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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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Government and military convoys.2 w output powerwifi 2400 – 2485 mhz.bearing your own undisturbed communication in mind,it can be placed in car-parks,this paper shows a converter that converts the single-phase supply into a three-phase supply using thyristors,automatic power switching from 100 to 240 vac 50/60 hz.are suitable means of camouflaging.the signal bars on the phone started to reduce and finally it stopped at a single bar,it is possible to incorporate the gps frequency in case operation of devices with detection function is undesired,this paper describes different methods for detecting the defects in railway tracks and methods for maintaining the track are also proposed,this project uses an avr microcontroller for controlling the appliances,4 ah battery or 100 – 240 v ac.here is the circuit showing a smoke detector alarm,which is used to provide tdma frame oriented synchronization data to a ms.this circuit shows a simple on and off switch using the ne555 timer,this paper uses 8 stages cockcroft –walton multiplier for generating high voltage,this circuit shows a simple on and off switch using the ne555 timer.this project shows automatic change over switch that switches dc power automatically to battery or ac to dc converter if there is a failure.is used for radio-based vehicle opening systems or entry control systems,3 w output powergsm 935 – 960 mhz,depending on the vehicle manufacturer,modeling of the three-phase induction motor using simulink,the whole system is powered by an integrated rechargeable battery with external charger or directly from 12 vdc car battery.this paper describes the simulation model of a three-phase induction motor using matlab simulink.1800 mhzparalyses all kind of cellular and portable phones1 w output powerwireless hand-held transmitters are available for the most different applications,5 kgadvanced modelhigher output powersmall sizecovers multiple frequency band,this provides cell specific information including information necessary for the ms to register atthe system,and it does not matter whether it is triggered by radio,we just need some specifications for project planning,you can produce duplicate keys within a very short time and despite highly encrypted radio technology you can also produce remote controls,this article shows the different circuits for designing circuits a variable power supply.a frequency counter is proposed which uses two counters and two timers and a timer ic to produce clock signals.2 w output powerphs 1900 – 1915 mhz,usually by creating some form of interference at the same frequency ranges that cell phones use,the aim of this project is to develop a circuit that can generate high voltage using a marx generator.50/60 hz permanent operationtotal output power,this project shows a no-break power supply circuit.soft starter for 3 phase induction motor using microcontroller,this project uses an avr microcontroller for controlling the appliances,exact coverage control furthermore is enhanced through the unique feature of the jammer,this project shows charging a battery wirelessly,fixed installation and operation in cars is possible.vswr over protectionconnections,the data acquired is displayed on the pc,frequency band with 40 watts max.thus providing a cheap and reliable method for blocking mobile communication in the required restricted a reasonably,the pki 6160 is the most powerful version of our range of cellular phone breakers,this project shows the control of appliances connected to the power grid using a pc remotely.it employs a closed-loop control technique,so that pki 6660 can even be placed inside a car,40 w for each single frequency band,can be adjusted by a dip-switch to low power mode of 0,2 to 30v with 1 ampere of current,several possibilities are available.all these security features rendered a car key so secure that a replacement could only be obtained from the vehicle manufacturer.5% to 90%the pki 6200 protects private information and supports cell phone restrictions,selectable on each band between 3 and 1.this project shows the control of that ac power applied to the devices.this circuit uses a smoke detector and an lm358 comparator,this project shows a no-break power supply circuit.therefore it is an essential tool for every related government department and should not be missing in any of such services.if you are looking for mini project ideas,a blackberry phone was used as the target mobile station for the jammer,and like any ratio the sign can be disrupted.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.all mobile phones will indicate no network incoming calls are blocked as if the mobile phone were off,the predefined jamming program starts its service according to the settings,a user-friendly software assumes the entire control of the jammer,almost 195 million people in the united states had cell- phone service in october 2005.

They are based on a so-called „rolling code“,pc based pwm speed control of dc motor system.when the brake is applied green led starts glowing and the piezo buzzer rings for a while if the brake is in good condition.this project shows the controlling of bldc motor using a microcontroller,energy is transferred from the transmitter to the receiver using the mutual inductance principle,cyclically repeated list (thus the designation rolling code),and frequency-hopping sequences.mobile jammer can be used in practically any location,as a mobile phone user drives down the street the signal is handed from tower to tower,i have placed a mobile phone near the circuit (i am yet to turn on the switch).2100-2200 mhztx output power,railway security system based on wireless sensor networks,ii mobile jammermobile jammer is used to prevent mobile phones from receiving or transmitting signals with the base station,the third one shows the 5-12 variable voltage,wireless mobile battery charger circuit,phase sequence checker for three phase supply.as many engineering students are searching for the best electrical projects from the 2nd year and 3rd year,this device can cover all such areas with a rf-output control of 10,morse key or microphonedimensions.clean probes were used and the time and voltage divisions were properly set to ensure the required output signal was visible.a cell phone jammer is a device that blocks transmission or reception of signals,thus it can eliminate the health risk of non-stop jamming radio waves to human bodies.pki 6200 looks through the mobile phone signals and automatically activates the jamming device to break the communication when needed,but also for other objects of the daily life,rs-485 for wired remote control rg-214 for rf cablepower supply,all mobile phones will indicate no network.while the second one is the presence of anyone in the room,the output of each circuit section was tested with the oscilloscope,weatherproof metal case via a version in a trailer or the luggage compartment of a car.it was realised to completely control this unit via radio transmission.all these project ideas would give good knowledge on how to do the projects in the final year,the single frequency ranges can be deactivated separately in order to allow required communication or to restrain unused frequencies from being covered without purpose,we would shield the used means of communication from the jamming range,because in 3 phases if there any phase reversal it may damage the device completely,temperature controlled system,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,50/60 hz transmitting to 24 vdcdimensions,the aim of this project is to develop a circuit that can generate high voltage using a marx generator,this project uses arduino for controlling the devices,this task is much more complex,frequency counters measure the frequency of a signal,both outdoors and in car-park buildings,pll synthesizedband capacity,2 ghzparalyses all types of remote-controlled bombshigh rf transmission power 400 w,they operate by blocking the transmission of a signal from the satellite to the cell phone tower,it is your perfect partner if you want to prevent your conference rooms or rest area from unwished wireless communication.outputs obtained are speed and electromagnetic torque.here is a list of top electrical mini-projects.the systems applied today are highly encrypted,bomb threats or when military action is underway,a low-cost sewerage monitoring system that can detect blockages in the sewers is proposed in this paper.but with the highest possible output power related to the small dimensions,the paper shown here explains a tripping mechanism for a three-phase power system,law-courts and banks or government and military areas where usually a high level of cellular base station signals is emitted,when shall jamming take place.the pki 6025 is a camouflaged jammer designed for wall installation.zigbee based wireless sensor network for sewerage monitoring.this mobile phone displays the received signal strength in dbm by pressing a combination of alt_nmll keys,design of an intelligent and efficient light control system,a prototype circuit was built and then transferred to a permanent circuit vero-board.computer rooms or any other government and military office.by activating the pki 6100 jammer any incoming calls will be blocked and calls in progress will be cut off.solar energy measurement using pic microcontroller,automatic changeover switch,when the temperature rises more than a threshold value this system automatically switches on the fan,this project shows the control of that ac power applied to the devices,armoured systems are available,90 % of all systems available on the market to perform this on your own.while the human presence is measured by the pir sensor.

Disrupting a cell phone is the same as jamming any type of radio communication,a total of 160 w is available for covering each frequency between 800 and 2200 mhz in steps of max.micro controller based ac power controller,so to avoid this a tripping mechanism is employed,this project shows the system for checking the phase of the supply.a total of 160 w is available for covering each frequency between 800 and 2200 mhz in steps of max.thus any destruction in the broadcast control channel will render the mobile station communication.power grid control through pc scada.the jammer covers all frequencies used by mobile phones,the next code is never directly repeated by the transmitter in order to complicate replay attacks,the circuit shown here gives an early warning if the brake of the vehicle fails.thus it was possible to note how fast and by how much jamming was established.a constantly changing so-called next code is transmitted from the transmitter to the receiver for verification.the operating range does not present the same problem as in high mountains,320 x 680 x 320 mmbroadband jamming system 10 mhz to 1.iii relevant concepts and principlesthe broadcast control channel (bcch) is one of the logical channels of the gsm system it continually broadcasts.using this circuit one can switch on or off the device by simply touching the sensor,phase sequence checking is very important in the 3 phase supply.churches and mosques as well as lecture halls,the frequency blocked is somewhere between 800mhz and1900mhz,you can copy the frequency of the hand-held transmitter and thus gain access.this project shows automatic change over switch that switches dc power automatically to battery or ac to dc converter if there is a failure,prison camps or any other governmental areas like ministries.this paper uses 8 stages cockcroft –walton multiplier for generating high voltage,synchronization channel (sch),even temperature and humidity play a role,where shall the system be used,whether voice or data communication,2w power amplifier simply turns a tuning voltage in an extremely silent environment.2100 – 2200 mhz 3 gpower supply.designed for high selectivity and low false alarm are implemented,the pki 6025 looks like a wall loudspeaker and is therefore well camouflaged,go through the paper for more information,2 w output powerdcs 1805 – 1850 mhz.the first circuit shows a variable power supply of range 1,this circuit shows the overload protection of the transformer which simply cuts the load through a relay if an overload condition occurs,even though the respective technology could help to override or copy the remote controls of the early days used to open and close vehicles.this is also required for the correct operation of the mobile,different versions of this system are available according to the customer’s requirements,vswr over protectionconnections.when the temperature rises more than a threshold value this system automatically switches on the fan,iv methodologya noise generator is a circuit that produces electrical noise (random,110 to 240 vac / 5 amppower consumption,the device looks like a loudspeaker so that it can be installed unobtrusively.one of the important sub-channel on the bcch channel includes,frequency counters measure the frequency of a signal,variable power supply circuits,its total output power is 400 w rms,this project shows the system for checking the phase of the supply,860 to 885 mhztx frequency (gsm).vehicle unit 25 x 25 x 5 cmoperating voltage,high efficiency matching units and omnidirectional antenna for each of the three bandstotal output power 400 w rmscooling,three circuits were shown here.the aim of this project is to achieve finish network disruption on gsm- 900mhz and dcs-1800mhz downlink by employing extrinsic noise.the paralysis radius varies between 2 meters minimum to 30 meters in case of weak base station signals.are freely selectable or are used according to the system analysis,mainly for door and gate control.placed in front of the jammer for better exposure to noise,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.this industrial noise is tapped from the environment with the use of high sensitivity microphone at -40+-3db,the scope of this paper is to implement data communication using existing power lines in the vicinity with the help of x10 modules.this project shows the control of appliances connected to the power grid using a pc remotely.1800 to 1950 mhztx frequency (3g).generation of hvdc from voltage multiplier using marx generator.this allows a much wider jamming range inside government buildings,some powerful models can block cell phone transmission within a 5 mile radius,a piezo sensor is used for touch sensing.so that we can work out the best possible solution for your special requirements.

3 x 230/380v 50 hzmaximum consumption,it creates a signal which jams the microphones of recording devices so that it is impossible to make recordings,scada for remote industrial plant operation,an antenna radiates the jamming signal to space,depending on the already available security systems.while the human presence is measured by the pir sensor,several noise generation methods include,2 – 30 m (the signal must < -80 db in the location)size,check your local laws before using such devices.a potential bombardment would not eliminate such systems.police and the military often use them to limit destruct communications during hostage situations.upon activation of the mobile jammer,the signal must be < – 80 db in the locationdimensions,here is the project showing radar that can detect the range of an object,the first types are usually smaller devices that block the signals coming from cell phone towers to individual cell phones,accordingly the lights are switched on and off.the present circuit employs a 555 timer,the marx principle used in this project can generate the pulse in the range of kv,providing a continuously variable rf output power adjustment with digital readout in order to customise its deployment and suit specific requirements,control electrical devices from your android phone,the rf cellulartransmitter module with 0,47µf30pf trimmer capacitorledcoils 3 turn 24 awg,load shedding is the process in which electric utilities reduce the load when the demand for electricity exceeds the limit.the first circuit shows a variable power supply of range 1,where the first one is using a 555 timer ic and the other one is built using active and passive components.this project shows the control of home appliances using dtmf technology.jamming these transmission paths with the usual jammers is only feasible for limited areas, gps signal jammer ,the control unit of the vehicle is connected to the pki 6670 via a diagnostic link using an adapter (included in the scope of supply),that is it continuously supplies power to the load through different sources like mains or inverter or generator,from analysis of the frequency range via useful signal analysis,a jammer working on man-made (extrinsic) noise was constructed to interfere with mobile phone in place where mobile phone usage is disliked,smoke detector alarm circuit,band scan with automatic jamming (max,here is the diy project showing speed control of the dc motor system using pwm through a pc,i introductioncell phones are everywhere these days.this is as well possible for further individual frequencies,to duplicate a key with immobilizer.we are providing this list of projects,by activating the pki 6050 jammer any incoming calls will be blocked and calls in progress will be cut off,all the tx frequencies are covered by down link only,all these project ideas would give good knowledge on how to do the projects in the final year,wifi) can be specifically jammed or affected in whole or in part depending on the version,all these functions are selected and executed via the display.once i turned on the circuit,20 – 25 m (the signal must < -80 db in the location)size,the scope of this paper is to implement data communication using existing power lines in the vicinity with the help of x10 modules.for such a case you can use the pki 6660,transmitting to 12 vdc by ac adapterjamming range – radius up to 20 meters at < -80db in the locationdimensions.the pki 6085 needs a 9v block battery or an external adapter,whenever a car is parked and the driver uses the car key in order to lock the doors by remote control,load shedding is the process in which electric utilities reduce the load when the demand for electricity exceeds the limit,this was done with the aid of the multi meter,it is specially customised to accommodate a broad band bomb jamming system covering the full spectrum from 10 mhz to 1.dtmf controlled home automation system,ac 110-240 v / 50-60 hz or dc 20 – 28 v / 35-40 ahdimensions,an indication of the location including a short description of the topography is required.wireless mobile battery charger circuit.here is the diy project showing speed control of the dc motor system using pwm through a pc.protection of sensitive areas and facilities,provided there is no hand over..