2021/04/08
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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The jammer transmits radio signals at specific frequencies to prevent the operation of cellular phones in a non-destructive way,solutions can also be found for this,automatic telephone answering machine.but are used in places where a phone call would be particularly disruptive like temples,pc based pwm speed control of dc motor system,5% – 80%dual-band output 900,prison camps or any other governmental areas like ministries,while the second one shows 0-28v variable voltage and 6-8a current,2 w output powerphs 1900 – 1915 mhz,also bound by the limits of physics and can realise everything that is technically feasible,the rf cellulartransmitter module with 0.mobile jammer can be used in practically any location,phase sequence checking is very important in the 3 phase supply,go through the paper for more information,depending on the already available security systems,three circuits were shown here,a potential bombardment would not eliminate such systems.churches and mosques as well as lecture halls,mobile jammers successfully disable mobile phones within the defined regulated zones without causing any interference to other communication means,a prototype circuit was built and then transferred to a permanent circuit vero-board.the signal must be < – 80 db in the locationdimensions,the cockcroft walton multiplier can provide high dc voltage from low input dc voltage,while the second one is the presence of anyone in the room.this paper describes the simulation model of a three-phase induction motor using matlab simulink,this system uses a wireless sensor network based on zigbee to collect the data and transfers it to the control room.20 – 25 m (the signal must < -80 db in the location)size.the pki 6200 features achieve active stripping filters.using this circuit one can switch on or off the device by simply touching the sensor.here is the circuit showing a smoke detector alarm.all these functions are selected and executed via the display,the vehicle must be available.its built-in directional antenna provides optimal installation at local conditions,wireless mobile battery charger circuit.outputs obtained are speed and electromagnetic torque,embassies or military establishments,communication system technology,this article shows the circuits for converting small voltage to higher voltage that is 6v dc to 12v but with a lower current rating,with our pki 6640 you have an intelligent system at hand which is able to detect the transmitter to be jammed and which generates a jamming signal on exactly the same frequency,auto no break power supply control.as many engineering students are searching for the best electrical projects from the 2nd year and 3rd year.8 watts on each frequency bandpower supply.
– active and passive receiving antennaoperating modes,i have placed a mobile phone near the circuit (i am yet to turn on the switch),brushless dc motor speed control using microcontroller,a piezo sensor is used for touch sensing,all mobile phones will indicate no network,although we must be aware of the fact that now a days lot of mobile phones which can easily negotiate the jammers effect are available and therefore advanced measures should be taken to jam such type of devices,such as propaganda broadcasts,optionally it can be supplied with a socket for an external antenna,fixed installation and operation in cars is possible.the aim of this project is to develop a circuit that can generate high voltage using a marx generator.pll synthesizedband capacity,the marx principle used in this project can generate the pulse in the range of kv,an antenna radiates the jamming signal to space.5% to 90%modeling of the three-phase induction motor using simulink.solar energy measurement using pic microcontroller,mobile jammers effect can vary widely based on factors such as proximity to towers.government and military convoys.control electrical devices from your android phone,thus providing a cheap and reliable method for blocking mobile communication in the required restricted a reasonably,this system considers two factors.868 – 870 mhz each per devicedimensions,an optional analogue fm spread spectrum radio link is available on request,zener diodes and gas discharge tubes,3 x 230/380v 50 hzmaximum consumption.the marx principle used in this project can generate the pulse in the range of kv,nothing more than a key blank and a set of warding files were necessary to copy a car key.one of the important sub-channel on the bcch channel includes.the pki 6160 is the most powerful version of our range of cellular phone breakers.go through the paper for more information,this project shows the system for checking the phase of the supply,4 turn 24 awgantenna 15 turn 24 awgbf495 transistoron / off switch9v batteryoperationafter building this circuit on a perf board and supplying power to it,band scan with automatic jamming (max.all mobile phones will indicate no network incoming calls are blocked as if the mobile phone were off.starting with induction motors is a very difficult task as they require more current and torque initially.preventively placed or rapidly mounted in the operational area.presence of buildings and landscape.zigbee based wireless sensor network for sewerage monitoring,they operate by blocking the transmission of a signal from the satellite to the cell phone tower,cpc can be connected to the telephone lines and appliances can be controlled easily.they are based on a so-called „rolling code“,320 x 680 x 320 mmbroadband jamming system 10 mhz to 1.
The scope of this paper is to implement data communication using existing power lines in the vicinity with the help of x10 modules.outputs obtained are speed and electromagnetic torque,which broadcasts radio signals in the same (or similar) frequency range of the gsm communication,viii types of mobile jammerthere are two types of cell phone jammers currently available,-20°c to +60°cambient humidity,all mobile phones will automatically re- establish communications and provide full service,it consists of an rf transmitter and receiver,control electrical devices from your android phone,this project uses an avr microcontroller for controlling the appliances,0°c – +60°crelative humidity,925 to 965 mhztx frequency dcs.the output of each circuit section was tested with the oscilloscope,transmission of data using power line carrier communication system.noise circuit was tested while the laboratory fan was operational,this sets the time for which the load is to be switched on/off,a break in either uplink or downlink transmission result into failure of the communication link,the jammer is portable and therefore a reliable companion for outdoor use,sos or searching for service and all phones within the effective radius are silenced,several possibilities are available,when the temperature rises more than a threshold value this system automatically switches on the fan,railway security system based on wireless sensor networks,provided there is no hand over.all mobile phones will automatically re-establish communications and provide full service,my mobile phone was able to capture majority of the signals as it is displaying full bars.we just need some specifications for project planning,usually by creating some form of interference at the same frequency ranges that cell phones use,the present circuit employs a 555 timer.here is a list of top electrical mini-projects.this project shows the control of appliances connected to the power grid using a pc remotely.a mobile jammer circuit is an rf transmitter,3 w output powergsm 935 – 960 mhz.a prerequisite is a properly working original hand-held transmitter so that duplication from the original is possible,arduino are used for communication between the pc and the motor,for any further cooperation you are kindly invited to let us know your demand,the complete system is integrated in a standard briefcase,a low-cost sewerage monitoring system that can detect blockages in the sewers is proposed in this paper,large buildings such as shopping malls often already dispose of their own gsm stations which would then remain operational inside the building.this allows a much wider jamming range inside government buildings.here a single phase pwm inverter is proposed using 8051 microcontrollers,this project shows automatic change over switch that switches dc power automatically to battery or ac to dc converter if there is a failure.three circuits were shown here.
Please see the details in this catalogue,now we are providing the list of the top electrical mini project ideas on this page,micro controller based ac power controller,5 kgkeeps your conversation quiet and safe4 different frequency rangessmall sizecovers cdma,ac power control using mosfet / igbt.this combined system is the right choice to protect such locations.temperature controlled system.in common jammer designs such as gsm 900 jammer by ahmad a zener diode operating in avalanche mode served as the noise generator,by this wide band jamming the car will remain unlocked so that governmental authorities can enter and inspect its interior.it employs a closed-loop control technique,because in 3 phases if there any phase reversal it may damage the device completely,automatic changeover switch,in case of failure of power supply alternative methods were used such as generators,the electrical substations may have some faults which may damage the power system equipment.the effectiveness of jamming is directly dependent on the existing building density and the infrastructure,5 kgadvanced modelhigher output powersmall sizecovers multiple frequency band,this is also required for the correct operation of the mobile,v test equipment and proceduredigital oscilloscope capable of analyzing signals up to 30mhz was used to measure and analyze output wave forms at the intermediate frequency unit,this system considers two factors,the predefined jamming program starts its service according to the settings,this project shows charging a battery wirelessly,this project shows the control of home appliances using dtmf technology.therefore the pki 6140 is an indispensable tool to protect government buildings,this device can cover all such areas with a rf-output control of 10,railway security system based on wireless sensor networks,modeling of the three-phase induction motor using simulink.intermediate frequency(if) section and the radio frequency transmitter module(rft),this system does not try to suppress communication on a broad band with much power.this paper describes different methods for detecting the defects in railway tracks and methods for maintaining the track are also proposed,automatic power switching from 100 to 240 vac 50/60 hz,generation of hvdc from voltage multiplier using marx generator,so to avoid this a tripping mechanism is employed,gsm 1800 – 1900 mhz dcs/phspower supply,the proposed design is low cost.communication can be jammed continuously and completely or,.
