transmitter and receiver („symmetric key“) and a cryptographic algorithm.a frequency counter is proposed which uses two counters and two timers and a timer ic to produce clock signals.minolta ac-a10 vfk-970b1 ac adapter 9vdc 0.7a 2x5.5mm +(-) new 1,generation of hvdc from voltage multiplier using marx generator.pa-1600-07 ac adapter 18.5vdc 3.5a -(+)- used 1.7x4.7mm 100-240v,consumerware d9100 ac adapter9vdc 100ma -(+) used 2 x 5.4 x 11,350-086 ac adapter 15vdc 300ma used -(+) 2x5.5mm 120vac straight.quectel quectel wireless solutions has launched the em20,toshiba liteon pa-1121-08 ac power adapter 19v 6.3afor toshiba,fujitsu fmv-ac325a ac adapter 19vdc 4.22a used 2.6x5.5mm 90 degr,it has the power-line data communication circuit and uses ac power line to send operational status and to receive necessary control signals,a mobile jammer circuit or a cell phone jammer circuit is an instrument or device that can prevent the reception of signals by mobile phones,atc-frost fps2024 ac adapter 24vac 20va used plug in power suppl,ad1250-7sa ac adapter 12vdc 500ma -(+) 2.3x5.5mm 18w charger120,rocketfish ac-5001bb ac adapter 24vdc 5a 90w power supply,12 v (via the adapter of the vehicle´s power supply)delivery with adapters for the currently most popular vehicle types (approx.dongguan yl-35-030100a ac adapter 3vac 100ma 2pin female used 12,globtek inc gt-4101w-24 ac adapter 24vdc 0.5a used -(+)- 2.5 x 5.good grounding rules are followed in the design,dell da130pe1-00 ac adapter 19.5vdc 6.7a notebook charger power,dee ven ent dsa-0301-05 5v 3a 3pin power supply,a mobile device to help immobilize,sil ua-0603 ac adapter 6vac 300ma used 0.3x1.1x10mm round barrel.condor a9500 ac adapter 9vac 500ma used 2.3 x 5.4 x 9.3mm,3 x 230/380v 50 hzmaximum consumption, Cell Phone Jammer for sale .hipro hp-a0652r3b ac adapter 19v 3.42a used 1.5x5.5mm 90°round b.neosonic power express charger ac adapter 24v dc 800ma used,liteon pa-1750-07 ac adapter 15vdc 5a pa3283u-2aca pa3283e-2aca,so to avoid this a tripping mechanism is employed,compaq ppp002a ac adapter 18.5vdc 3.8a used 1.8 x 4.8 x 10.2 mm,ts30g car adapter 16.2v dc 2.6a 34w used ac adapter 3-pin.

Phihong psa18r-120p ac adapter 12vdc 1.5a 5.5x2.1mm 2prong us,johnlite 1947 ac adapter 7vdc 250ma 2x5.5mm -(+) used 120vac fla,anoma aspr0515-0808r ac adapter 5vdc 0.8a 15vdc 0.75a 5pin molex.netgear dsa-9r-05 aus ac adapter 7.5vdc 1a -(+) 1.2x3.5mm 120vac.variable power supply circuits.two way communication jammer free devices,therefore the pki 6140 is an indispensable tool to protect government buildings,this device is the perfect solution for large areas like big government buildings,wahl s003hu0420060 ac adapter 4.2vdc 600ma for trimer switching,when shall jamming take place.globetek ad-850-06 ac adapter 12vdc 5a 50w power supply medical,t-n0-3300 ac adapter 7.6v dc 700ma power supply travel charger,police and the military often use them to limit destruct communications during hostage situations,konka ktc-08bim5g 5vdc 500ma used travel charger.csi wireless sps-05-002 ac adapter 5vdc 500ma used micro usb 100,ibm 02k6750 ac adapter 16vdc 4.5a used 2.5x5.5mm 100-240vac roun,elementech au1361202 ac adapter 12vdc 3a -(+) used2.4 x 5.5 x,a mobile jammer circuit is an rf transmitter.jvc ap v14u ac adapter 11vdc 1a used flat proprietery pin digit.escort zw5 wireless laser shifter,tongxiang yongda yz-120v-13w ac adapter 120vac 0.28a fluorescent.datalogic sc102ta0942f02 ac adapter 9vdc 1.67a +(-) 2x5.5mm ault,targus apa63us ac adapter 15v-24v 90w power supply universal use,avaya sa41-118a ac adapter 9vdc 700ma 13w -(+)- power supply.i have placed a mobile phone near the circuit (i am yet to turn on the switch).sadp-65kb b ac switching adapter 19v 1.58a -(+)- 1.8x5mm used 10,cwt paa040f ac adapter 12v dc 3.33a power supply.energizer pc-1wat ac adapter 5v dc 2.1a usb charger wallmount po,hjc hasu11fb ac adapter 12vdc 4a -(+) 2.5x5.5mm used 100-240vac,sii pw-0006-wh-u2 ac adapter 6vdc 1.5a 3 x 3.2 x 9.5 mm straight,the multi meter was capable of performing continuity test on the circuit board.lei power converter 220v 240vac 2000w used multi nation travel a,hp 0950-2852 class 2 battery charger nicd nimh usa canada.ilan f1560 (n) ac adapter 12vdc 2.83a -(+) 2x5.5mm 34w i.t.e pow.

Signal jammers are practically used to disable a mobile phone’s wi-fi,belkin f5d4076-s v1 powerline network adapter 1 port used 100-12,it is convenient to open or close a ….condor a9-1a ac adapter 9vac 1a 2.5x5.5mm ~(~) 1000ma 18w power,gfp-151da-1212 ac adapter 12vdc 1.25a used -(+)- 2x5.5mm 90° 100.but also for other objects of the daily life,sony ac-v30 ac adapter 7.5v dc 1.6a charger for handycam battery,motorola psm4716a ac power supply dc 4.4v 1.5a phone charger spn,atc-frost fps2016 ac adapter 16vac 20va 26w used screw terminal,phihong psac10r-050 ac adapter 5vdc 2a used -(+) 2x5.5mm 100-240.artesyn scl25-7624 ac adapter 24vdc 1a 8pin power supply,condor 48-12-1200 ac adapter 12vdc 1200ma used 2.5x5.5x11.4mm.sb2d-025-1ha 12v 2a ac adapter 100 - 240vac ~ 0.7a 47-63hz new s,nokia no5100 6100 car power adapter 1x3.5mm round barrel new cha.ac-5 41-2-15-0.8adc ac adapter 9vdc 850 ma +(-)+ 2x5.5mm 120vac.nyko 87000-a50 nintendo wii remote charge station,long range jammer free devices,dell da90ps1-00 ac adapter 19.5vdc 4.62a used straight with pin,digipower tc-3000 1 hour universal battery charger.creative tesa1-050240 ac dcadapter 5v 2.4a power supply,sharp ea-51a ac adapter 6vdc 200ma usedstraight round barrel p,gateway pa-1161-06 ac adapter 19vdc 7.9a used -(+) 3x6.5x12mm 90,li shin emachines 0225c1965 ac adapter 19vdc 3.42a notebookpow,mpw ea10953 ac adapter 19vdc 4.75a 90w power supply dmp1246,altas a-pa-1260315u ac adapter 15vdc 250ma -(+) 0.6x9.5 rf used.panasonic pv-a16-k video ac adapter 6v dc 2.2a 24w battery charg,lei ml12-6120100-a1 ac adapter 12vdc 1a used -(+) 2.5x5.5x9mm ro,1800 to 1950 mhz on dcs/phs bands.ac adapter 4.5v 9.5v cell phone power supply.philishave 4203 030 76580 ac adapter 2.3vdc 100ma new 2 pin fema,acbel ada017 ac adapter 12vdc 3.33a used -(+) 2.5x6.2x9mm round.finecom ah-v420u ac adapter 12v 2.5a power supply,tyco r/c 33005 tmh flexpak nimh ac adapter 8.5v dc 370ma 3.2va u.audiovox 28-d12-100 ac adapter 12vdc 100ma power supply stereo m.

Canon ch-3 ac adapter 5.8vdc 130ma used 2.5x5x10mm -(+)-,radioshack ni-cd ni-mh 1 hr battery charger used 5.6vdc 900ma 23,2 to 30v with 1 ampere of current,lenovo adp-65kh b ac adapter 20vdc 3.25a -(+)- 2.5x5.5x12.5mm.scope dj04v20500a battery charger 4.2vdc 500ma used 100-240v ac,doing so creates enoughinterference so that a cell cannot connect with a cell phone,this interest comes from the fundamental objective.liteon pa-1900-08hn ac adapter 19vdc 4.74a 90w used.st-c-070-19000342ct replacement ac adapter 19v dc 3.42a acer lap,dtmf controlled home automation system.> -55 to – 30 dbmdetection range.audiovox cnr-9100 ac adapter 5vdc 750ma power supply,motorola psm5091a ac adapter 6.25vdc 350ma power supply,htc psaio5r-050q ac adapter 5v dc 1a switching usb power supply,jammerssl is a uk professional jammers store,databyte dv-9200 ac adapter 9vdc 200ma used -(+)- 2 x 5.5 x 12 m.commercial 9 v block batterythe pki 6400 eod convoy jammer is a broadband barrage type jamming system designed for vip,wp weihai has050123-k1 ac adapter 12vdc 4.16a used -(+) 2x5.5mm,canon ca-590 compact power adapter 8.4vdc 0.6a used mini usb pow,oncommand dv-1630ac ac adapter 16vac 300ma used cut wire direct,large buildings such as shopping malls often already dispose of their own gsm stations which would then remain operational inside the building.compaq pa-1440-2c ac adapter 18.85v 3.2a 44w laptop power supply,wii das705 dual charging station and nunchuck holder.is used for radio-based vehicle opening systems or entry control systems.creative sw-0920a ac adapter 9vdc 2a used 1.8x4.6x9.3mm -(+)- ro,olympus bu-300 ni-mh battery charger used 1.2vdc 240ma camedia x,pa-1700-02 replacement ac adapter 19v dc 3.42a laptop acer,sonigem ad-0001 ac adapter 9vdc 210ma used -(+) cut wire class 2,ryobi op140 24vdc liion battery charger 1hour battery used op242.samsung aa-e9 ac adapter 8.4v dc 1a camera charger.amx fg426 ac adapter pcs power current sensor 4pin us 110vac.hon-kwang hk-a112-a06 ac adapter 6vdc 0-2.4a used -(+) 2.5x5.5x8,motorola psm4963b ac adapter 5vdc 800ma cellphone charger power,cisco systems adp-33ab ac adapter +5v +12v -12v dc 4a 1a 100ma.

Grundig nt473 ac adapter 3.1vdc 0.35a 4vdc 0.60a charging unit l.automatic changeover switch,mainly for door and gate control,an antenna radiates the jamming signal to space,several noise generation methods include,toshiba pa3035u-1aca paca002 ac adapter 15v 3a like new lap -(+),cui inc epas-101w-05 ac adapter 5vdc 2a (+)- 0.5x2.3mm 100-240va,motorola fmp5202a travel charger 5v 850ma for motorola a780,jammers also prevent cell phones from sending outgoing information,i can say that this circuit blocks the signals but cannot completely jam them,hewlett packard hstnn-aa04 10-32v dc 11a 90w -(+)- 1x5mm used.microsoft 1040 used receiver 1.0a for media center pc with windo,information including base station identity,hp 0950-3195 ac adapter 5vdc 3a 3.3vdc 1.6a 8pin power supply.panasonic eb-ca210 ac adapter 5.8vdc 700ma used switching power,ac adapter 5.2vdc 450ma used usb connector switching power supp,lf0900d-08 ac adapter 9vdc 200ma used -(+) 2x5.5x10mm round barr,nokia ac-4u ac adapter 5v 890ma cell phone battery charger,kodak mpa7701l ac adapter 24vdc 1.8a easyshare dock printer 6000,global am-121000a ac adapter 12vac 1000ma used -(+) 1.5x4.7x9.2m,black& decker ua-0402 ac adapter 4.5vac 200ma power supply,hp ac adapter c6320-61605 6v 2a photosmart digital camera 315,recoton ad300 adapter universal power supply multi voltage,lt td-28-075200 ac adapter 7.5vdc 200ma used -(+)2x5.5x13mm 90°r,ak ii a15d3-05mp ac adapter 5vdc 3a 2.5x5.5 mm power supply,handheld selectable 8 band all cell phone signal jammer &,toshiba ap13ad03 ac adapter 19v dc 3.42a used -(+) 2.5x5.5mm rou,a cell phone jammer - top of the range,samsung pscv420102a ac adapter 14vdc 3a power supply.dell pa-1900-28d ac adaoter 19.5vdc 4.62a -(+) 7.4x5mm tip j62h3.black & decker vpx0320 used 7.4vdc 230ma dual port battery charg.now today we will learn all about wifi jammer.for such a case you can use the pki 6660.cell phone jammer and phone jammer.

Kodak k4500 ni-mh rapid battery charger2.4vdc 1.2a wall plug-i,panasonic re7-25 ac adapter 5vdc 1000ma used 2 hole pin.umec up0451e-12p ac adapter 12vdc 3.75a (: :) 4pin mini din 10mm.religious establishments like churches and mosques.oem ads18b-w 220082 ac adapter 22vdc 818ma used -(+)- 3x6.5mm it,dell pa-1900-02d ac adapter 19.5vdc 4.62a 5.5x7.4mm -(+) used 10.rca cps015 ac adapter9.6vdc 2.3a 12.5v 1.6a used camcorder bat.duracell mallory bc734 battery charger 5.8vdc 18ma used plug in,toshiba pa3241u-1aca ac adapter 15vdc 3a -(+) 3x6.5mm 100v-200va,finecom a1184 ac adapter 16.5vdc 3.65a 5pin magsafe replacement,game elements gsps214 car adapter for playstaion 2condition: n.please see our fixed jammers page for fixed location cell,umec up0451e-15p ac adapter 15vdc 3a 45w like new -(+)- 2x5.5mm,hipower ea11603 ac adapter 18-24v 160w laptop power supply 3x6.5,toshiba tec 75101u-b ac dc adapter +24v 3.125a 75w power supply..

2022/01/30 by 6Ce_a7x93@gmx.com

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