foreword
This series starts with the advancement of GNSS, mainly on the basis of the previous series of tutorials "How to Get Started with GNSS Algorithms for Undergraduates in Surveying and Mapping Engineering", and begins to introduce how to realize your own idea.
The single-point calculation logic in rtklib only uses the first frequency point for positioning. The advanced tutorial will make the following improvements:
① Expand from single-frequency to multi-frequency positioning
② Add simple tolerance logic
Pseudorange formula
First of all, multi-frequency single point can be considered as the superposition of single frequency, but the following two points need to be paid special attention to: the first point, the calculation of ionospheric delay, rtklib has actually calculated the delay of the first frequency point, we need to calculate The ionospheric delay of other frequency points; the second point, the satellite code deviation needs to be corrected. In fact, the code deviation at the receiver side also needs to be considered, but we will not consider this this time.
The pseudorange formula is as follows:
It is defined as the distance between two antenna phase centers. For satellites, the antenna phase center is definitely not the place where the signal is generated. How to consider the time-consuming distance from the signal generator to the antenna phase center?
Pseudo-range hardware delay
For the same system and the same frequency, the time-consuming from signal generation to the phase center is basically the same, but there is a deviation between different frequencies. For the pseudorange, this deviation is the code deviation, which is our protagonist today. Why do we emphasize the deviation between different frequencies, can't the absolute hardware latency be directly determined? First of all, it is difficult to measure the absolute delay; secondly, as the hardware ages and other issues, the delay will also change, so the relative value is generally calculated.
In order to facilitate the use of different frequency receivers or modules, corresponding parameters are provided in the broadcast ephemeris for modification. But there is another doubt. Since the absolute delay cannot be obtained, how does the satellite clock broadcast by the broadcast ephemeris deal with this absolute delay?
As mentioned earlier, for the same frequency, the satellite’s pseudo-range hardware delay is the same, and the error is the same for all satellites, then it can be absorbed by the receiver clock state quantity when solving the equation; so if we know the second frequency Point relative to the correction amount of the first frequency point, if the pseudo-range delay at the receiver end is ignored, then the processing of the second frequency point is the same as that of the first frequency point. So the problem has shifted, from finding the absolute delay to finding the hardware delay difference between the first frequency point and the second frequency point, that is, the code deviation. How to calculate the code deviation is beyond the scope of this paper, which is also one of the research directions of GNSS.
But with pseudo-range bias and satellite clock bias, more knowledge is still needed to use the code bias product correctly. During use, we need to know how the satellite clock error is obtained.
satellite clock
A single satellite operates in the sky, and its time mainly depends on its own satellite clock for time maintenance; although the satellite clock is stable, there will be deviations for a long time. The satellite cannot calculate its own clock difference by itself. It needs the ground operation and control station to calculate the satellite clock difference, and upload it to the satellite, and broadcast it to the user through the satellite signal for correction.
How is the satellite clock difference calculated? In fact, it also uses the principle of positioning, and needs to use the satellite clock as the parameter to be estimated, and it will converge after a period of time. In order to estimate satellite clocks with high precision, traditional algorithms use ionosphere-free combined observations for calculation. What is the ionosphere-free combination? As mentioned above, the non-diffusion characteristics of the ionosphere are inversely proportional to the square of the frequency. By combining the observations of the two frequencies, the effect of the ionosphere can be eliminated.
When using ionospheric-free combined observations to estimate satellite clock offsets, the original dual-frequency data is used directly, and the pseudo-range hardware delay is not corrected. Therefore, the clock error in the broadcast ephemeris broadcast by the satellite is based on the ionosphere-free combination.
But not all the clocks of satellite systems are based on the ionosphere-free combination, such as our Beidou system.
TGD
The figure below shows the regulations in the Beidou ICD. The time delay difference of the on-board equipment is the pseudo-range deviation mentioned above. The broadcast ephemeris clock error broadcast by Beidou is based on the third frequency point.
The full name of Beidou ICD is Beidou Satellite Navigation System Space Interface Control File, which can be downloaded from the Beidou official website.
In addition, a master's thesis was prepared, titled "Research on Key Technology of System-wide GNSS Combined Pseudo-range Single Point Positioning". Chapter 3.1 has a detailed method on how to use the broadcast ephemeris to correct the hardware delay of each frequency. We will use the formulas in the programming implementation process. In addition, the paper also has relevant basic knowledge, which can be used as an introductory reading. I have written so much above, I just hope to help you understand the paper more quickly.
ICD and the official account of the paper reply to the "single point positioning" acquisition.
The next chapter will talk about code implementation.
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