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Study on accuracy of GPS for its application in SAR interferometry
Multipath Error
In measuring the distance to each satellite, we assume that the satellite signal travels directly from the satellite to the antenna of the receiver. But in addition to the direct signal, there are reflected signals, from the ground and the objects near the antenna, that also reach the antenna through indirect paths and interfere with the direct signal. This has a number of effects: it may cause signal interference between the direct and reflected signal (see Figure 2 below) leading to noisier measurement, or it may confuse the tracking electronics of the hardware resulting in a biased measurement that is the sum of the satellite-to-reflector distance and the reflector-to-antenna distance.
The magnitude of the multipath effect on a phase observation can be estimated from the following mathematical relation (HOFMANN-WELLENHOF et al, 1998):
where
Dfm
is the shift in carrier phase of the combined signal received at the antenna
due to multipath,
Is a damping factor which varies between 0 (no reflection) and 1 (reflected
signal as strong as direct signal).
Some options for reducing the effect of multipath are:
- Make a careful selection of antenna site in order to avoid reflective environments.
- Use a good quality antenna that is multipath-resistant.
- Use an antenna groundplane or choke-ring assembly.
- Use a receiver that can internally digitally filter out the effect of multipath signal disturbance.
- Do not observe low elevation satellites (signals are more susceptible to multipath).
- In the case of pseudo-range positioning
(single point or differential), averaging the computed results
over a period of time will reduce the contribution of multipath
errors on the averaged pseudo-range solution.
In the case of carrier phase positioning, longer observation sessions will tend to diminish the impact of multipath on the final baseline results.
Selecting a GPS Receiver
There are two main groups of receivers; those designed to track multiple GPS satellites simultaneously and those that sequence between satellites.
Sequencing Receivers - use a single channel to measure the C/A code and move it (multiplex) from one satellite to the next to gather this data. They usually have less components and circuitry so are cheaper and consume less power. Unfortunately, the sequencing can interrupt signal measurement and timing resolution (noise errors) of the satellite signal detection and can limit their overall accuracy.
Parallel Receivers - also know as Continuous Receivers, can monitor several satellites simultaneously. These units are valuable in high dynamic or high accuracy applications, so they are often used for mapping, surveying and scientific purposes. Besides the obvious advantage of being able to continuously measure a position, these multi-channel receivers can also eliminate the 'noise measurement' problem and provide for 'all in view' satellite tracking. Another capability of these receiver types is that with modern signal processing techniques, by the comparison of channels to each other, the units can 'calibrate out' any interchannel biases that can affect timing measurement and signal detection accuracy resolution.
Other Considerations - commercial single frequency (L1 signal) GPS receivers are achieving greater accuracies by tracking both the pseudo-random code and the L1 carrier frequency. Called 'carrier-aided tracking', this technique makes it possible for the receiver to resolve, with good precision, the exact 'edge' of the psuedo-random code signal. Thus more precise timing measurements, which in turn, translate into a better calculated positions can be achieved. Of course, dual frequency receivers provide for double satellite signal range measurement, plus compute the atmospheric 'delay' errors and use the carrier-phase observation techniques to provide accurate positioning improvement.
Atmospheric Effects
Atmospheric effect is divided in two types i.e. Ionospheric effect and Tropospheric effect depending on layers of atmosphere. From ground to above around 40 Kms is the troposphere and from 40 Kms to around 1000 Kms it is considered to be Ionosphere. The effects of atmosphere on GPS are discussed in separate section in results and discussion.
Results and Discussion
The atmospheric effect on GPS signals are studied and meteorological data obtained at Indian Meteorological Department Pune is used to fined out at what extent it can effect the measurement.
Ionospheric delay
The magnitude of the effect of the ionosphere is much more during the day than during the night. The magnitude also has a cyclical period of 11 years that reaches a maximum and a minimum. For the current cycle, the ionosphere will reach its peak magnitude in 1998 and its minimum in 2004. The cycle will then be repeated. The effects of the ionosphere, if not mitigated, can introduce measurement errors greater than 10 meters. The impact of the ionosphere on electronic signals depends on the frequency of the signal. The higher the frequency, the less is the impact. So if we transmit the patterns simultaneously via two different frequencies, the ionosphere may delay the code on one frequency, for example, by 5 meters and on the other frequency, say, by 6 meters. We cannot measure the magnitude of these delays, but we can measure their difference by observing the difference on their arrival time, which in this case translates into 1 meter of effective distance between them. By measuring this difference and using known formula for frequency dependency of the ionosphere delay, ionosphere effect can be removed.
For the GPS system with single frequency there will be the ionospheric error involved in the measurements. depending on radiosonde data available at meteorological department in Ahmedabad, phase shift in the signal with increasing Total Electron Content (TEC) for Indian atmospheric conditions is plotted as shown in figure 3.
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