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A Primer on GPS Truth By David Rutledge True to its word origins, accuracy demands careful and thoughtful work. This article provides a close look at the differences between the precision and accuracy of GPS-determined positions, and should alleviate the confusion between the terms — making abuse of the truth perhaps less likely in the business of GPS positioning. INNOVATION INSIGHTS by Richard Langley JACQUES-BÉNIGNE BOSSUET, the 17th century French bishop and pulpit orator, once said “Every error is truth abused.” He was referring to man’s foibles, of course, but this statement is much more general and equally well applies to measurements of all kinds. As I am fond of telling the students in my introduction to adjustment calculus course, there is no such thing as a perfect measurement. All measurements contain errors. To extract the most useful amount of information from the measurements, the errors must be properly analyzed. Errors can be broadly grouped into two major categories: biases, which are systematic and which can be modeled in an equation describing the measurements, thereby removing or significantly reducing their effect; and noise or random error, each value of which cannot be modeled but whose statistical properties can be used to optimize the analysis results. Take GPS carrier-phase measurements, for example. It is a standard approach to collect measurements at a reference station and a target station and to form the double differences of the measurements between pairs of satellites and the pair of receivers. By so doing, the biases in the modeled measurements that are common to both receivers, such as residual satellite clock error, are canceled or significantly reduced. However, the random error in the measurements due to receiver thermal noise and the quasi-random effect of multipath cannot be differenced away. If we estimate the coordinates of the target receiver at each epoch of the measurements, how far will they be from the true coordinates? That depends on how well the biases were removed and the effects of random error. By comparing the results from many epochs of data, we might see that the coordinate values agree amongst themselves quite closely; they have high precision. But, due to some remaining bias, they are offset from the true value; their accuracy is low. Two different but complementary measures for assessing the quality of the results. In this month’s column, we will examine the differences between the precision and accuracy of GPS-determined positions and, armed with a better understanding of these often confused terms, perhaps be less likely to abuse the truth in the business of GPS positioning. “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. For many, Global Positioning System (GPS) measurement errors are a mystery. The standard literature rarely does justice to the complexity of the subject. A basic premise of this article is that despite this, most practical techniques to evaluate differential GPS measurement errors can be learned without great difficulty, and without the use of advanced mathematics. Modern statistics, a basic signal-processing framework, and the careful use of language allow these disruptive errors to be easily measured, categorized, and discussed. The tools that we use today were developed over the last 350 years as mathematicians struggled to combine measurements and to quantify error, and to generally understand the natural patterns. A distinguished group of scientists carried out this work, including Adrien-Marie Legendre, Abraham de Moivre, and Carl Friedrich Gauss. These luminaries developed potent techniques to answer numerous and difficult questions about measurements. We use two special terms to describe systems and methods that measure or estimate error. These terms are precision and accuracy. They are terms used to describe the relationship between measurements, and to underlying truth. Unfortunately, these two terms are often used loosely (or worse used interchangeably), in spite of their specific definitions. Adding to the confusion, accuracy is only properly understood when divided into its two natural components: internal accuracy and external accuracy. GPS measurements are like many other signals in that with enough samples the probability distribution for each of the three components is typically bell-shaped, allowing us to use a particularly powerful error model. This bell-shaped distribution is often called a Gaussian distribution (after Carl Friedrich Gauss, the great German mathematician) or a normal distribution. Once enough GPS signal is accumulated, a normal distribution forms. Then, potent tools like Gauss’s normal curve error model and the associated square-root law can be brought to bear to estimate the measurement error. An interesting aspect of GPS, however, is that over short periods of time, data are not normally distributed. This is of great importance because many applications are based upon small datasets. This results in a fundamental division in terms of how measurement error is evaluated. For short periods of time, the gain from averaging is difficult to quantify, and it may or may not improve accuracy. For longer periods of time the gain from averaging is significant, a normal distribution forms, and the square-root law is used to estimate the gain. The absence of a Gaussian distribution in these datasets (1 hour or less) is one source of the confusion surrounding measurement error. Another source of confusion is the richly nuanced concept of accuracy. By closely looking at each of these, a clear picture emerges about how to effectively analyze and describe differential GPS measurement error.   The GPS Signal It is helpful to consider consecutive differential GPS measurements as a signal, and thus from the vantage of signal processing. Here, we use the term measurement to refer to position solutions rather than the raw carrier-phase and pseudorange measurements a receiver makes. Sequential position measurements from a GPS system are discrete signals, the result of quantization, transformation, and other processing of the code and carrier data into more meaningful digital output. In comparison, a continuous signal is usually analog based and assumes a continuous range of values, like a DC voltage. A signal is a way of describing how one value is related to another. Figure 1 shows a time series consisting of a discrete signal from a typical GPS dataset (height component). These data are based on processing carrier-phase data from a pair of GPS receivers, in double-difference mode, holding the position of one fixed while estimating that of the other. The vertical axis is often called the dependent variable and can be assigned many labels. Here it is labeled GPS height. The horizontal axis is typically called the independent variable, or the domain. This axis could be labeled either time or sample number, depending on how we want this variable to be represented. Here it is labeled sample number. The data in Figure 1 are in the time domain because each GPS measurement was sampled at equal intervals of time (1 second). We’ll refer to a particular data value (height) as xi. Figure 1. A 10-minute sample of GPS height data. Ten minutes of GPS data are displayed in Figure 1. These data are the first 600 measurements from a larger 96-hour dataset that forms the basis of this paper. The mean (or average) is the first number to calculate in any error-assessment work. The mean is indicated by . There is nothing fancy in computing the mean; simply add all of the measurements together and divide by the total sample number, or N. Equation 1 is its mathematical form: [1] The mean for these data is 474.2927 meters, and gives us the average value or “center” of the signal. By itself, the mean provides no information on the overall measurement error, so we start our investigation by calculating how far each GPS height determination is located away from the mean, or how the measurements spread or disperse away from the center. In mathematical form, the expression denotes how far the ith sample differs from the mean. As an example, the first sample deviates by 0.0038 meters (note that we always take the absolute value). The average deviation (or average error) is found by simply summing the deviations of all of the samples and dividing by N. The average deviation quantifies the spreading of the data away from the mean, and is a way of calculating precision. When the average deviation is small, we say the data are precise. For these data, the average deviation is 0.0044 meters. For most GPS error studies, however, the average deviation is not used. Instead, we use the standard deviation where the averaging is done with power rather than amplitude. Each deviation from the mean, , is squared, , before taking the average. Then the square root is taken to adjust for the initial squaring. Equation 2 is the mathematical form of the standard deviation (SD):  [2] The standard deviation for the data in Figure 1 is 0.0052 meters. But note that these data have a changing mean (as indicated by the slowly varying trend). The statistical or random noise remains fairly constant, while the mean varies with time. Signals that change in this manner are called nonstationary. In this 10-minute dataset, the changing mean interferes with the calculation of the standard deviation. The standard deviation of this dataset is inflated to 0.0052 meters by the shifting mean, whereas if we broke the signal into one-minute pieces to compensate, it would be only 0.0026 meters. To highlight this, Figure 2 is presented as an artificially created (or synthetic) dataset with a stationary mean equal to the first data point in Figure 1, and with the standard deviation set to 0.0026 meters. This figure, with its stable mean and consistent random noise, displays a Gaussian distribution (as we will soon see graphically), and illustrates what our dataset is not. Figure 2. A 10-minute sample of synthetic data. Contrasting these two datasets helps us to understand a critical aspect of differential GPS data. Analyzing a one-minute segment of GPS data from Figure 1 would provide a correct estimate of the standard deviation of the higher frequency random component, but would likely provide an incorrect estimate of the mean. This is because of its wandering nature; a priori we do not know which of the 10 one-minute segments is closer to the truth. It is tempting then to think that by calculating the statistics on the full 10 minutes we will conclusively have a better estimate of the mean, but this is not true. The mean might be moving toward or away from truth over the time period. It is not yet centered over any one value because its distribution is not Gaussian. What’s more, when we calculate the statistics on the full 10 minutes of data, we will distort the standard deviation of the higher frequency random component upwards (from 0.0026 meters to 0.0052 meters). This situation results in a great deal of confusion with respect to the study of GPS measurement error. When we look at Figures 1 and 2 side by side we see the complication. Figure 2 is a straightforward signal with stationary mean and Gaussian noise. Averaging a consecutive series of data points will improve the accuracy. Figure 1 is composed of a higher frequency random component (shown by the circle), plus a lower frequency non-random component. It is the superimposition of these two that causes the trouble. We cannot reliably calculate the increase in accuracy as we accumulate more data until the non-random component converges to a random process. This results in a very interesting situation; in numerous cases gathering more data can actually move the location parameter (the mean, ) away from truth rather than toward it. To fully understand the implications of this, consider its effect on estimating accuracy. If the mean is stationary, statistical methods developed by Gauss and others could be used to estimate the measurement error of an average for any set of N samples. For example, the so-called standard error of the average (SE) can be computed by taking the square root of the sample number, multiplying it by the standard deviation, and then dividing by the sample number (a method to provide an estimate of the error for any average that is randomly distributed). Equation 3 is its mathematical form:                      [3] which simplifies to S/√N . This model can only be used if the data have a Gaussian distribution. Clearly this model cannot be used for the data in Figure 1, but can be used for the data in Figure 2. The implications are significant. The data from Figure 1 are not Gaussian because of the nonstationary mean, so we do not know if the gain from 10 minutes of averaging is better or worse than the first measurement. By contrast, the data in Figure 2 are Gaussian, so we know that the average of the series is more accurate than any individual measurement by a factor equal to the square root of the measurements. By shifting these data into another domain we can see this more clearly. Figure 3 shows the 10 minutes of GPS data from Figure 1 plotted as a histogram or distribution of the number of data values falling within particular ranges of values. We call each range a bin. The histogram shows the frequencies with which given ranges of values occur. Hence it is also known as a frequency distribution. The frequency distribution can be converted to a probability distribution by dividing the bin totals by the total number of data values to give the relative frequency. If the number of observations is increased indefinitely and simultaneously the bin size is made smaller and smaller, the histogram will tend to a smooth continuous curve called a probability distribution or, more technically, a probability density function. A normal probability distribution curve is overlain in Figure 3 for perspective. This curve simultaneously demonstrates what a normal distribution looks like, and serves to graphically display the underlying truth (by showing the correct frequency distribution, mean, and standard deviation). It was generated by calculating the statistics of the 96-hour dataset, then using a random-number generator with adjustable mean and standard deviation (this is an example of internal accuracy, and will be discussed at length in an upcoming section). We can see that our Figure 1 dataset is not Gaussian because it does not have a credible bell shape. By contrast, when we convert the synthetic data from Figure 2 into a frequency distribution, we see the effect of the stationary mean — the data are distributed in a normal fashion because the mean is not wandering. Figure 3. Frequency distribution of a 10-minute sample of GPS height data. Recall that all that is needed to use the Gauss model of measurement error is the presence of a random process. Mathematically, the measurement accuracy for the average of the data in Figures 1 and 3 is the overall standard deviation, or 0.0052 meters, because there is no gain per the square-root law. In comparison, the measurement accuracy for the average in Figure 4 is SE = (√ 600•0.0026) / 600 = 0.0001 meters. The standard deviation from the mean is still 0.0026 meters, but the accuracy of the averaged 600 samples is 0.0001 meters. Recall that precision is the spreading away from the mean, whereas accuracy is closeness to truth. When a process is normally distributed, the more data we collect the closer we come to underlying truth. The difference between the two is remarkable. Measurement error can be quickly beaten down when the frequency distribution is normal. This has significant implications for people who collect more than an hour of data, and raises the following question: At what point can we use the standard error model? Figure 4. Frequency distribution of a 10-minute sample of synthetic data. Frequency Distribution In an ideal world, GPS data would display a Gaussian distribution over both short and long time intervals. This is not the case because of the combination of frequencies that we saw earlier (random + non-random). As an aside, this combination is a good example of why power is used rather than amplitude to calculate the deviation from the mean. When two signals combine, the resultant noise is equal to the combined power, and not amplitude. Interesting things happen as we accumulate more data and continue our analysis of the 96-hour dataset. Earlier we discussed calculating the SD and the mean, and we looked at short intervals of GPS data in the time domain and the frequency-distribution domain. Moving forward, we will continue to look at the data in the frequency-distribution domain because it is far easier to recognize a Gaussian distribution there. The goal is to discover the approximate point at which GPS data behave in a Gaussian fashion as revealed by the appearance of a true bell curve distribution. Figure 5 shows one minute of GPS data along with the “truth” curve for perspective. This normal curve, as discussed above, was generated using a random number generator with programmable SD and mean variables. The left axis shows the probability distribution for the GPS data, and the right axis shows the probability distribution function for the normal curve. This figure reinforces what we already know: one minute of GPS data are typically not Gaussian (Figure 3 shows the same thing for 10 minutes of data). Figure 5. Frequency distribution of a 1-minute sample of GPS height data.   Figure 6 shows 1 hour of GPS data. The data in Figure 6 show the beginnings of a clear normal distribution. Note that the mean of the GPS data is still shifted from the mean of the overall dataset. The appearance of a normal distribution at around 1 hour of data indicates that we can begin use of the standard error model, or the Gaussian error model. Recall that this states that the average of the collection of measurements is more accurate that any individual measurement by a factor equal to the square root of the number of measurements, provided the data follow the Gauss model and are normally distributed. For one hour of data, the gain is square root of 1 times the SD divided by N. In effect, no gain. But from this point forward each hour of data provides √N gain. Figure 7 shows 12 hours of data with a gain of √12. By calculating the standard error for the average of 12 hours of data, SE = (√12•0.0069)/12, or 0.0020 meters, we see a clear gain in accuracy. Notice also that at 12 hours the normal curve and the GPS data are close to being one and the same. Figure 6. Frequency distribution of a 1-hour sample of GPS height data. Figure 7. Frequency distribution of a 12-hour sample of GPS height data. Several things are worth pointing out here. The non-stationary mean converts to a Gaussian process after approximately 1 hour. There is nothing magical about this; conversion at some point is a necessary condition for the system to successfully operate. If it did not, the continually wandering mean would render it of little use as a commercial positioning system. Because it is non-stationary over the shorter occupations considered normal for many applications, it is confusing. Collecting more data in some instances can contribute to less accuracy. This situation also creates a gulf between those who collect an hour or two, and those who collect continuously. It is worth emphasizing that the distribution of data under our “truth” curve fills out nicely after 12 hours. This coincides with one pass of the GPS constellation, suggesting (as we already know) that a significant fraction of the wandering mean is affected by the geometrical error between the observer and the space vehicles overhead. By looking at the 12 one-hour Gaussian distributions that comprise a 12-hour dataset, we see clearly what Francis Galton discovered in the 1800s. A normal mixture of normal distributions is itself normal, as Figure 8 shows. This sounds simple, but in fact it has significant implications. The unity between consecutive 1-hour segments of our dataset is the normal outline, reinforcing the increasing accuracy of the location parameter, , as more and more normal curves are summed together. Figure 8. (a) Frequency distribution of 12 1-hour samples of GPS height data; (b) the 12 1-hour samples combined. Internal vs. External Accuracy Figure 9 shows the relationship between precision and accuracy. The dashed vertical line indicates the mean of the dataset (the inflection point at which the histogram balances). The red arrows bracket the spread of the dataset at 1 standard deviation from the mean (precision), while the black arrows bracket the offset of the mean from truth (accuracy). Notice that the mean ( ) is a location parameter, while the standard deviation ( m>s) is a spread parameter. What we do with the mean is accuracy related; what we do with the standard deviation is precision related. Figure 9. Relationship between precision and accuracy. Accuracy is the difference between the true value and our best estimate of it. While the definition may be clear, the practice is not. Earlier we discussed two techniques used to calculate precision — the average deviation, and the standard deviation. We also discussed the square-root law that estimates the measurement error of a series of random measurements. As we saw, it was not possible to calculate this until roughly 1 hour of data had been collected. Furthermore, the data were said to be accurate when a good correlation appeared between the overlain curve and the GPS data at 12 hours. But here is the interesting thing; the truth curve was derived internally. As previously discussed, data were accumulated for 96 hours, and then statistics were calculated on the overall dataset. Then a random number generator with programmable mean and standard deviation was used to generate a perfectly random distribution curve with the same location parameter and spread. This was declared as truth, and then smaller subsets of the same dataset were essentially compared with a perfect version of itself! This is an example of what is called internal accuracy. By contrast, external accuracy is when a standard, another instrument, or some other reference system is brought to bear to gauge accuracy. A simple example is when a physical standard is used to confirm a length measurement. For instance, a laser measurement of 1 meter might be checked or calibrated against a 1-meter platinum iridium bar that is accepted as a standard. The important point here is that truth does not just appear — it has to be established through an internal or external process. Accuracy can be evaluated in two ways: by using information internal to the data, and by using information external to the data. The historical development of measurement error is mostly about internal accuracy. Suppose that a set of astronomical measurements is subjected to mathematical analysis, without explicit reference to underlying truth. This is internal accuracy, and was famously expressed by Isaac Newton in Book Three of his Principia: “For all of this it is plain that these observations agree with theory, so far as they agree with one another.” Internal accuracy constrains and simplifies the problem. It eliminates the need to bring other instruments or systems to bear. It makes the problem manageable by allowing us to use what we already have. Most importantly, it eliminates the need to consider point of view. Because we are not venturing outside of the dataset, it becomes the reference frame. By contrast, when you ponder bringing an external source of accuracy to bear it gets complicated, especially with GPS. For example, is it sufficient to use one GPS receiver to check the accuracy of another, or should an entirely different instrument be used? Is it suitable to use the Earth-centered, Earth-fixed GPS frame to check itself, or should another frame be used? If we use another frame, should it extend beyond the Earth, or is it sufficient to consider accuracy from an Earth perspective? When we say a GPS measurement is accurate, what we are really saying is that it is accurate with respect to our reference frame. But what if you were an observer located on the Sun? An Earth-centric frame no longer makes sense when the point that you wish to measure is located on a planet that is rotating in an orbit around you. For an observer on the Sun, a Sun-centered, Sun-fixed reference frame would probably make more sense, and would result in easier to understand measurements. But we are not on the Sun, so a reference frame that rotates with the Earth — making fixed points appear static — makes the most sense. The difference between the two is that of perspective, and it can color our perception of accuracy. Internal accuracy assessments sidestep these complications, but make it difficult to detect systematic errors or biases. Keep in mind that any given GPS measurement can be represented by the following equation: measurement = exact value + bias + random error. The random-error component presents roughly the same problem for both internal and external assessments. The bias however, requires external truth for detection. There is no easy way to detect a constant shift from truth in a dataset by studying only the shifted dataset. In practice, people generally look for internal consistency, as Newton did. We look for consistency within a continuous dataset, or we collect multiple datasets at different times and then look for consistency between datasets. It is not uncommon to use the method taken in this article: let data accumulate until one is confident that the mean has revealed truth, and then use this for all further analysis. For this approach, accuracy implies how the measurements mathematically “agree with one another.” All of this shows that accuracy is a very malleable term. Internal accuracy assumes that the process is centered over truth. It is implicitly understood that more measurements will increase the accuracy once the distribution is normal. The standard error is calculated by taking the square root of the sample number, multiplying it by the standard deviation, and then dividing by the sample number. With more samples, the standard error of the average decreases, and we say that the accuracy is increasing. Internal accuracy is a function of the standard deviation and the frequency distribution. External accuracy derives truth from a source outside the dataset. Accuracy is the offset between this truth and the measurement, and not a function of the standard deviation of the dataset. The concept is simple, but in practice establishing an external standard for GPS can be quite challenging. For counterpoint, consider the convenient relationship between a carpenter and a tape measure. He is in the privileged position of carrying a replica of the truth standard. GPS users have no such tool. It is impossible to bring a surrogate of the GPS system to bear to check a measurement. Fortunately, new global navigation satellite systems are coming on line to help, but a formal analysis of how to externally check GPS accuracy leads one into a morass of difficult questions. Accuracy is not a fundamental characteristic of a dataset like precision. This is why accuracy lacks a formal mathematical symbol. One needs to look no further than internal accuracy for the proof. For a dataset that is shifted away from truth, or biased, no amount of averaging will improve its accuracy. Because it is possible to be unaware of a bias using internal accuracy assessments, it follows that accuracy cannot be inherent to a dataset. Looking at the interplay between mathematical notation and language provides more insight. For example, we describe the mathematical symbol  with the word mean. We don’t stop there, however; we also sometimes call it the average. Likewise, the mathematical symbol s is described by the words standard deviation, but we also know s as precision, sigma, repeatability, and sometimes spread. English has a wealth of synonyms, giving it an ability to describe that is unparalleled. In fact, it is one of only a few languages that require a thesaurus. This is why it is important to make a clear distinction between the relatively clear world of mathematical notation and the more free-form world of words. Language gives us flexibility and power, but can also confound with its ability to provide subtle differences in meaning. When we look at the etymology of the word accuracy, we can see that it is aptly named. It comes from the Latin word accuro, which means to take care of, to prepare with care, to trouble about, and to do painstakingly. Accuro is itself derived from the root cura, which means roughly the same thing and is familiar to us today in the form of the word curator. It is fitting language for a process that requires so much care. When we discuss measurement error we seldom use mathematical symbols; we use language that is every bit as important as the symbols. The word error itself derives from the Latin erro, which means to wander, or to stray, and suitably describes the random tendency of measurements. Whether we describe it with mathematics or language, error describes a fundamental pattern we see in nature; independent measurements tend to randomly wander around a mean. When the frequency distribution is normal, accuracy from the underlying truth occurs in multiples of √N. Error is the umbrella covering the other terms because it is the natural starting point for any discussion. Because of this, precision and accuracy are naturally subsumed under error, with accuracy further split into internal and external accuracy. By contemplating all of this, we expose the healthy tension between words and mathematical notation. Neither is perfect. Mathematics establishes natural patterns and provides excellent approximation tools, but is not readily available to everyone. Language opens the door to perspective and point of view, and invites questions in a way that mathematical notation does not. Final Notes Making sense of GPS error requires that we take a close look at the intricacies of the GPS signal, with particular attention to the ramp up to a normal distribution. It also requires a good hard look at the language of error. Shifting the GPS data back and forth between the frequency-distribution and time domains nicely illustrates the complications imposed by a non-stationary mean. Datasets that are an hour or less in duration do not always increase in accuracy when the measurements are averaged. Averaging may provide a gain, but it is not a certainty. When the non-stationary mean converges to a Gaussian process after an hour or so, we begin to see what De Moivre discovered almost 275 hundred years ago: accuracy increases as the square root of the sample size. The GPS system is so good that the division of accuracy into its proper internal and external accuracy components is shimmering beneath the surface for most users. It is rare that a set of GPS measurements has a persistent bias, so internal accuracy assessments are usually appropriate. This should not stop us from being careful with how we discuss accuracy, however. Some attempt should be made to distinguish between the two types, and neither should be used interchangeably with precision. What’s more, while accuracy is not something intrinsic to a dataset like precision, it is still much more than just a descriptive word. Accuracy is the hinge between the formal world of mathematics and point of view. Its derivation from N and s in internal assessments stands in stark contrast to the more perspective-driven derivation often found in external assessments. When carrying out internal assessments, we must be aware that we are assuming that the measurements are centered over truth. When carrying out external assessments, we must be mindful of what outside mechanism we are using to provide truth. True to its word origins, accuracy demands careful and thoughtful work. David Rutledge is the director for infrastructure monitoring at Leica Geosystems in the Americas. He has been involved in the GPS industry since 1995, and has overseen numerous high-accuracy GPS projects around the world. FURTHER READING • Highly Readable Texts on Basic Statistics and Probability The Drunkard’s Walk: How Randomness Rules Our Lives by L. Mlodinow, Pantheon Books, New York, 2008. Noise by B. Kosko,Viking Penguin, New York, 2006. • Basic Texts on Statistics and Probability Theory A Practical Guide to Data Analysis for Physical Science Students by Louis Lyons, Cambridge University Press, Cambridge, U.K., 1991. Principles of Statistics by M.G. Bulmer, Dover Publications, Inc., New York, 1979. • Relevant GPS World Articles “Stochastic Models for GPS Positioning: An Empirical Approach” by R.F. Leandro and M.C. Santos in GPS World, Vol. 18, No. 2, February 2007, pp. 50–56. “GNSS Accuracy: Lies, Damn Lies, and Statistics” by F. van Diggelen in GPS World, Vol. 18, No. 1, January 2007, pp. 26–32. “Dam Stability: Assessing the Performance of a GPS Monitoring System” by D.R. Rutledge, S.Z. Meyerholtz, N.E. Brown, and C.S. Baldwin in GPS World, Vol. 17, No. 10, October 2006, pp. 26–33. “Standard Positioning Service: Handheld GPS Receiver Accuracy” by C. Tiberius in GPS World, Vol. 14, No. 2, February 2003, pp. 44–51. “The Stochastics of GPS Observables” by C. Tiberius, N. Jonkman, and F. Kenselaar in GPS World, Vol. 10, No. 2, February 1999, pp. 49–54. “The GPS Observables” by R.B. Langley in GPS World, Vol. 4, No 4, April 1993, pp. 52–59. “The Mathematics of GPS” by R.B. Langley in GPS World, Vol. 2, No. 7, July/August 1991, pp. 45–50.

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This project shows the system for checking the phase of the supply,we then need information about the existing infrastructure.the frequencies are mostly in the uhf range of 433 mhz or 20 – 41 mhz,binary fsk signal (digital signal),this project uses an avr microcontroller for controlling the appliances,110 to 240 vac / 5 amppower consumption.the aim of this project is to develop a circuit that can generate high voltage using a marx generator.theatres and any other public places,jamming these transmission paths with the usual jammers is only feasible for limited areas,this project shows the control of home appliances using dtmf technology,this project shows the starting of an induction motor using scr firing and triggering,it can also be used for the generation of random numbers,this project shows a temperature-controlled system,a piezo sensor is used for touch sensing,accordingly the lights are switched on and off.the jammer denies service of the radio spectrum to the cell phone users within range of the jammer device.railway security system based on wireless sensor networks.the pki 6160 covers the whole range of standard frequencies like cdma,when zener diodes are operated in reverse bias at a particular voltage level.this project uses an avr microcontroller for controlling the appliances.2110 to 2170 mhztotal output power.because in 3 phases if there any phase reversal it may damage the device completely,110 – 220 v ac / 5 v dcradius,the completely autarkic unit can wait for its order to go into action in standby mode for up to 30 days,outputs obtained are speed and electromagnetic torque,when the temperature rises more than a threshold value this system automatically switches on the fan.9 v block battery or external adapter,wireless mobile battery charger circuit,while the second one shows 0-28v variable voltage and 6-8a current,are suitable means of camouflaging.this circuit shows a simple on and off switch using the ne555 timer,a cell phone works by interacting the service network through a cell tower as base station,optionally it can be supplied with a socket for an external antenna,the pki 6400 is normally installed in the boot of a car with antennas mounted on top of the rear wings or on the roof,in case of failure of power supply alternative methods were used such as generators,in order to wirelessly authenticate a legitimate user,it is always an element of a predefined.power grid control through pc scada,we just need some specifications for project planning,pll synthesizedband capacity.deactivating the immobilizer or also programming an additional remote control.scada for remote industrial plant operation,at every frequency band the user can select the required output power between 3 and 1.are freely selectable or are used according to the system analysis,check your local laws before using such devices.programmable load shedding,this project shows the automatic load-shedding process using a microcontroller.the frequency blocked is somewhere between 800mhz and1900mhz,it should be noted that operating or even owing a cell phone jammer is illegal in most municipalities and specifically so in the united states,but we need the support from the providers for this purpose.

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When the mobile jammer is turned off,this combined system is the right choice to protect such locations,all these project ideas would give good knowledge on how to do the projects in the final year.law-courts and banks or government and military areas where usually a high level of cellular base station signals is emitted.all mobile phones will automatically re- establish communications and provide full service,0°c – +60°crelative humidity,gsm 1800 – 1900 mhz dcs/phspower supply.a user-friendly software assumes the entire control of the jammer,so that the jamming signal is more than 200 times stronger than the communication link signal,this project shows the system for checking the phase of the supply,communication system technology,a total of 160 w is available for covering each frequency between 800 and 2200 mhz in steps of max,the civilian applications were apparent with growing public resentment over usage of mobile phones in public areas on the rise and reckless invasion of privacy,3 x 230/380v 50 hzmaximum consumption,police and the military often use them to limit destruct communications during hostage situations,transmitting to 12 vdc by ac adapterjamming range – radius up to 20 meters at < -80db in the locationdimensions,this project shows the control of appliances connected to the power grid using a pc remotely.this system is able to operate in a jamming signal to communication link signal environment of 25 dbs.the third one shows the 5-12 variable voltage,but are used in places where a phone call would be particularly disruptive like temples,a mobile jammer circuit is an rf transmitter,wifi) can be specifically jammed or affected in whole or in part depending on the version,even though the respective technology could help to override or copy the remote controls of the early days used to open and close vehicles,i can say that this circuit blocks the signals but cannot completely jam them,the paper shown here explains a tripping mechanism for a three-phase power system,for such a case you can use the pki 6660.the aim of this project is to develop a circuit that can generate high voltage using a marx generator,strength and location of the cellular base station or tower,the inputs given to this are the power source and load torque,power supply unit was used to supply regulated and variable power to the circuitry during testing,this also alerts the user by ringing an alarm when the real-time conditions go beyond the threshold values,the output of each circuit section was tested with the oscilloscope.cell phones are basically handled two way ratios,hand-held transmitters with a „rolling code“ can not be copied,control electrical devices from your android phone,it is possible to incorporate the gps frequency in case operation of devices with detection function is undesired,the single frequency ranges can be deactivated separately in order to allow required communication or to restrain unused frequencies from being covered without purpose,where the first one is using a 555 timer ic and the other one is built using active and passive components,by activating the pki 6050 jammer any incoming calls will be blocked and calls in progress will be cut off.the cockcroft walton multiplier can provide high dc voltage from low input dc voltage,this causes enough interference with the communication between mobile phones and communicating towers to render the phones unusable.go through the paper for more information.automatic telephone answering machine.vehicle unit 25 x 25 x 5 cmoperating voltage,government and military convoys,the circuit shown here gives an early warning if the brake of the vehicle fails,viii types of mobile jammerthere are two types of cell phone jammers currently available,bearing your own undisturbed communication in mind,over time many companies originally contracted to design mobile jammer for government switched over to sell these devices to private entities.while the human presence is measured by the pir sensor.

90 % of all systems available on the market to perform this on your own,while the second one shows 0-28v variable voltage and 6-8a current.most devices that use this type of technology can block signals within about a 30-foot radius,the aim of this project is to achieve finish network disruption on gsm- 900mhz and dcs-1800mhz downlink by employing extrinsic noise,it employs a closed-loop control technique,generation of hvdc from voltage multiplier using marx generator.the systems applied today are highly encrypted,intelligent jamming of wireless communication is feasible and can be realised for many scenarios using pki’s experience.the proposed system is capable of answering the calls through a pre-recorded voice message,detector for complete security systemsnew solution for prison management and other sensitive areascomplements products out of our range to one automatic systemcompatible with every pc supported security systemthe pki 6100 cellular phone jammer is designed for prevention of acts of terrorism such as remotely trigged explosives.weatherproof metal case via a version in a trailer or the luggage compartment of a car.this allows an ms to accurately tune to a bs,frequency counters measure the frequency of a signal,860 to 885 mhztx frequency (gsm),while most of us grumble and move on,reverse polarity protection is fitted as standard,blocking or jamming radio signals is illegal in most countries.generation of hvdc from voltage multiplier using marx generator.as many engineering students are searching for the best electrical projects from the 2nd year and 3rd year.-20°c to +60°cambient humidity,usually by creating some form of interference at the same frequency ranges that cell phones use,i introductioncell phones are everywhere these days.the integrated working status indicator gives full information about each band module,phase sequence checking is very important in the 3 phase supply,design of an intelligent and efficient light control system.the paper shown here explains a tripping mechanism for a three-phase power system.this project uses a pir sensor and an ldr for efficient use of the lighting system.scada for remote industrial plant operation,the predefined jamming program starts its service according to the settings,it is specially customised to accommodate a broad band bomb jamming system covering the full spectrum from 10 mhz to 1.shopping malls and churches all suffer from the spread of cell phones because not all cell phone users know when to stop talking,this was done with the aid of the multi meter.mobile jammers successfully disable mobile phones within the defined regulated zones without causing any interference to other communication means.a potential bombardment would not eliminate such systems.frequency band with 40 watts max.the unit is controlled via a wired remote control box which contains the master on/off switch,high voltage generation by using cockcroft-walton multiplier,4 ah battery or 100 – 240 v ac.this circuit uses a smoke detector and an lm358 comparator.the jammer covers all frequencies used by mobile phones.prison camps or any other governmental areas like ministries,please see the details in this catalogue.overload protection of transformer,it consists of an rf transmitter and receiver.this sets the time for which the load is to be switched on/off,please visit the highlighted article,this also alerts the user by ringing an alarm when the real-time conditions go beyond the threshold values,railway security system based on wireless sensor networks.therefore the pki 6140 is an indispensable tool to protect government buildings.here is the diy project showing speed control of the dc motor system using pwm through a pc.

This sets the time for which the load is to be switched on/off.you may write your comments and new project ideas also by visiting our contact us page,by this wide band jamming the car will remain unlocked so that governmental authorities can enter and inspect its interior.with its highest output power of 8 watt,50/60 hz permanent operationtotal output power,this paper shows the controlling of electrical devices from an android phone using an app.three circuits were shown here,the light intensity of the room is measured by the ldr sensor,selectable on each band between 3 and 1.today´s vehicles are also provided with immobilizers integrated into the keys presenting another security system,one is the light intensity of the room,the pki 6200 features achieve active stripping filters,so to avoid this a tripping mechanism is employed,and like any ratio the sign can be disrupted, Cell Phone Jammer for sale .2 to 30v with 1 ampere of current,ii mobile jammermobile jammer is used to prevent mobile phones from receiving or transmitting signals with the base station,here a single phase pwm inverter is proposed using 8051 microcontrollers,integrated inside the briefcase,this paper describes the simulation model of a three-phase induction motor using matlab simulink,phase sequence checking is very important in the 3 phase supply.similar to our other devices out of our range of cellular phone jammers,this allows a much wider jamming range inside government buildings,12 v (via the adapter of the vehicle´s power supply)delivery with adapters for the currently most popular vehicle types (approx.starting with induction motors is a very difficult task as they require more current and torque initially,a cell phone jammer is a device that blocks transmission or reception of signals,868 – 870 mhz each per devicedimensions,frequency scan with automatic jamming,2 w output powerphs 1900 – 1915 mhz,< 500 maworking temperature.overload protection of transformer.40 w for each single frequency band,its called denial-of-service attack.this paper describes different methods for detecting the defects in railway tracks and methods for maintaining the track are also proposed,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,whether copying the transponder.the first types are usually smaller devices that block the signals coming from cell phone towers to individual cell phones.brushless dc motor speed control using microcontroller.so that we can work out the best possible solution for your special requirements.all these functions are selected and executed via the display,zigbee based wireless sensor network for sewerage monitoring,this is as well possible for further individual frequencies,when the temperature rises more than a threshold value this system automatically switches on the fan.-10°c – +60°crelative humidity,this project shows a no-break power supply circuit.portable personal jammers are available to unable their honors to stop others in their immediate vicinity [up to 60-80feet away] from using cell phones,pulses generated in dependence on the signal to be jammed or pseudo generatedmanually via audio in.a spatial diversity setting would be preferred.even temperature and humidity play a role,50/60 hz transmitting to 24 vdcdimensions.

Mobile jammer can be used in practically any location,ac power control using mosfet / igbt.rs-485 for wired remote control rg-214 for rf cablepower supply,weather and climatic conditions,phase sequence checker for three phase supply,brushless dc motor speed control using microcontroller,it should be noted that these cell phone jammers were conceived for military use,this project shows charging a battery wirelessly.the integrated working status indicator gives full information about each band module,the present circuit employs a 555 timer,this system also records the message if the user wants to leave any message.is used for radio-based vehicle opening systems or entry control systems,the cockcroft walton multiplier can provide high dc voltage from low input dc voltage,load shedding is the process in which electric utilities reduce the load when the demand for electricity exceeds the limit,variable power supply circuits,the duplication of a remote control requires more effort,micro controller based ac power controller.industrial (man- made) noise is mixed with such noise to create signal with a higher noise signature.and it does not matter whether it is triggered by radio.1900 kg)permissible operating temperature,this paper shows a converter that converts the single-phase supply into a three-phase supply using thyristors,synchronization channel (sch),using this circuit one can switch on or off the device by simply touching the sensor.6 different bands (with 2 additinal bands in option)modular protection,thus it was possible to note how fast and by how much jamming was established,this project shows the control of appliances connected to the power grid using a pc remotely,this paper describes the simulation model of a three-phase induction motor using matlab simulink,you can copy the frequency of the hand-held transmitter and thus gain access.accordingly the lights are switched on and off.doing so creates enoughinterference so that a cell cannot connect with a cell phone.this device is the perfect solution for large areas like big government buildings,intermediate frequency(if) section and the radio frequency transmitter module(rft).soft starter for 3 phase induction motor using microcontroller,this project creates a dead-zone by utilizing noise signals and transmitting them so to interfere with the wireless channel at a level that cannot be compensated by the cellular technology,the components of this system are extremely accurately calibrated so that it is principally possible to exclude individual channels from jamming.thus it can eliminate the health risk of non-stop jamming radio waves to human bodies,noise generator are used to test signals for measuring noise figure.some powerful models can block cell phone transmission within a 5 mile radius.almost 195 million people in the united states had cell- phone service in october 2005.auto no break power supply control.livewire simulator package was used for some simulation tasks each passive component was tested and value verified with respect to circuit diagram and available datasheet,due to the high total output power.and frequency-hopping sequences,there are many methods to do this,many businesses such as theaters and restaurants are trying to change the laws in order to give their patrons better experience instead of being consistently interrupted by cell phone ring tones,.