Shak Thanks for telling us about the problem. Other books in this series. Amazon Music Stream millions of songs. Brock rated it really liked it Jun 20, The Global Position System offers professionals and students an up-to-date, easy-to-understand treatment of this tremendously important technology.

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TE Figure 3. Examples of such technologies are the Strobe correlator Ashtech, Inc. With these multipath-mitigation techniques, the pseudorange multipath error is reduced to several meters, even in a highly reflective environment [9]. Under the same environment, the presence of multipath errors can be verified using a day-to-day correlation of the estimated residuals [3]. This is because the satellite-reflector-antenna geometry repeats every sidereal day.

However, multipath errors in the undifferenced pseudorange measurements can be identified if dual-frequency observations are available. A good general multipath model is still not available, mainly because of the variant satellite-reflector-antenna geometry. There are, however, several options to reduce the effect of multipath. The straightforward option is to select an observation site with no reflecting objects in the vicinity of the receiver antenna. Another option to reduce the effect of multipath is to use 34 Introduction to GPS a chock ring antenna a chock ring device is a ground plane that has several concentric metal hoops, which attenuate the reflected signals.

As the GPS signal is right-handed circularly polarized while the reflected signal is lefthanded, reducing the effect of multipath may also be achieved by using an antenna with a matching polarization to the GPS signal i.

The disadvantage of this option, however, is that the polarization of the multipath signal becomes right-handed again if it is reflected twice [9]. The point at which the GPS signal is received is called the antenna phase center [3]. Generally, the antenna phase center does not coincide with the physical geometrical center of the antenna.

It varies depending on the elevation and the azimuth of the GPS satellite as well as the intensity of the observed signal. As a result, additional range error can be expected [3]. The size of the error caused by the antenna-phase-center variation depends on the antenna type, and is typically in the order of a few centimeters. It is, however, difficult to model the antenna-phase-center variation and, therefore, care has to be taken when selecting the antenna type [1].

For short baselines with the same types of antennas at each end, the phasecenter error can be canceled if the antennas are oriented in the same direction [11]. Mixing different types of antennas or using different orientations will not cancel the error. Due to its rather small size, this error is neglected in most of the practical GPS applications. It should be pointed out that phase-center errors could be different on L1 and L2 carrier-phase observations.

This can affect the accuracy of the ionosphere free linear combination, particularly when observing short baselines. As mentioned before, for short baselines, the errors are highly correlated over distance and cancel sufficiently through differencing. Therefore, using a single frequency might be more appropriate for short baselines in the static mode see Chapter 5 for details on the static GPS positioning mode.

GPS Errors and Biases 35 3. A good GPS system should have a minimum noise level. Generally, a GPS receiver performs a self-test when the user turns it on. However, for high-cost precise GPS systems, it might be important for the user to perform the system evaluation. Two tests can be performed for evaluating a GPS receiver system : zero baseline and short baseline tests [12].

A zero baseline test is used to evaluate the receiver performance. Several receiver problems such as interchannel biases and cycle slips can be detected with this test. As one antenna is used, the baseline solution should be zero.

In other words, any nonzero value is attributed to the receiver noise. The contribution of the receiver measurement noise to the range error will depend very much on the quality of the GPS receiver. Figure 3. This can be done using short baselines of a few meters apart, observed on two consecutive days see Figure 3. In this case, the double difference residuals of one day would contain the system noise and the multipath effect.

All other errors would cancel sufficiently. As the multipath signature repeats every sidereal day, differencing the double difference residuals between the two consecutive days eliminates the effect of multipath and leaves only the system noise.

Such a region of the atmosphere where gas ionization takes place is called the ionosphere. It extends from an altitude of approximately 50 km to about 1, km or even more see Figure 3. In fact, the upper limit of the ionospheric region is not clearly defined [14, 15]. GPS Errors and Biases 37 The electron density within the ionospheric region is not constant; it changes with altitude. As such, the ionospheric region is divided into subregions, or layers, according to the electron density.

For example, the F1 layer disappears during the night and is more pronounced in the summer than in the winter [14]. The question that may arise is: How would the ionosphere affect the GPS measurements? The ionosphere is a dispersive medium, which means it bends the GPS radio signal and changes its speed as it passes through the various ionospheric layers to reach a GPS receiver.

It is the change in the propagation speed that causes a significant range error, and therefore should be accounted for. The ionosphere speeds up the propagation of the carrier phase beyond the speed of light, while it slows down the PRN code and the navigation message by the same amount. That is, the receiver-satellite distance will be too short if measured by the carrier phase and too long if measured by the code, compared with the actual distance [3].

The ionospheric delay is proportional to the number of free electrons along the GPS signal path, called the total electron content TEC. As the ionosphere is a dispersive medium, it causes a delay that is frequency dependent. The lower the frequency, the greater the delay; that is, the L2 ionospheric delay is greater than that of L1. Generally, ionospheric delay is of the order of 5m to 15m, but can reach over m under extreme solar activities, at midday, and near the horizon [5].

It is, however, highly correlated over relatively short distances, and therefore differencing the GPS observations between users of short separation can remove the major part of the ionospheric delay. Unfortunately, however, the P-code is accessible by authorized users only. The L1 and L2 carrier-phase measurements may be combined in a similar fashion to determine the variation in the ionospheric delay, not the absolute value. Users with dualfrequency receivers can combine the L1 and L2 carrier-phase measurements to generate the ionosphere-free linear combination to remove the ionospheric delay [5].

The disadvantages of the ionosphere-free linear combination, however, are: 1 it has a relatively higher observation noise, and 2 it does not preserve the integer nature of the ambiguity parameters.

As such, the ionosphere-free linear combination is not recommended for short baselines. Single-frequency users cannot take advantage of the dispersive nature of the ionosphere.

The most widely used model is the Klobuchar model, whose coefficients are transmitted as part of the navigation message. Another solution for users with single-frequency GPS receivers is to use corrections from regional networks [15]. Such corrections can be received in real time through communication links.

The troposphere is a nondispersive medium for radio frequencies below 15 GHz [16]. As a result, it delays the GPS carriers and codes identically.

That is, the measured satellite-to-receiver range will be longer than the actual geometric range, which means that a distance between two receivers will be longer than the actual distance. Unlike the ionospheric delay, the tropospheric delay cannot be removed by combining the L1 and the L2 observations. This is mainly because the tropospheric delay is frequency independent. GPS Errors and Biases 39 The tropospheric delay depends on the temperature, pressure, and humidity along the signal path through the troposphere.

Signals from satellites at low elevation angles travel a longer path through the troposphere than those at higher elevation angles. Tropospheric delay results in values of about 2. Tropospheric delay may be broken into two components, dry and wet. The wet component of the tropospheric delay depends on the water vapor along the GPS signal path.

Unlike the dry component, the wet component is not easy to predict. Several mathematical models use surface meteorological measurements atmospheric pressure, temperature, and partial water vapor pressure to compute the wet component. Unfortunately, however, the wet component is weakly correlated with surface meteorological data, which limits its prediction accuracy. However, these are not the only factors that affect the resulting GPS accuracy.

The satellite geometry, which represents the geometric locations of the GPS satellites as seen by the receiver s , plays a very important role in the total positioning accuracy [5]. The better the satellite geometry strength, the better the obtained positioning accuracy. As such, the overall positioning accuracy of GPS is measured by the combined effect of the unmodeled measurement errors and the effect of the satellite geometry.

Good satellite geometry is obtained when the satellites are spread out in the sky [19]. In general, the more spread out the satellites are in the sky,





Introduction to GPS: The Global Positioning System, Second Edition


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